”I taught you logic. So, if I hadn't taught you logic, you never would have learned logic at all. |
A counterfactual fallacy occurs when someone states a fact, states that something would be true if the stated fact were not true, and provides no evidence for this position.
The fallacy is a causation fallacy and an informal fallacy .
Or even more egregiously:
The second form doesn't even explain the causal connection between A and B; it really is just wild speculation. The first form is a special case of denying the antecedent , applied to counterfactual reasoning; it ignores the possibility of B still occurring as an effect of causes other than A, even if A had not occurred.
You commit this fallacy if you draw conclusions from evidence that hasn't been collected yet, but that, one supposes, would have come out in favor of one's own opinion.
If there is no evidence to support a particular point, do not rely on that point to carry your argument. If pressed on a point where there is not valid evidence to support it, acknowledge the lack of data and suggest that the matter needs to be investigated in order to resolve the disputed issue.
Confusing "what might have been" with "what ought to have been"; speculating what would have happened in other circumstances, then drawing conclusions from the speculation.
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Avoiding logical fallacies.
Logic can go wrong in many ways. We’ve talked about building logical arguments. Now let’s consider how to avoid building illogical ones. The logical fallacies below can slip into your own and others’ arguments. Learn to identify them.
(Instead of engaging the claim, the response dismisses its importance.)
(Does this mean we need to minimize or maximize the amount of water?)
(This claim dismisses opposition by saying poverty is just a fact of life.)
(This claim generalizes from some spousal abuse to all domestic violence.)
(In place of an argument, the same assertion is made three times.)
(To answer the question would be to admit to destroying the country.)
(This statement incorrectly assumes that the president’s location caused the 9/11 attacks.)
(This analogy does not accurately represent the process, in which the winner becomes arguably the most powerful person in the world.)
(This claim swaps the cause and the effect. The worsening economy causes the Fed to lower interest rates, not the other way around.)
(This claim ignores the difference between free speech and treason.)
(The agency can function on a reduced budget without shutting down.)
(This statement ignores the long evolution of both parties.)
(Both candidates won’t back down, so both should get the same praise or blame.)
(This statement does not follow. A person’s body fat percentage does not relate to his or her ability to balance governmental budgets.)
Your Turn Find a political debate online and listen to it. Write down as many examples as you can of the fallacies on these two pages.
(Instead of changing the false assumption that all Scotsmen are brave, the person discounts the counterexample of cowardly Andrew.)
(This statement means “We should get rid of harmful influences,” an idea so obvious that it really doesn’t need to be stated.)
(This oversimplification ignores the fact that such an act would catastrophically devalue the dollar.)
(This statement applies a reasonable principle to absurd specificity.)
(The language in this statement allows for no reasonable discussion.)
(Immigration reform does not require pardoning all illegal activity.)
(That a politician wants to destroy the country is a dummy argument.)
Your Turn Pick four of the fallacies on this page and write your own examples. Share your answers with a partner and discuss the faulty logic in each.
(Someone else’s bad behavior doesn’t justify one’s own bad behavior.)
(Absence of evidence is not evidence of absence.)
(A proposal should be accepted on its own merits, not due to hard work.)
(A sentimental name doesn’t make peanut butter worth buying.)
(An actor who plays a doctor is not a medical authority.)
(The horror of the idea does not preclude its possibility.)
(Actually, quantum physicists have proven this idea.)
(This ad hominem attack diverts attention from the real issue: taxes.)
(A stronger argument would focus on the value of the paper.)
(The thousands who are injured are a tiny fraction of the millions who use power tools safely and who rely on them to make a living.)
(There is no way to prove or disprove what would have happened if the other candidate had won, so the argument is meaningless.)
(The use of numbers baffles the audience into acceptance.)
(World hunger is a serious problem that shouldn’t be dismissed with a joke.)
(The Ebola virus, a separate problem, should not be used to distract from the abhorrent use of child soldiers.)
(Threats are never an acceptable form of persuasion.)
Your Turn Watch commercials on television or on the Internet and write down two examples of the misuse of evidence on pages 111–112 .
Web Site: Fallacies
Web Page: Logical Fallacies
Web Page: Common Fallacies in Reasoning
Web Page: Fallacies of Ambiguity
Web Page: Marketing Plots
Web Page: Hasty Generalization
Video: Correlation and Causation
Web Page: False Cause
Web Page: False Dichotomy
Web Page: Non Sequitur
Blog Post: The New Illiteracy--Obfuscation
Web Page: Reductio ad Absurdum
Web Page: Slippery Slope
Web Page: Argumentum Ad Hominem
Web Page: Bandwagon Appeal
Web Page: Red Herring
© 2014 Thoughtful Learning
Understanding the behavior of systems is essential for human survival — with Dennis L. Holeman
A remarkably large number of logical fallacies used in reasoning and arguments has been identified. Following is a partial list of such fallacies. More complete information on logical fallacies is available in the two references below. It is important to recognize logical fallacies when they are being used, particularly for persuasive purposes. Once identified, the fallacy should be corrected and the argument repaired with non-faulty reasoning.
I suggest that an interesting avenue for artificial intelligence research to pursue would be a set of tools to aid human thinkers in identifying and correcting logical fallacies. This would be an extension of current writing assistance tools that provide spell checking, grammar checking, punctuation checking, and the like. The tools could be used both by original authors and by those reviewing work by others.
In a case where artificial intelligence systems are being used for making choices and decisions, the reasoning involved should be examined by the systems to identify and flag possible logical fallacies.
See also references on logical fallacies:
https://web.cn.edu/kwheeler/fallacies_list.html
https://en.wikipedia.org/wiki/List_of_fallacies
What a great list, thank you! I suspect we can all identify having seen (or worse, used) items from this list.
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A logical fallacy occurs when someone tries to persuade you with a faulty argument. Sometimes, logical fallacies are innocuous: the writer has a good argument to make, it was just set up through faulty logic. However, logical fallacies run rampant among less-than-sincere writers, and if you want to write well and read well, then knowing our list of logical fallacies will help arm you against faulty arguments.
Because people are constantly trying to persuade you of something—politicians, advertisers, social media posts, etc.—logical fallacies occur all the time. Good persuasive writers will know how to avoid these common logical fallacies, and good readers will know how to identify them without being persuaded.
So, what is a logical fallacy? And why do they matter for my writing? Understanding the arguments in this list of logical fallacies will help strengthen your writing and ability to write effective arguments. But before we look at some examples of logical fallacies, let’s get clear on these persuasive and invasive mistakes in rhetoric.
Common types of logical fallacies, a note on good persuasive writing, logical fallacies examples: fallacies of relevance, logical fallacies examples: fallacies of unacceptable premises, logical fallacies examples: formal fallacies, other logical fallacies examples.
Simply put, a logical fallacy is an error in reasoning that undermines the logic of an argument. It does not necessarily undermine the persuasiveness of that argument, however; unless you are well-versed in the different types of logical fallacies, you can certainly be persuaded by one yourself.
A logical fallacy is an error in reasoning that undermines the logic, but not necessarily the persuasiveness, of an argument.
A common logical fallacy example is a red herring. A red herring is an attempt to divert the audience’s attention from the argument itself. It might look something like this:
Some people criticize the SAT for measuring test taking skills, not college readiness. Nonetheless, a high SAT score will get you into better colleges.
This statement isn’t actually addressing the issue of the SAT’s validity, it’s distracting you by bringing up the importance of a high test score, going so far as dismissing the original claim entirely.
All logical fallacies have one thing in common: they don’t hold up to scrutiny. But there are different ways in which writers might present less-than-foolproof arguments. Let’s examine the common types of logical fallacies.
All logical fallacies have one thing in common: they don’t hold up to scrutiny.
Most logical fallacies can be sorted into one of three categories:
We’ll examine these three categories shortly. But before we examine some examples of logical fallacies, let’s talk about good persuasive writing.
By now, you’re probably familiar with the basic structure of an argumentative essay. Most essays, including those at the higher academic level, generally follow a thesis statement , followed by supporting claims , evidence , and a conclusion . Most essays also address potential counterclaims and offer rebuttal arguments .
The structure is the easy part. Aside from side-stepping all logical fallacies, how do you write a persuasive essay that’s actually, well, persuasive?
Here are a few tips:
Of course, these strategies alone don’t make for great persuasive writing. Having solid logic behind your reasoning and carefully crafted arguments will make your essays shine. As such, let’s look at some common logical fallacies and discuss how you can avoid them.
A good persuasive essay requires good thinking, writing, researching, and revising. Nonetheless, even the best thinkers are prone to these common logical fallacies. Understanding the errors of logic in this list, how they happen, and how to avoid them will strengthen your ability to argue and to identify faulty arguments.
We’ve sectioned this list by the different types of logical fallacies. Let’s examine them below!
Fallacies of Relevance are any number of informal logical fallacies in which an irrelevant argument is presented as relevant, distorting the conclusion or misdirecting the audience. You may have heard of the red herring logical fallacy before; most fallacies of relevance are, in some way, red herrings.
Fallacies of Relevance are logical fallacies in which an irrelevant argument is presented as relevant, distorting the conclusion or misdirecting the audience.
Let’s look closer at each one.
An Ad Hominem (Latin: “against the person”) attack is a logical fallacy in which the person is argued against, rather than the argument the person is making. In other words, it attacks the source but not the credibility of the argument.
Here are a few examples:
None of these examples actually engage with logic. Accusing someone of lying or ignorance is a lazy way of avoiding the argument. And, while someone who commits a hit and run has questionable ethics, there isn’t a clear relationship between bad driving and bad leadership.
If any of these attacks sound familiar, it’s because Ad Hominem is a prominent feature of our cultural and political landscape. Now, there is something to be said about questioning the ethos of the person making an argument. There are plenty of people, politicians and otherwise, who do have ulterior motives and hidden agendas behind their logic and reasoning.
However, in good argumentation, you cannot simply question the ethos of the person. You must engage with the arguments themselves; an Ad Hominem attack is simply a distraction, meant to make the audience angry or distracted from the issues at hand.
In good argumentation, you must engage with the arguments themselves.
The Appeal to Consequences argues that a premise is correct or incorrect based on whether the outcome is positive or negative. In other words, if a certain hypothesis leads to an undesirable consequence, the hypothesis “must” be wrong; if the consequence is positive, it “must” be right.
For example:
Of course, valid hypotheses can result in negative outcomes, because an argument is valid irrespective of its outcome. And invalid hypotheses can suggest positive outcomes because “wishful thinking” is inherently a logical fallacy.
An Appeal to Emotion occurs when an argument tries to evoke an emotional response, rather than a logical one. For example:
Now, this logical fallacy is similar to the rhetorical device “pathos.” The difference is that, in good rhetoric, pathos is not the central argument. Pathos is a feature of good argumentation, because a good rhetorician knows which emotions to evoke from the audience and how those emotions inspire action or belief. But, when that emotional response is the desired outcome of the argument, without credible logic to back it up, then the speaker is trying to twist your feelings without good reasoning.
An Appeal to Force argues that physical or emotional harm is a consequence of certain arguments. It is related to the Appeal to Emotion in that it inspires fear.
Obviously, these arguments aren’t arguments at all: they’re trying to coerce you into agreeing with something that has no logical backing.
The Appeal to Ignorance is a logical fallacy in which something must be true because there is no evidence against it . In other words, the fallacy is that the absence of counterevidence means there is no counterevidence. However, the absence of something is not an argument for its own absence: “absence of evidence is not evidence of absence.”
The Appeal to Ignorance is especially consequential in the courtroom. For example, if you don’t have an alibi, that means you must have killed the victim. The logic isn’t sound, but the wrong jury, or a jury with strong prejudices, might buy it.
The Appeal to Improper Authority argues that an argument must be true because it came from an authority figure. This is misplaced ethos, because the logical fallacy assumes one’s authority automatically grants ethos on a position, instead of that ethos being earned through argumentation.
Sometimes, the Appeal to Improper Authority is an appeal to the wrong kind of authority. Being a psychology major isn’t justification for diagnosing someone; you should have an advanced degree and research experience. You should also have conducted a psych evaluation on the person in question. Other times, this Appeal isn’t enough justification; you still need to back your arguments with logic. What knowledge does your degree as a psych major give you to make a certain conclusion?
However, this is not license to assume something is incorrect just because it comes from an authority figure. For example, many people assume that the advice from a doctor must be wrong. While doctors do make mistakes, attacking the credibility of a doctor, rather than the science behind the decisions they make, is just an Ad Hominem.
The Appeal to Tradition logical fallacy says “we’ve always done it this way.” Rather than interrogate the logic behind a certain action, the argument assumes the action is logically sound because it’s been done for a certain amount of time.
Sometimes, tradition is rooted in logic. But a good argument will illuminate that logic, and that logic’s relevance to the modern day, rather than assume the logic exists.
An argument from incredulity occurs when you argue that something can’t be true solely because it’s difficult to imagine, hard to understand, or else doesn’t conform to your particular worldview.
This logical fallacy is often at play among conspiracy theorists, but it’s just another easy way to avoid the hard work of understanding and responding to logically sound arguments.
The Argumentum ad Populum (Argument to the People, or “to Popularity”) is based on the premise that, if a certain number of people believe in the argument, it must be correct. This logical fallacy has a few different manifestations, including:
This argument can be difficult to respond to, because if the argument is wrong, you might be implying that the masses have poor logic. Well, sometimes they do. Argumentum ad Populum is simply peer pressure, not sound logic.
The Genetic Fallacy occurs when you base the validity, or invalidity, of an argument solely on its source. Ad Hominem can be a type of Genetic Fallacy, but you can also attack an argument’s validity by saying it came from Wikipedia, YouTube, or a certain publisher or newspaper.
You should certainly interrogate the source of information. However, good critical arguments will examine the research and methodologies behind that data, instead of just assuming invalidity.
The logical fallacy Irrelevant Conclusion, also known as ignoratio elenchi, describes a conclusion that is irrelevant to the premises allegedly supporting it.
Most logical fallacies of relevance are, in some way, fallacies of Irrelevant Conclusion.
The Straw Man Argument occurs when you refute someone’s argument by responding to a completely different, utterly warped argument that the original person did not make. In other words, you distort an argument to make it easier to attack. The Straw Man is often a kind of Ad Hominem. It might look something like this:
Person 1: Investing money in your happiness today helps keep you motivated for longer term goals.
Person 2: What are you, some kind of hedonist?
This logical fallacy also occurs when you quote someone out of context. Think Fred Jones saying “I think Coolsville sucks !” in Scooby-Doo 2: Monsters Unleashed .
Tu Quoque is another form of Ad Hominem, in which a person’s behavior or past beliefs are called into question to discredit their current argument.
Tu Quoque is sometimes called the Appeal to Hypocrisy. The importance of hypocrisy is not to be understated, but when it comes to logic and reasoning, someone being a hypocrite doesn’t necessarily discredit the argument at hand.
Fallacies of Unacceptable Premises attempt to introduce premises that, though possibly true, do not ultimately support the argument’s conclusions. This is different from fallacies of relevance because the premises are relevant, they just don’t support the conclusions.
Fallacies of Unacceptable Premises attempt to introduce premises that, though possibly true, do not ultimately support the argument’s conclusions.
Begging the Question is a logical fallacy in which the validity of the conclusion is buried in the premise of the argument. In other words, the logic undergirding an argument makes assumptions that, when questioned, reveal the argument’s lack of reasoning. It is a premise restating the conclusion without supporting the conclusion.
Begging the Question happens a lot more often than you might think. By knowing this logical fallacy and noticing it, you’ll be able to question a person’s logic (or lack thereof) much more directly.
The division fallacy occurs when you assume that something true for a whole entity is also true for each individual component of that entity. For example:
Plenty of people make a lot of money in tech, but this assumption is riddled with errors. There are some low-paying positions in tech, and this argument does not take into account how money is distributed in tech.
A False Dilemma occurs when an argument presents the audience a limited number of sides to an issue, when many more sides exist. By doing this, the argument hopes to make you choose its side over the other, when the situation is actually much more nuanced.
Binary thinking is a prominent—and dangerous —way of thinking. Good, honest rhetoricians will recognize that one issue can have many sides, and that good thinking acknowledges gray spaces and ambiguities, rather than trying to paint a black and white picture of the world. Rhetoricians should be confident in their arguments, but if someone presents themselves as knowing everything , especially if they present a limited number of sides to an issue, be skeptical.
The Slippery Slope fallacy argues that a small first step will result in a later, usually catastrophic major event. It amplifies the stakes of an argument without providing clear justification that the catastrophe will occur.
This isn’t to say that all catastrophizing is automatically a Slippery Slope. Rather, it’s to note that small decisions can lead to a variety of outcomes; if a catastrophic outcome is predicted, that prediction must be underscored with clear, structurally sound logic.
A Hasty Generalization is a logical fallacy where a conclusion is drawn from a limited amount of information. The argument simply does not have enough data to support the conclusion it arrives at.
As you can see, Hasty Generalizations are really useful tools for assigning blame and turning the audience against a certain group of people. If you want to claim something about a group or an outcome, a good argument uses robust, clearly organized data to support that claim.
A Faulty Analogy is the use of an analogy to compare two things that do not merit a direct comparison. (In brief, an analogy is a literary device in which two or more discrete things are compared as equals.) Using a Faulty Analogy misrepresents the topic at hand.
When someone makes an argument using an analogy, ask yourself whether the items being compared exist on the same playing field. If they don’t, a logical fallacy is likely at play.
The Fallacy Fallacy occurs when you assume that an argument is incorrect because it contains a logical fallacy.
Now, that might seem ironic , or even completely contradictory. Isn’t that the entire point of this article?
What this means is, an argument can have the correct conclusion even if it uses a logical fallacy. The argument itself is incorrect, but the conclusion can still be true, it just needs to be reached using a different logic or set of data.
Don’t disregard the existence of this common logical fallacy. If a conclusion seems accurate, or even just intriguing, approach it with a sense of curiosity. Sure, the argument you’re given might be wrong, but under what conditions might it be right? And why is that?
Good logical thinking doesn’t just call out bad arguments, it also creates opportunities to discover more about the world.
Formal fallacies are logical fallacies involving an error in deductive reasoning. As a refresher, deductive reasoning is the use of existing information (premises) to create new information (conclusions).
Formal fallacies are logical fallacies involving an error in deductive reasoning.
Formal fallacies include the following:
You may have heard of the term non sequitur before. All formal fallacies are non sequiturs, because their conclusions do not follow the claims associated with them.
Affirming the Consequent occurs when the premise and the conclusion are switched in a formal argument. Let’s say you argue the following:
Affirming the Consequent means switching the order of the latter two bullets. So, the logical fallacy would be:
This isn’t true, because it can be cloudy without it raining. The “if” and “then” statements have been reversed, resulting in a conclusion that can’t be supported.
Denying the Antecedent occurs when you take a standard argument, put it in the negative, and then argue that the negative is just as true. In other words, you argue that the opposite of a true argument is just as true.
Let’s take the above example. This argument is correct:
The “antecedent” would look like this:
Obviously, it can be cloudy without it being rainy. The premise remains true, but assuming the inverse is also true leads to poor logic.
Affirming a Disjunct arises out of the ambiguity of the word “or”. In formal logic, “or” can be inclusive (meaning “and/or”), or it can be exclusive (meaning “either/or”). Because of this ambiguity, an argument can seem as though it is creating a false binary, leading to a false conclusion.
It is possible that the conclusion is true. It is equally possible that you worked hard and networked well. Affirming a Disjunct occurs when that “or” is interpreted as “exclusive,” rather than “inclusive.”
Denying a Conjunct follows a similar formal fallacy as Affirming a Disjunct, in which the argument seems to be creating a binary that actually cannot be supported. In this logical fallacy, you argue that two things cannot both be true, then conclude that if one is false, the other must be true.
Obviously, you can be something other than American or North Korean. The premise of the argument is true, because you can’t have dual citizenship between the two countries, but the interpretation of that premise as a binary is false.
In the Fallacy of the Undistributed Middle, the middle term, which links the premise to the conclusion, doesn’t actually have a relationship to the premise or the conclusion, leading to a faulty conclusion.
The conclusion is obviously incorrect. Moreover, the middle term isn’t doing any work for the argument. It tells us that octopi and birds have beaks, but it doesn’t tell us the relationship between birds and octopi, nor does the argument say that birds are the only organisms with beaks. The argument is creating a connection that doesn’t exist in the argument, leading to a conclusion it cannot support.
The Fallacy of Four Terms occurs when a standard syllogistic argument (the kind we’ve been referencing throughout this section) has four or more terms, rather than the requisite three.
By terms, we don’t mean bullet points, we mean the points of comparison in an argument. Here’s a proper syllogism:
The letters in parentheses highlight that a syllogism follows this structure:
There are variations to a proper syllogistic argument, but they always have 3 terms: a PQ term, a P term, and a Q term.
Here’s the Fallacy of Four Terms:
This fallacy rests on the assumption that a grid and a gridded iron are the same term, but they’re distinct. You thus arrive at an incorrect conclusion because you’ve made a random comparison between completely unalike ideas.
Here’s another example, to further illustrate the point, as well as to show how subtle this fallacy can be:
“Nothing” is being used in multiple colloquial senses, which creates a really confusing argument here. It seems like there are only 3 terms, but “nothing” is employed in two different senses (there is nothing superior vs. something is better than nothing). As a result, you get a conclusion that, well, some people might agree with, but ultimately isn’t grounded in any meaningful logic.
The common logical fallacies above all rely in some way on faulty syllogistic reasoning, whether the fallacy is in the logic or in the premises themselves. The following fallacies are different errors in logic and reasoning, which can contribute to faulty arguments, but are not necessarily syllogistic.
Correlation Vs Causation occurs when you assume that a correlation implies an actual relationship between two things. For example, you might notice that people who get spray tans often wear flip flops. If you assume that getting a spray tan encourages you to wear flip flops, you’re committing this logical fallacy—there are plenty of reasons why this correlation might occur, but spray tans do not cause flip flop wearing.
A Hypothesis Contrary to Fact is, simply, speculation without concrete evidence. It is an argument that, under different circumstances or historical events, the present or the future would certainly look a certain way. For example, “if you had gotten a job in finance, you’d be making loads of money right now.” This claim doesn’t take into account any number of factors: the state of the finance industry, your ability to perform finance-related work, etc.
This logical fallacy conflates opinion with fact. It is ultimately a kind of red herring. Let’s say I argue “it always rains when it’s sunny.” This is wrong; you call me out on this. I might reply saying “you can tell me I’m wrong, but I’m entitled to my opinion.” As a result, I’ve evaded the work of defending my argument or responding to yours, but the issue in question is not a matter of opinion.
A Loaded Question inserts an unfounded claim into a question in an attempt to make the audience assume something untrue. I might ask you “Are you really going to eat strawberry ice cream when artificial strawberry flavoring gives you cancer?” I’ve stated a claim as though it were true, offering no justification and ultimately coercing you into believing something false.
The Middle Ground fallacy assumes that the truth lies somewhere between two opposing sides. Let’s say two people are arguing about the color of Kirkjubøargarður , a farm in the Faroe Islands. One person argues it’s black; the other says it’s white. The person who says it’s white then argues “well, it must be somewhere in the middle. Let’s say it’s steel gray.” Yet the house is undeniably black.
This logical fallacy makes use of the existence of the False Dilemma; some things simply are black and white. Many politicians will use this argument to gain some concessions in their favor even when their position is ultimately and entirely wrong.
The No True Scotsman argument is an appeal to “purity,” in which a person argues that a true example of something doesn’t perform a certain behavior. See it played out in this conversation:
This logical fallacy creates an arbitrary purity test, and often makes unfair arguments about a certain identity. You can imagine how this argument can be wielded much more perniciously: “only true Americans eat meat. Since you’re a vegan, you must be a Communist.”
The Single Cause fallacy assumes something occurs because of only one cause. A topical example of this is inflation in the year 2023. Some people argue inflation is because of supply chain issues; others argue it’s because of poor trade policy; others argue it’s because of corporate greed; others argue it’s because of rising wages and low unemployment. In truth, all of these are causes of inflation, as well as other causes not mentioned here.
Slothful Induction can also be called an Appeal to Coincidence. Instead of acknowledging the likely relationship between two things, you argue that something keeps happening because of coincidence. “Sure, I keep drinking while driving, but all of my DUIs are because people keep slowing their cars in front of me.” It is an abnegation of accountability.
The Texas Sharpshooter fallacy occurs when you draw a conclusion from a limited amount of data. It is a process of shooting a gun at a wall and then painting a bullseye around the bullet hole. As a result, you exclude the information that actually negates or challenges your argument.
For example, you might argue “I got into Harvard because I studied hard, did athletics and extracurriculars, and wrote a good essay.” What you failed to mention is the $5,000,000 donation your dad gave to the school.
Or, “Brian and Sally were made for each other: they both like ice cream, Russian novels, knitting, long walks on the beach, and they both dislike hypocrisy.” Perhaps you didn’t know this: Brian is also gay.
Good arguments rarely happen in a vacuum: they develop out of a process of feedback, debate, and collaboration. If you’re writing for periodicals, news outlets, or any other form of CNF, our upcoming creative nonfiction classes might be for you.
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Conspiracy Theory PWR 1, Fall 2008 Stanford University Jonah Willihnganz
Logical Fallacies (Handout developed by Kimberly Moekle)
All of these definitions come from “Stephen’s Guide to the Logical Fallacies,” located at http://datanation.com/fallacies/index.htm , where you can find further information on all of the fallacies listed below. Stephen Downes is a Senior Researcher for the National Research Council of Canada, where he currently works as an “information architect,” and has become a leading voice in the areas of learning objects and metadata, as well as the emerging field of weblogs in education and content syndication.
Fallacies of Distraction
Appeals to Motives in Place of Support |
Changing the Subject
Inductive Fallacies
Fallacies Involving Statistical Syllogisms
Causal Fallacies
Missing the Point
Fallacies of Ambiguity
Category Errors
Non Sequitur
Syllogistic Errors
Fallacies of Explanation
Fallacies of Definition
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The term “counterfactual” was coined by philosopher Nelson Goodman ( 1947 ) to capture Roderick Chisholm’s more convoluted locution “contrary-to-fact” (Chisholm 1946 ). “Counterfactual” was initially used in reference to conditional statements with false antecedents such as “If kangaroos had no tails, they would topple over” (Lewis 1973 ). Since, in reality, Kangaroos do have tails, this counterfactual conditional expresses a relation between a false antecedent and its consequent. The concept behind the term, however, has a longer history. For instance, Newton, Leibniz, and Laplace famously discussed various philosophical issues involving ways in which the world could have been, and many argue that Hume employed counterfactual considerations to define cause . Nevertheless, for most of the twentieth century, research on the meaning of counterfactual statements was very much confined to philosophy, and to areas such as logic, semantics, metaphysics, and epistemology. There was...
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De Brigard, F. (2022). Counterfactual Thinking. In: The Palgrave Encyclopedia of the Possible. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-98390-5_43-1
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Aristotle’s logic, especially his theory of the syllogism, has had an unparalleled influence on the history of Western thought. It did not always hold this position: in the Hellenistic period, Stoic logic, and in particular the work of Chrysippus, took pride of place. However, in later antiquity, following the work of Aristotelian Commentators, Aristotle’s logic became dominant, and Aristotelian logic was what was transmitted to the Arabic and the Latin medieval traditions, while the works of Chrysippus have not survived.
This unique historical position has not always contributed to the understanding of Aristotle’s logical works. Kant thought that Aristotle had discovered everything there was to know about logic, and the historian of logic Prantl drew the corollary that any logician after Aristotle who said anything new was confused, stupid, or perverse. During the rise of modern formal logic following Frege and Peirce, adherents of Traditional Logic (seen as the descendant of Aristotelian Logic) and the new mathematical logic tended to see one another as rivals, with incompatible notions of logic. More recent scholarship has often applied the very techniques of mathematical logic to Aristotle’s theories, revealing (in the opinion of many) a number of similarities of approach and interest between Aristotle and modern logicians.
This article is written from the latter perspective. As such, it is about Aristotle’s logic, which is not always the same thing as what has been called “Aristotelian” logic.
2. aristotle’s logical works: the organon, 3.1 induction and deduction, 3.2 aristotelian deductions and modern valid arguments, 4.2 affirmations, denials, and contradictions, 4.3 all, some, and none, 5.1 the figures, 5.2 methods of proof: “perfect” deductions, conversion, reduction, 5.3 disproof: counterexamples and terms, 5.4 the deductions in the figures (“moods”), 5.5 metatheoretical results, 5.6 syllogisms with modalities, 6.1 aristotelian sciences, 6.2 the regress problem, 6.3 aristotle’s solution: “it eventually comes to a stop”, 6.4 knowledge of first principles: nous, 7.1 definitions and essences, 7.2 species, genus, and differentia, 7.3 the categories, 7.4 the method of division, 7.5 definition and demonstration, 8.1 dialectical premises: the meaning of endoxos, 8.2 the two elements of the art of dialectic, 8.3 the uses of dialectic and dialectical argument, 9. dialectic and rhetoric, 10. sophistical arguments, 11. non-contradiction and metaphysics, 12. time and necessity: the sea-battle, 13. glossary of aristotelian terminology, other internet resources, related entries.
Aristotle’s logical works contain the earliest formal study of logic that we have. It is therefore all the more remarkable that together they comprise a highly developed logical theory, one that was able to command immense respect for many centuries: Kant, who was ten times more distant from Aristotle than we are from him, even held that nothing significant had been added to Aristotle’s views in the intervening two millennia.
In the last century, Aristotle’s reputation as a logician has undergone two remarkable reversals. The rise of modern formal logic following the work of Frege and Russell brought with it a recognition of the many serious limitations of Aristotle’s logic; today, very few would try to maintain that it is adequate as a basis for understanding science, mathematics, or even everyday reasoning. At the same time, scholars trained in modern formal techniques have come to view Aristotle with new respect, not so much for the correctness of his results as for the remarkable similarity in spirit between much of his work and modern logic. As Jonathan Lear has put it, “Aristotle shares with modern logicians a fundamental interest in metatheory”: his primary goal is not to offer a practical guide to argumentation but to study the properties of inferential systems themselves.
The ancient commentators grouped together several of Aristotle’s treatises under the title Organon (“Instrument”) and regarded them as comprising his logical works:
In fact, the title Organon reflects a much later controversy about whether logic is a part of philosophy (as the Stoics maintained) or merely a tool used by philosophy (as the later Peripatetics thought); calling the logical works “The Instrument” is a way of taking sides on this point. Aristotle himself never uses this term, nor does he give much indication that these particular treatises form some kind of group, though there are frequent cross-references between the Topics and the Analytics . On the other hand, Aristotle treats the Prior and Posterior Analytics as one work, and On Sophistical Refutations is a final section, or an appendix, to the Topics ). To these works should be added the Rhetoric , which explicitly declares its reliance on the Topics .
All Aristotle’s logic revolves around one notion: the deduction ( sullogismos ). A thorough explanation of what a deduction is, and what they are composed of, will necessarily lead us through the whole of his theory. What, then, is a deduction? Aristotle says:
A deduction is speech ( logos ) in which, certain things having been supposed, something different from those supposed results of necessity because of their being so. ( Prior Analytics I.2, 24b18–20)
Each of the “things supposed” is a premise ( protasis ) of the argument, and what “results of necessity” is the conclusion ( sumperasma ).
The core of this definition is the notion of “resulting of necessity” ( ex anankês sumbainein ). This corresponds to a modern notion of logical consequence: \(X\) results of necessity from \(Y\) and \(Z\) if it would be impossible for \(X\) to be false when \(Y\) and \(Z\) are true. We could therefore take this to be a general definition of “valid argument”.
Deductions are one of two species of argument recognized by Aristotle. The other species is induction ( epagôgê ). He has far less to say about this than deduction, doing little more than characterize it as “argument from the particular to the universal”. However, induction (or something very much like it) plays a crucial role in the theory of scientific knowledge in the Posterior Analytics : it is induction, or at any rate a cognitive process that moves from particulars to their generalizations, that is the basis of knowledge of the indemonstrable first principles of sciences.
Despite its wide generality, Aristotle’s definition of deduction is not a precise match for a modern definition of validity. Some of the differences may have important consequences:
Of these three possible restrictions, the most interesting would be the third. This could be (and has been) interpreted as committing Aristotle to something like a relevance logic . In fact, there are passages that appear to confirm this. However, this is too complex a matter to discuss here.
However the definition is interpreted, it is clear that Aristotle does not mean to restrict it only to a subset of the valid arguments. This is why I have translated sullogismos with ‘deduction’ rather than its English cognate. In modern usage, ‘syllogism’ means an argument of a very specific form. Moreover, modern usage distinguishes between valid syllogisms (the conclusions of which follow from their premises) and invalid syllogisms (the conclusions of which do not follow from their premises). The second of these is inconsistent with Aristotle’s use: since he defines a sullogismos as an argument in which the conclusion results of necessity from the premises, “invalid sullogismos ” is a contradiction in terms. The first is also at least highly misleading, since Aristotle does not appear to think that the sullogismoi are simply an interesting subset of the valid arguments. Moreover (see below), Aristotle expends great efforts to argue that every valid argument, in a broad sense, can be “reduced” to an argument, or series of arguments, in something like one of the forms traditionally called a syllogism. If we translate sullogismos as “syllogism”, this becomes the trivial claim “Every syllogism is a syllogism”,
Syllogisms are structures of sentences each of which can meaningfully be called true or false: assertions ( apophanseis ), in Aristotle’s terminology. According to Aristotle, every such sentence must have the same structure: it must contain a subject ( hupokeimenon ) and a predicate and must either affirm or deny the predicate of the subject. Thus, every assertion is either the affirmation kataphasis or the denial ( apophasis ) of a single predicate of a single subject.
In On Interpretation , Aristotle argues that a single assertion must always either affirm or deny a single predicate of a single subject. Thus, he does not recognize sentential compounds, such as conjunctions and disjunctions, as single assertions. This appears to be a deliberate choice on his part: he argues, for instance, that a conjunction is simply a collection of assertions, with no more intrinsic unity than the sequence of sentences in a lengthy account (e.g. the entire Iliad , to take Aristotle’s own example). Since he also treats denials as one of the two basic species of assertion, he does not view negations as sentential compounds. His treatment of conditional sentences and disjunctions is more difficult to appraise, but it is at any rate clear that Aristotle made no efforts to develop a sentential logic. Some of the consequences of this for his theory of demonstration are important.
Subjects and predicates of assertions are terms . A term ( horos ) can be either individual, e.g. Socrates , Plato or universal, e.g. human , horse , animal , white . Subjects may be either individual or universal, but predicates can only be universals: Socrates is human , Plato is not a horse , horses are animals , humans are not horses .
The word universal ( katholou ) appears to be an Aristotelian coinage. Literally, it means “of a whole”; its opposite is therefore “of a particular” ( kath’ hekaston ). Universal terms are those which can properly serve as predicates, while particular terms are those which cannot.
This distinction is not simply a matter of grammatical function. We can readily enough construct a sentence with “Socrates” as its grammatical predicate: “The person sitting down is Socrates”. Aristotle, however, does not consider this a genuine predication. He calls it instead a merely accidental or incidental ( kata sumbebêkos ) predication. Such sentences are, for him, dependent for their truth values on other genuine predications (in this case, “Socrates is sitting down”).
Consequently, predication for Aristotle is as much a matter of metaphysics as a matter of grammar. The reason that the term Socrates is an individual term and not a universal is that the entity which it designates is an individual, not a universal. What makes white and human universal terms is that they designate universals.
Further discussion of these issues can be found in the entry on Aristotle’s metaphysics .
Aristotle takes some pains in On Interpretation to argue that to every affirmation there corresponds exactly one denial such that that denial denies exactly what that affirmation affirms. The pair consisting of an affirmation and its corresponding denial is a contradiction ( antiphasis ). In general, Aristotle holds, exactly one member of any contradiction is true and one false: they cannot both be true, and they cannot both be false. However, he appears to make an exception for propositions about future events, though interpreters have debated extensively what this exception might be (see further discussion below). The principle that contradictories cannot both be true has fundamental importance in Aristotle’s metaphysics (see further discussion below).
One major difference between Aristotle’s understanding of predication and modern (i.e., post-Fregean) logic is that Aristotle treats individual predications and general predications as similar in logical form: he gives the same analysis to “Socrates is an animal” and “Humans are animals”. However, he notes that when the subject is a universal, predication takes on two forms: it can be either universal or particular . These expressions are parallel to those with which Aristotle distinguishes universal and particular terms, and Aristotle is aware of that, explicitly distinguishing between a term being a universal and a term being universally predicated of another.
\(P\) affirmed of all of \(S\) | Every \(S\) is \(P\), All \(S\) is (are) \(P\) | \(P\) denied of all of \(S\) | No \(S\) is \(P\) | |
\(P\) affirmed of some of \(S\) | Some \(S\) is (are) \(P\) | \(P\) denied of some of \(S\) | Some \(S\) is not \(P\), Not every \(S\) is \(P\) | |
\(P\) affirmed of \(S\) | \(S\) is \(P\) | \(P\) denied of \(S\) | \(S\) is not \(P\) |
Whatever is affirmed or denied of a universal subject may be affirmed or denied of it it universally ( katholou or “of all”, kata pantos ), in part ( kata meros , en merei ), or indefinitely ( adihoristos ).
In On Interpretation , Aristotle spells out the relationships of contradiction for sentences with universal subjects as follows:
Every \(A\) is \(B\) | No \(A\) is \(B\) | |
Some \(A\) is \(B\) | Not every \(A\) is \(B\) |
Simple as it appears, this table raises important difficulties of interpretation (for a thorough discussion, see the entry on the square of opposition ).
In the Prior Analytics , Aristotle adopts a somewhat artificial way of expressing predications: instead of saying “\(X\) is predicated of \(Y\)” he says “\(X\) belongs ( huparchei ) to \(Y\)”. This should really be regarded as a technical expression. The verb huparchein usually means either “begin” or “exist, be present”, and Aristotle’s usage appears to be a development of this latter use.
For clarity and brevity, I will use the following semi-traditional abbreviations for Aristotelian categorical sentences (note that the predicate term comes first and the subject term second ):
\(Aab\) | \(a\) belongs to all \(b\) (Every \(b\) is \(a\)) |
\(Eab\) | \(a\) belongs to no \(b\) (No \(b\) is \(a\)) |
\(Iab\) | \(a\) belongs to some \(b\) (Some \(b\) is \(a\)) |
\(Oab\) | \(a\) does not belong to all \(b\) (Some \(b\) is not \(a\)) |
Aristotle’s most famous achievement as logician is his theory of inference, traditionally called the syllogistic (though not by Aristotle). That theory is in fact the theory of inferences of a very specific sort: inferences with two premises, each of which is a categorical sentence, having exactly one term in common, and having as conclusion a categorical sentence the terms of which are just those two terms not shared by the premises. Aristotle calls the term shared by the premises the middle term ( meson ) and each of the other two terms in the premises an extreme ( akron ). The middle term must be either subject or predicate of each premise, and this can occur in three ways: the middle term can be the subject of one premise and the predicate of the other, the predicate of both premises, or the subject of both premises. Aristotle refers to these term arrangements as figures ( schêmata ):
\(a\) | \(b\) | \(a\) | \(b\) | \(a\) | \(c\) | |
\(b\) | \(c\) | \(a\) | \(c\) | \(b\) | \(c\) | |
\(a\) | \(c\) | \(b\) | \(c\) | \(a\) | \(b\) |
Aristotle calls the term which is the predicate of the conclusion the major term and the term which is the subject of the conclusion the minor term. The premise containing the major term is the major premise , and the premise containing the minor term is the minor premise .
Aristotle then systematically investigates all possible combinations of two premises in each of the three figures. For each combination, he either demonstrates that some conclusion necessarily follows or demonstrates that no conclusion follows. The results he states are correct.
Aristotle’s proofs can be divided into two categories, based on a distinction he makes between “perfect” or “complete” ( teleios ) deductions and “imperfect” or “incomplete” ( atelês ) deductions. A deduction is perfect if it “needs no external term in order to show the necessary result” (24b23–24), and it is imperfect if it “needs one or several in addition that are necessary because of the terms supposed but were not assumed through premises” (24b24–25). The precise interpretation of this distinction is debatable, but it is at any rate clear that Aristotle regards the perfect deductions as not in need of proof in some sense. For imperfect deductions, Aristotle does give proofs, which invariably depend on the perfect deductions. Thus, with some reservations, we might compare the perfect deductions to the axioms or primitive rules of a deductive system.
In the proofs for imperfect deductions, Aristotle says that he “reduces” ( anagein ) each case to one of the perfect forms and that they are thereby “completed” or “perfected”. These completions are either probative ( deiktikos : a modern translation might be “direct”) or through the impossible ( dia to adunaton ).
A direct deduction is a series of steps leading from the premises to the conclusion, each of which is either a conversion of a previous step or an inference from two previous steps relying on a first-figure deduction. Conversion, in turn, is inferring from a proposition another which has the subject and predicate interchanged. Specifically, Aristotle argues that three such conversions are sound:
He undertakes to justify these in An. Pr. I.2. From a modern standpoint, the third is sometimes regarded with suspicion. Using it we can get Some monsters are chimeras from the apparently true All chimeras are monsters ; but the former is often construed as implying in turn There is something which is a monster and a chimera , and thus that there are monsters and there are chimeras. In fact, this simply points up something about Aristotle’s system: Aristotle in effect supposes that all terms in syllogisms are non-empty. (For further discussion of this point, see the entry on the square of opposition ).
As an example of the procedure, we may take Aristotle’s proof of Camestres . He says:
If \(M\) belongs to every \(N\) but to no \(X\), then neither will \(N\) belong to any \(X\). For if \(M\) belongs to no \(X\), then neither does \(X\) belong to any \(M\); but \(M\) belonged to every \(N\); therefore, \(X\) will belong to no \(N\) (for the first figure has come about). And since the privative converts, neither will \(N\) belong to any \(X\). ( An. Pr. I.5, 27a9–12)
From this text, we can extract an exact formal proof, as follows:
Step | Justification | Aristotle’s Text |
1. \(MaN\) | ||
2. \(MeX\) | ||
To prove: \(NeX\) | ||
3. \(MeX\) | (2, premise) | |
4. \(XeM\) | (3, conversion of \(e\)) | |
5. \(MaN\) | (1, premise) | |
6. \(XeN\) | (4, 5, ) | |
7. \(NeX\) | (6, conversion of \(e\)) |
A completion or proof “through the impossible” shows that a certain conclusion follows from a pair of premises by assuming as a third premise the denial of that conclusion and giving a deduction, from it and one of the original premises, the denial (or the contrary) of the other premises. This is the deduction of an “impossible”, and Aristotle’s proof ends at that point. An example is his proof of Baroco in 27a36–b1:
Step | Justification | Aristotle’s Text |
1. \(MaN\) | ||
2. \(MoX\) | ||
To prove: \(NoX\) | ||
3. \(NaX\) | Contradictory of the desired conclusion | |
4. \(MaN\) | Repetition of premise 1 | |
5. \(MaX\) | (3, 4, Barbara) | |
6. \(MoX\) | (5 is the contradictory of 2) |
Aristotle proves invalidity by constructing counterexamples. This is very much in the spirit of modern logical theory: all that it takes to show that a certain form is invalid is a single instance of that form with true premises and a false conclusion. However, Aristotle states his results not by saying that certain premise-conclusion combinations are invalid but by saying that certain premise pairs do not “syllogize”: that is, that, given the pair in question, examples can be constructed in which premises of that form are true and a conclusion of any of the four possible forms is false.
When possible, he does this by a clever and economical method: he gives two triplets of terms, one of which makes the premises true and a universal affirmative “conclusion” true, and the other of which makes the premises true and a universal negative “conclusion” true. The first is a counterexample for an argument with either an \(E\) or an \(O\) conclusion, and the second is a counterexample for an argument with either an \(A\) or an \(I\) conclusion.
In Prior Analytics I.4–6, Aristotle shows that the premise combinations given in the following table yield deductions and that all other premise combinations fail to yield a deduction. In the terminology traditional since the middle ages, each of these combinations is known as a mood Latin modus , “way”, which in turn is a translation of Greek tropos ). Aristotle, however, does not use this expression and instead refers to “the arguments in the figures”.
In this table, “\(\vdash\)” separates premises from conclusion; it may be read “therefore”. The second column lists the medieval mnemonic name associated with the inference (these are still widely used, and each is actually a mnemonic for Aristotle’s proof of the mood in question). The third column briefly summarizes Aristotle’s procedure for demonstrating the deduction.
Form | Mnemonic | Proof |
FIRST FIGURE | ||
\(Aab, Abc \vdash Aac\) | Perfect | |
\(Eab, Abc \vdash Eac\) | Perfect | |
\(Aab, Ibc \vdash Iac\) | Perfect; also by impossibility, from | |
\(Eab, Ibc \vdash Oac\) | Perfect; also by impossibility, from | |
SECOND FIGURE | ||
\(Eab, Aac \vdash Ebc\) | \((Eab, Aac)\rightarrow (Eba, Aac)\) \(\vdash_{Cel} Ebc\) | |
\(Aab, Eac \vdash Ebc\) | \((Aab, Eac) \rightarrow (Aab, Eca)= (Eca, Aab)\) \(\vdash_{Cel} Ecb \rightarrow Ebc\) | |
\(Eab, Iac \vdash Obc\) | \((Eab, Iac) \rightarrow (Eba,Iac)\) \(\vdash_{Fer} Obc\) | |
\(Aab, Oac \vdash Obc\) | \((Aab, Oac +Abc) \vdash_{Bar} (Aac,Oac)\) \(\vdash_{Imp} Obc\) | |
THIRD FIGURE | ||
\(Aac, Abc \vdash Iab\) | \((Aac, Abc) \rightarrow (Aac,Icb)\) \(\vdash_{Dar} Iab\) | |
\(Eac, Abc \vdash Oab\) | \((Eac, Abc) \rightarrow (Eac,Icb)\) \(\vdash_{Fer} Oab\) | |
\(Iac, Abc \vdash Iab\) | \((Iac, Abc) \rightarrow (Ica, Abc)=(Abc,Ica)\) \(\vdash_{Dar} Iba \rightarrow Iab\) | |
\(Aac, Ibc \vdash Iab\) | \((Aac, Ibc) \rightarrow (Aac,Icb)\) \(\vdash_{Dar} Iab\) | |
\(Oac, Abc \vdash Oab\) | \((Oac, +Aab, Abc) \vdash_{Bar} (Aac,Oac)\) \(\vdash_{Imp} Oab\) | |
\(Eac, Ibc \vdash Oab\) | \((Eac, Ibc) \rightarrow (Eac, Icb)\) \(\vdash_{Fer} Oab\) |
Table of the Deductions in the Figures
Having established which deductions in the figures are possible, Aristotle draws a number of metatheoretical conclusions, including:
He also proves the following metatheorem:
All deductions can be reduced to the two universal deductions in the first figure.
His proof of this is elegant. First, he shows that the two particular deductions of the first figure can be reduced, by proof through impossibility, to the universal deductions in the second figure:
He then observes that since he has already shown how to reduce all the particular deductions in the other figures except Baroco and Bocardo to Darii and Ferio , these deductions can thus be reduced to Barbara and Celarent . This proof is strikingly similar both in structure and in subject to modern proofs of the redundancy of axioms in a system.
Many more metatheoretical results, some of them quite sophisticated, are proved in Prior Analytics I.45 and in Prior Analytics II. As noted below, some of Aristotle’s metatheoretical results are appealed to in the epistemological arguments of the Posterior Analytics .
Aristotle follows his treatment of “arguments in the figures” with a much longer, and much more problematic, discussion of what happens to these figured arguments when we add the qualifications “necessarily” and “possibly” to their premises in various ways. In contrast to the syllogistic itself (or, as commentators like to call it, the assertoric syllogistic), this modal syllogistic appears to be much less satisfactory and is certainly far more difficult to interpret. Here, I only outline Aristotle’s treatment of this subject and note some of the principal points of interpretive controversy.
Modern modal logic treats necessity and possibility as interdefinable: “necessarily P” is equivalent to “not possibly not P”, and “possibly P” to “not necessarily not P”. Aristotle gives these same equivalences in On Interpretation . However, in Prior Analytics , he makes a distinction between two notions of possibility. On the first, which he takes as his preferred notion, “possibly P” is equivalent to “not necessarily P and not necessarily not P”. He then acknowledges an alternative definition of possibility according to the modern equivalence, but this plays only a secondary role in his system.
Aristotle builds his treatment of modal syllogisms on his account of non-modal ( assertoric ) syllogisms: he works his way through the syllogisms he has already proved and considers the consequences of adding a modal qualification to one or both premises. Most often, then, the questions he explores have the form: “Here is an assertoric syllogism; if I add these modal qualifications to the premises, then what modally qualified form of the conclusion (if any) follows?”. A premise can have one of three modalities: it can be necessary, possible, or assertoric. Aristotle works through the combinations of these in order:
Though he generally considers only premise combinations which syllogize in their assertoric forms, he does sometimes extend this; similarly, he sometimes considers conclusions in addition to those which would follow from purely assertoric premises.
Since this is his procedure, it is convenient to describe modal syllogisms in terms of the corresponding non-modal syllogism plus a triplet of letters indicating the modalities of premises and conclusion: \(N\) = “necessary”, \(P\) = “possible”, \(A\) = “assertoric”. Thus, “Barbara \(NAN\)” would mean “The form Barbara with necessary major premise, assertoric minor premise, and necessary conclusion”. I use the letters “\(N\)” and “\(P\)” as prefixes for premises as well; a premise with no prefix is assertoric. Thus, Barbara \(NAN\) would be \(NAab, Abc \vdash NAac\).
As in the case of assertoric syllogisms, Aristotle makes use of conversion rules to prove validity. The conversion rules for necessary premises are exactly analogous to those for assertoric premises:
Possible premises behave differently, however. Since he defines “possible” as “neither necessary nor impossible”, it turns out that \(x\) is possibly \(F\) entails, and is entailed by, \(x\) is possibly not \(F\). Aristotle generalizes this to the case of categorical sentences as follows:
In addition, Aristotle uses the intermodal principle \(N\rightarrow A\): that is, a necessary premise entails the corresponding assertoric one. However, because of his definition of possibility, the principle \(A\rightarrow P\) does not generally hold: if it did, then \(N\rightarrow P\) would hold, but on his definition “necessarily \(P\)” and “possibly \(P\)” are actually inconsistent (“possibly \(P\)” entails “possibly not \(P\)”).
This leads to a further complication. The denial of “possibly \(P\)” for Aristotle is “either necessarily \(P\) or necessarily not \(P\)”. The denial of “necessarily \(P\)” is still more difficult to express in terms of a combination of modalities: “either possibly \(P\) (and thus possibly not \(P\)) or necessarily not \(P\)” This is important because of Aristotle’s proof procedures, which include proof through impossibility. If we give a proof through impossibility in which we assume a necessary premise, then the conclusion we ultimately establish is simply the denial of that necessary premise, not a “possible” conclusion in Aristotle’s sense. Such propositions do occur in his system, but only in exactly this way, i.e., as conclusions established by proof through impossiblity from necessary assumptions. Somewhat confusingly, Aristotle calls such propositions “possible” but immediately adds “ not in the sense defined”: in this sense, “possibly \(Oab\)” is simply the denial of “necessarily \(Aab\)”. Such propositions appear only as premises, never as conclusions.
Aristotle holds that an assertoric syllogism remains valid if “necessarily” is added to its premises and its conclusion: the modal pattern \(NNN\) is always valid. He does not treat this as a trivial consequence but instead offers proofs; in all but two cases, these are parallel to those offered for the assertoric case. The exceptions are Baroco and Bocardo , which he proved in the assertoric case through impossibility: attempting to use that method here would require him to take the denial of a necessary \(O\) proposition as hypothesis, raising the complication noted above, and he uses the procedure he calls ecthesis instead (see Smith 1982).
Since a necessary premise entails an assertoric premise, every \(AN\) or \(NA\) combination of premises will entail the corresponding \(AA\) pair, and thus the corresponding \(A\) conclusion. Thus, \(ANA\) and \(NAA\) syllogisms are always valid. However, Aristotle holds that some, but not all, \(ANN\) and \(NAN\) combinations are valid. Specifically, he accepts Barbara \(NAN\) but rejects Barbara \(ANN\). Almost from Aristotle’s own time, interpreters have found his reasons for this distinction obscure, or unpersuasive, or both, and often have not followed his view. His close associated Theophrastus, for instance, adopted the simpler rule that the modality of the conclusion of a syllogism was always the “weakest” modality found in either premise, where \(N\) is stronger than \(A\) and \(A\) is stronger than \(P\) (and where \(P\) probably has to be defined as “not necessarily not”).
Beginning with Albrecht Becker, interpreters using the methods of modern formal logic to interpret Aristotle’s modal logic have seen the Two-Barbaras problem as only one of a series of difficulties in giving a coherent interpretation of the modal syllogistic. A very wide range of reconstructions has been proposed: see Becker 1933, McCall 1963, Nortmann 1996, Van Rijen 1989, Patterson 1995, Thomason 1993, Thom 1996, Rini 2012, Malink 2013. The majority of reconstructions do not attempt to reproduce every detail of Aristotle’s exposition but instead produce modified reconstructions that abandon some of those results. Malink 2013, however, offers a reconstruction that reproduces everything Aristotle says, although the resulting model introduces a high degree of complexity. (This subject quickly becomes too complex for summarizing in this brief article.
A demonstration ( apodeixis ) is “a deduction that produces knowledge”. Aristotle’s Posterior Analytics contains his account of demonstrations and their role in knowledge. From a modern perspective, we might think that this subject moves outside of logic to epistemology. From Aristotle’s perspective, however, the connection of the theory of sullogismoi with the theory of knowledge is especially close.
The subject of the Posterior Analytics is epistêmê . This is one of several Greek words that can reasonably be translated “knowledge”, but Aristotle is concerned only with knowledge of a certain type (as will be explained below). There is a long tradition of translating epistêmê in this technical sense as science , and I shall follow that tradition here. However, readers should not be misled by the use of that word. In particular, Aristotle’s theory of science cannot be considered a counterpart to modern philosophy of science, at least not without substantial qualifications.
We have scientific knowledge, according to Aristotle, when we know:
the cause why the thing is, that it is the cause of this, and that this cannot be otherwise. ( Posterior Analytics I.2)
This implies two strong conditions on what can be the object of scientific knowledge:
He then proceeds to consider what science so defined will consist in, beginning with the observation that at any rate one form of science consists in the possession of a demonstration ( apodeixis ), which he defines as a “scientific deduction”:
by “scientific” ( epistêmonikon ), I mean that in virtue of possessing it, we have knowledge.
The remainder of Posterior Analytics I is largely concerned with two tasks: spelling out the nature of demonstration and demonstrative science and answering an important challenge to its very possibility. Aristotle first tells us that a demonstration is a deduction in which the premises are:
The interpretation of all these conditions except the first has been the subject of much controversy. Aristotle clearly thinks that science is knowledge of causes and that in a demonstration, knowledge of the premises is what brings about knowledge of the conclusion. The fourth condition shows that the knower of a demonstration must be in some better epistemic condition towards them, and so modern interpreters often suppose that Aristotle has defined a kind of epistemic justification here. However, as noted above, Aristotle is defining a special variety of knowledge. Comparisons with discussions of justification in modern epistemology may therefore be misleading.
The same can be said of the terms “primary”, “immediate” and “better known”. Modern interpreters sometimes take “immediate” to mean “self-evident”; Aristotle does say that an immediate proposition is one “to which no other is prior”, but (as I suggest in the next section) the notion of priority involved is likely a notion of logical priority that it is hard to detach from Aristotle’s own logical theories. “Better known” has sometimes been interpreted simply as “previously known to the knower of the demonstration” (i.e., already known in advance of the demonstration). However, Aristotle explicitly distinguishes between what is “better known for us” with what is “better known in itself” or “in nature” and says that he means the latter in his definition. In fact, he says that the process of acquiring scientific knowledge is a process of changing what is better known “for us”, until we arrive at that condition in which what is better known in itself is also better known for us.
In Posterior Analytics I.2, Aristotle considers two challenges to the possibility of science. One party (dubbed the “agnostics” by Jonathan Barnes) began with the following two premises:
They then argued that demonstration is impossible with the following dilemma:
A second group accepted the agnostics’ view that scientific knowledge comes only from demonstration but rejected their conclusion by rejecting the dilemma. Instead, they maintained:
Aristotle does not give us much information about how circular demonstration was supposed to work, but the most plausible interpretation would be supposing that at least for some set of fundamental principles, each principle could be deduced from the others. (Some modern interpreters have compared this position to a coherence theory of knowledge.) However their position worked, the circular demonstrators claimed to have a third alternative avoiding the agnostics’ dilemma, since circular demonstration gives us a regress that is both unending (in the sense that we never reach premises at which it comes to a stop) and finite (because it works its way round the finite circle of premises).
Aristotle rejects circular demonstration as an incoherent notion on the grounds that the premises of any demonstration must be prior (in an appropriate sense) to the conclusion, whereas a circular demonstration would make the same premises both prior and posterior to one another (and indeed every premise prior and posterior to itself). He agrees with the agnostics’ analysis of the regress problem: the only plausible options are that it continues indefinitely or that it “comes to a stop” at some point. However, he thinks both the agnostics and the circular demonstrators are wrong in maintaining that scientific knowledge is only possible by demonstration from premises scientifically known: instead, he claims, there is another form of knowledge possible for the first premises, and this provides the starting points for demonstrations.
To solve this problem, Aristotle needs to do something quite specific. It will not be enough for him to establish that we can have knowledge of some propositions without demonstrating them: unless it is in turn possible to deduce all the other propositions of a science from them, we shall not have solved the regress problem. Moreover (and obviously), it is no solution to this problem for Aristotle simply to assert that we have knowledge without demonstration of some appropriate starting points. He does indeed say that it is his position that we have such knowledge ( An. Post. I.2,), but he owes us an account of why that should be so.
Aristotle’s account of knowledge of the indemonstrable first premises of sciences is found in Posterior Analytics II.19, long regarded as a difficult text to interpret. Briefly, what he says there is that it is another cognitive state, nous (translated variously as “insight”, “intuition”, “intelligence”), which knows them. There is wide disagreement among commentators about the interpretation of his account of how this state is reached; I will offer one possible interpretation. First, Aristotle identifies his problem as explaining how the principles can “become familiar to us”, using the same term “familiar” ( gnôrimos ) that he used in presenting the regress problem. What he is presenting, then, is not a method of discovery but a process of becoming wise. Second, he says that in order for knowledge of immediate premises to be possible, we must have a kind of knowledge of them without having learned it, but this knowledge must not be as “precise” as the knowledge that a possessor of science must have. The kind of knowledge in question turns out to be a capacity or power ( dunamis ) which Aristotle compares to the capacity for sense-perception: since our senses are innate, i.e., develop naturally, it is in a way correct to say that we know what e.g. all the colors look like before we have seen them: we have the capacity to see them by nature, and when we first see a color we exercise this capacity without having to learn how to do so first. Likewise, Aristotle holds, our minds have by nature the capacity to recognize the starting points of the sciences.
In the case of sensation, the capacity for perception in the sense organ is actualized by the operation on it of the perceptible object. Similarly, Aristotle holds that coming to know first premises is a matter of a potentiality in the mind being actualized by experience of its proper objects: “The soul is of such a nature as to be capable of undergoing this”. So, although we cannot come to know the first premises without the necessary experience, just as we cannot see colors without the presence of colored objects, our minds are already so constituted as to be able to recognize the right objects, just as our eyes are already so constituted as to be able to perceive the colors that exist.
It is considerably less clear what these objects are and how it is that experience actualizes the relevant potentialities in the soul. Aristotle describes a series of stages of cognition. First is what is common to all animals: perception of what is present. Next is memory, which he regards as a retention of a sensation: only some animals have this capacity. Even fewer have the next capacity, the capacity to form a single experience ( empeiria ) from many repetitions of the same memory. Finally, many experiences repeated give rise to knowledge of a single universal ( katholou ). This last capacity is present only in humans.
See Section 7 of the entry on Aristotle’s psychology for more on his views about mind.
The definition ( horos , horismos ) was an important matter for Plato and for the Early Academy. Concern with answering the question “What is so-and-so?” are at the center of the majority of Plato’s dialogues, some of which (most elaborately the Sophist ) propound methods for finding definitions. External sources (sometimes the satirical remarks of comedians) also reflect this Academic concern with definitions. Aristotle himself traces the quest for definitions back to Socrates.
For Aristotle, a definition is “an account which signifies what it is to be for something” ( logos ho to ti ên einai sêmainei ). The phrase “what it is to be” and its variants are crucial: giving a definition is saying, of some existent thing, what it is, not simply specifying the meaning of a word (Aristotle does recognize definitions of the latter sort, but he has little interest in them).
The notion of “what it is to be” for a thing is so pervasive in Aristotle that it becomes formulaic: what a definition expresses is “the what-it-is-to-be” ( to ti ên einai ), or in modern terminology, its essence.
Since a definition defines an essence, only what has an essence can be defined. What has an essence, then? That is one of the central questions of Aristotle’s metaphysics; once again, we must leave the details to another article. In general, however, it is not individuals but rather species ( eidos : the word is one of those Plato uses for “Form”) that have essences. A species is defined by giving its genus ( genos ) and its differentia ( diaphora ): the genus is the kind under which the species falls, and the differentia tells what characterizes the species within that genus. As an example, human might be defined as animal (the genus) having the capacity to reason (the differentia).
Underlying Aristotle’s concept of a definition is the concept of essential predication ( katêgoreisthai en tôi ti esti , predication in the what it is). In any true affirmative predication, the predicate either does or does not “say what the subject is”, i.e., the predicate either is or is not an acceptable answer to the question “What is it?” asked of the subject. Bucephalus is a horse, and a horse is an animal; so, “Bucephalus is a horse” and “Bucephalus is an animal” are essential predications. However, “Bucephalus is brown”, though true, does not state what Bucephalus is but only says something about him.
Since a thing’s definition says what it is, definitions are essentially predicated. However, not everything essentially predicated is a definition. Since Bucephalus is a horse, and horses are a kind of mammal, and mammals are a kind of animal, “horse” “mammal” and “animal” are all essential predicates of Bucephalus. Moreover, since what a horse is is a kind of mammal, “mammal” is an essential predicate of horse. When predicate \(X\) is an essential predicate of \(Y\) but also of other things, then \(X\) is a genus ( genos ) of \(Y\).
A definition of \(X\) must not only be essentially predicated of it but must also be predicated only of it: to use a term from Aristotle’s Topics , a definition and what it defines must “counterpredicate” ( antikatêgoreisthai ) with one another. \(X\) counterpredicates with \(Y\) if \(X\) applies to what \(Y\) applies to and conversely. Though X’s definition must counterpredicate with \(X\), not everything that counterpredicates with \(X\) is its definition. “Capable of laughing”, for example, counterpredicates with “human” but fails to be its definition. Such a predicate (non-essential but counterpredicating) is a peculiar property or proprium ( idion ).
Finally, if \(X\) is predicated of \(Y\) but is neither essential nor counterpredicates, then \(X\) is an accident ( sumbebêkos ) of \(Y\).
Aristotle sometimes treats genus, peculiar property, definition, and accident as including all possible predications (e.g. Topics I). Later commentators listed these four and the differentia as the five predicables , and as such they were of great importance to late ancient and to medieval philosophy (e.g., Porphyry).
The notion of essential predication is connected to what are traditionally called the categories ( katêgoriai ). In a word, Aristotle is famous for having held a “doctrine of categories”. Just what that doctrine was, and indeed just what a category is, are considerably more vexing questions. They also quickly take us outside his logic and into his metaphysics. Here, I will try to give a very general overview, beginning with the somewhat simpler question “What categories are there?”
We can answer this question by listing the categories. Here are two passages containing such lists:
We should distinguish the kinds of predication ( ta genê tôn katêgoriôn ) in which the four predications mentioned are found. These are ten in number: what-it-is, quantity, quality, relative, where, when, being-in-a-position, having, doing, undergoing. An accident, a genus, a peculiar property and a definition will always be in one of these categories. ( Topics I.9, 103b20–25) Of things said without any combination, each signifies either substance or quantity or quality or a relative or where or when or being-in-a-position or having or doing or undergoing. To give a rough idea, examples of substance are man, horse; of quantity: four-foot, five-foot; of quality: white, literate; of a relative: double, half, larger; of where: in the Lyceum, in the market-place; of when: yesterday, last year; of being-in-a-position: is-lying, is-sitting; of having: has-shoes-on, has-armor-on; of doing: cutting, burning; of undergoing: being-cut, being-burned. ( Categories 4, 1b25–2a4, tr. Ackrill, slightly modified)
These two passages give ten-item lists, identical except for their first members. What are they lists \(of\)? Here are three ways they might be interpreted:
The word “category” ( katêgoria ) means “predication”. Aristotle holds that predications and predicates can be grouped into several largest “kinds of predication” ( genê tôn katêgoriôn ). He refers to this classification frequently, often calling the “kinds of predication” simply “the predications”, and this (by way of Latin) leads to our word “category”.
Which of these interpretations fits best with the two passages above? The answer appears to be different in the two cases. This is most evident if we take note of point in which they differ: the Categories lists substance ( ousia ) in first place, while the Topics list what-it-is ( ti esti ). A substance, for Aristotle, is a type of entity, suggesting that the Categories list is a list of types of entity.
On the other hand, the expression “what-it-is” suggests most strongly a type of predication. Indeed, the Topics confirms this by telling us that we can “say what it is” of an entity falling under any of the categories:
an expression signifying what-it-is will sometimes signify a substance, sometimes a quantity, sometimes a quality, and sometimes one of the other categories.
As Aristotle explains, if I say that Socrates is a man, then I have said what Socrates is and signified a substance; if I say that white is a color, then I have said what white is and signified a quality; if I say that some length is a foot long, then I have said what it is and signified a quantity; and so on for the other categories. What-it-is, then, here designates a kind of predication, not a kind of entity.
This might lead us to conclude that the categories in the Topics are only to be interpreted as kinds of predicate or predication, those in the Categories as kinds of being. Even so, we would still want to ask what the relationship is between these two nearly-identical lists of terms, given these distinct interpretations. However, the situation is much more complicated. First, there are dozens of other passages in which the categories appear. Nowhere else do we find a list of ten, but we do find shorter lists containing eight, or six, or five, or four of them (with substance/what-it-is, quality, quantity, and relative the most common). Aristotle describes what these lists are lists of in different ways: they tell us “how being is divided”, or “how many ways being is said”, or “the figures of predication” (ta schêmata tês katêgorias). The designation of the first category also varies: we find not only “substance” and “what it is” but also the expressions “this” or “the this” ( tode ti , to tode , to ti ). These latter expressions are closely associated with, but not synonymous with, substance. He even combines the latter with “what-it-is” ( Metaphysics Z 1, 1028a10: “… one sense signifies what it is and the this, one signifies quality …”).
Moreover, substances are for Aristotle fundamental for predication as well as metaphysically fundamental. He tells us that everything that exists exists because substances exist: if there were no substances, there would not be anything else. He also conceives of predication as reflecting a metaphysical relationship (or perhaps more than one, depending on the type of predication). The sentence “Socrates is pale” gets its truth from a state of affairs consisting of a substance (Socrates) and a quality (whiteness) which is in that substance. At this point we have gone far outside the realm of Aristotle’s logic into his metaphysics, the fundamental question of which, according to Aristotle, is “What is a substance?”. (For further discussion of this topic, see the entry on Aristotle’s Categories and the entry on Aristotle’s metaphysics , ( Section 2 ).
See Frede 1981, Ebert 1985 for additional discussion of Aristotle’s lists of categories.
For convenience of reference, I include a table of the categories, along with Aristotle’s examples and the traditional names often used for them. For reasons explained above, I have treated the first item in the list quite differently, since an example of a substance and an example of a what-it-is are necessarily (as one might put it) in different categories.
Substance | substance “this” what-it-is | | man, horse Socrates “Socrates is a man” |
Quantity | How much | four-foot, five-foot | |
Quality | What sort | white, literate | |
Relation | related to what | double, half, greater | |
Location | Where | in the Lyceum, in the marketplace | |
Time | when | yesterday, last year | |
Position | being situated | lies, sits | |
Habit | having, possession | is shod, is armed | |
Action | doing | cuts, burns | |
Passion | undergoing | is cut, is burned |
In the Sophist , Plato introduces a procedure of “Division” as a method for discovering definitions. To find a definition of \(X\), first locate the largest kind of thing under which \(X\) falls; then, divide that kind into two parts, and decide which of the two \(X\) falls into. Repeat this method with the part until \(X\) has been fully located.
This method is part of Aristotle’s Platonic legacy. His attitude towards it, however, is complex. He adopts a view of the proper structure of definitions that is closely allied to it: a correct definition of \(X\) should give the genus ( genos : kind or family) of \(X\), which tells what kind of thing \(X\) is, and the differentia ( diaphora : difference) which uniquely identifies \(X\) within that genus. Something defined in this way is a species ( eidos : the term is one of Plato’s terms for “Form”), and the differentia is thus the “difference that makes a species” ( eidopoios diaphora , “specific difference”). In Posterior Analytics II.13, he gives his own account of the use of Division in finding definitions.
However, Aristotle is strongly critical of the Platonic view of Division as a method for establishing definitions. In Prior Analytics I.31, he contrasts Division with the syllogistic method he has just presented, arguing that Division cannot actually prove anything but rather assumes the very thing it is supposed to be proving. He also charges that the partisans of Division failed to understand what their own method was capable of proving.
Closely related to this is the discussion, in Posterior Analytics II.3–10, of the question whether there can be both definition and demonstration of the same thing (that is, whether the same result can be established either by definition or by demonstration). Since the definitions Aristotle is interested in are statements of essences, knowing a definition is knowing, of some existing thing, what it is. Consequently, Aristotle’s question amounts to a question whether defining and demonstrating can be alternative ways of acquiring the same knowledge. His reply is complex:
As an example of case 3, Aristotle considers the definition “Thunder is the extinction of fire in the clouds”. He sees this as a compressed and rearranged form of this demonstration:
We can see the connection by considering the answers to two questions: “What is thunder?” “The extinction of fire in the clouds” (definition). “Why does it thunder?” “Because fire is extinguished in the clouds” (demonstration).
As with his criticisms of Division, Aristotle is arguing for the superiority of his own concept of science to the Platonic concept. Knowledge is composed of demonstrations, even if it may also include definitions; the method of science is demonstrative, even if it may also include the process of defining.
Aristotle often contrasts dialectical arguments with demonstrations. The difference, he tells us, is in the character of their premises, not in their logical structure: whether an argument is a sullogismos is only a matter of whether its conclusion results of necessity from its premises. The premises of demonstrations must be true and primary , that is, not only true but also prior to their conclusions in the way explained in the Posterior Analytics . The premises of dialectical deductions, by contrast, must be accepted ( endoxos ).
Recent scholars have proposed different interpretations of the term endoxos . Aristotle often uses this adjective as a substantive: ta endoxa , “accepted things”, “accepted opinions”. On one understanding, descended from the work of G. E. L. Owen and developed more fully by Jonathan Barnes and especially Terence Irwin, the endoxa are a compilation of views held by various people with some form or other of standing: “the views of fairly reflective people after some reflection”, in Irwin’s phrase. Dialectic is then simply “a method of argument from [the] common beliefs [held by these people]”. For Irwin, then, endoxa are “common beliefs”. Jonathan Barnes, noting that endoxa are opinions with a certain standing, translates with “reputable”.
My own view is that Aristotle’s texts support a somewhat different understanding. He also tells us that dialectical premises differ from demonstrative ones in that the former are questions , whereas the latter are assumptions or assertions : “the demonstrator does not ask, but takes”, he says. This fits most naturally with a view of dialectic as argument directed at another person by question and answer and consequently taking as premises that other person’s concessions. Anyone arguing in this manner will, in order to be successful, have to ask for premises which the interlocutor is liable to accept, and the best way to be successful at that is to have an inventory of acceptable premises, i.e., premises that are in fact acceptable to people of different types.
In fact, we can discern in the Topics (and the Rhetoric , which Aristotle says depends on the art explained in the Topics ) an art of dialectic for use in such arguments. My reconstruction of this art (which would not be accepted by all scholars) is as follows.
Given the above picture of dialectical argument, the dialectical art will consist of two elements. One will be a method for discovering premises from which a given conclusion follows, while the other will be a method for determining which premises a given interlocutor will be likely to concede. The first task is accomplished by developing a system for classifying premises according to their logical structure. We might expect Aristotle to avail himself here of the syllogistic, but in fact he develops quite another approach, one that seems less systematic and rests on various “common” terms. The second task is accomplished by developing lists of the premises which are acceptable to various types of interlocutor. Then, once one knows what sort of person one is dealing with, one can choose premises accordingly. Aristotle stresses that, as in all arts, the dialectician must study, not what is acceptable to this or that specific person, but what is acceptable to this or that type of person, just as the doctor studies what is healthful for different types of person: “art is of the universal”.
The method presented in the Topics for classifying arguments relies on the presence in the conclusion of certain “common” terms ( koina ) — common in the sense that they are not peculiar to any subject matter but may play a role in arguments about anything whatever. We find enumerations of arguments involving these terms in a similar order several times. Typically, they include:
The four types of opposites are the best represented. Each designates a type of term pair, i.e., a way two terms can be opposed to one another. Contraries are polar opposites or opposed extremes such as hot and cold, dry and wet, good and bad. A pair of contradictories consists of a term and its negation: good, not good. A possession (or condition) and privation are illustrated by sight and blindness. Relatives are relative terms in the modern sense: a pair consists of a term and its correlative, e.g. large and small, parent and child.
The argumentative patterns Aristotle associated with cases generally involve inferring a sentence containing adverbial or declined forms from another sentence containing different forms of the same word stem: “if what is useful is good, then what is done usefully is done well and the useful person is good”. In Hellenistic grammatical usage, ptôsis meant “case” (e.g. nominative, dative, accusative); Aristotle’s use here is obviously an early form of that.
Under the heading more and less and likewise , Aristotle groups a somewhat motley assortment of argument patterns all involving, in some way or other, the terms “more”, “less”, and “likewise”. Examples: “If whatever is \(A\) is \(B\), then whatever is more (less) \(A\) is more (less) \(B\)”; “If \(A\) is more likely \(B\) than \(C\) is, and \(A\) is not \(B\), then neither is \(C\)”; “If \(A\) is more likely than \(B\) and \(B\) is the case, then \(A\) is the case”.
At the heart of the Topics is a collection of what Aristotle calls topoi , “places” or “locations”. Unfortunately, though it is clear that he intends most of the Topics (Books II–VI) as a collection of these, he never explicitly defines this term. Interpreters have consequently disagreed considerably about just what a topos is. Discussions may be found in Brunschwig 1967, Slomkowski 1996, Primavesi 1997, and Smith 1997.
An art of dialectic will be useful wherever dialectical argument is useful. Aristotle mentions three such uses; each merits some comment.
First, there appears to have been a form of stylized argumentative exchange practiced in the Academy in Aristotle’s time. The main evidence for this is simply Aristotle’s Topics , especially Book VIII, which makes frequent reference to rule-governed procedures, apparently taking it for granted that the audience will understand them. In these exchanges, one participant took the role of answerer, the other the role of questioner. The answerer began by asserting some proposition (a thesis : “position” or “acceptance”). The questioner then asked questions of the answerer in an attempt to secure concessions from which a contradiction could be deduced: that is, to refute ( elenchein ) the answerer’s position. The questioner was limited to questions that could be answered by yes or no; generally, the answerer could only respond with yes or no, though in some cases answerers could object to the form of a question. Answerers might undertake to answer in accordance with the views of a particular type of person or a particular person (e.g. a famous philosopher), or they might answer according to their own beliefs. There appear to have been judges or scorekeepers for the process. Gymnastic dialectical contests were sometimes, as the name suggests, for the sake of exercise in developing argumentative skill, but they may also have been pursued as a part of a process of inquiry.
Aristotle also mentions an “art of making trial”, or a variety of dialectical argument that “puts to the test” (the Greek word is the adjective peirastikê , in the feminine: such expressions often designate arts or skills, e.g. rhêtorikê , “the art of rhetoric”). Its function is to examine the claims of those who say they have some knowledge, and it can be practiced by someone who does not possess the knowledge in question. The examination is a matter of refutation, based on the principle that whoever knows a subject must have consistent beliefs about it: so, if you can show me that my beliefs about something lead to a contradiction, then you have shown that I do not have knowledge about it.
This is strongly reminiscent of Socrates’ style of interrogation, from which it is almost certainly descended. In fact, Aristotle often indicates that dialectical argument is by nature refutative.
Dialectical refutation cannot of itself establish any proposition (except perhaps the proposition that some set of propositions is inconsistent). More to the point, though deducing a contradiction from my beliefs may show that they do not constitute knowledge, failure to deduce a contradiction from them is no proof that they are true. Not surprisingly, then, Aristotle often insists that “dialectic does not prove anything” and that the dialectical art is not some sort of universal knowledge.
In Topics I.2, however, Aristotle says that the art of dialectic is useful in connection with “the philosophical sciences”. One reason he gives for this follows closely on the refutative function: if we have subjected our opinions (and the opinions of our fellows, and of the wise) to a thorough refutative examination, we will be in a much better position to judge what is most likely true and false. In fact, we find just such a procedure at the start of many of Aristotle’s treatises: an enumeration of the opinions current about the subject together with a compilation of “puzzles” raised by these opinions. Aristotle has a special term for this kind of review: a diaporia , a “puzzling through”.
He adds a second use that is both more difficult to understand and more intriguing. The Posterior Analytics argues that if anything can be proved, then not everything that is known is known as a result of proof. What alternative means is there whereby the first principles of sciences are known? Aristotle’s own answer as found in Posterior Analytics II.19 is difficult to interpret, and recent philosophers have often found it unsatisfying since (as often construed) it appears to commit Aristotle to a form of apriorism or rationalism both indefensible in itself and not consonant with his own insistence on the indispensability of empirical inquiry in natural science.
Against this background, the following passage in Topics I.2 may have special importance:
It is also useful in connection with the first things concerning each of the sciences. For it is impossible to say anything about the science under consideration on the basis of its own principles, since the principles are first of all, and we must work our way through about these by means of what is generally accepted about each. But this is peculiar, or most proper, to dialectic: for since it is examinative with respect to the principles of all the sciences, it has a way to proceed.
A number of interpreters (beginning with Owen 1961) have built on this passage and others to find dialectic at the heart of Aristotle’s philosophical method. Further discussion of this issue would take us far beyond the subject of this article (the fullest development is in Irwin 1988; see also Nussbaum 1986 and Bolton 1990; for criticism, Hamlyn 1990, Smith 1997).
Aristotle says that rhetoric, i.e., the study of persuasive speech, is a “counterpart” ( antistrophos ) of dialectic and that the rhetorical art is a kind of “outgrowth” ( paraphues ti ) of dialectic and the study of character types. The correspondence with dialectical method is straightforward: rhetorical speeches, like dialectical arguments, seek to persuade others to accept certain conclusions on the basis of premises they already accept. Therefore, the same measures useful in dialectical contexts will, mutatis mutandis, be useful here: knowing what premises an audience of a given type is likely to believe, and knowing how to find premises from which the desired conclusion follows.
The Rhetoric does fit this general description: Aristotle includes both discussions of types of person or audience (with generalizations about what each type tends to believe) and a summary version (in II.23) of the argument patterns discussed in the Topics . For further discussion of his rhetoric see Aristotle’s rhetoric .
Demonstrations and dialectical arguments are both forms of valid argument, for Aristotle. However, he also studies what he calls contentious ( eristikos ) or sophistical arguments: these he defines as arguments which only apparently establish their conclusions. In fact, Aristotle defines these as apparent (but not genuine) dialectical sullogismoi . They may have this appearance in either of two ways:
Arguments of the first type in modern terms, appear to be valid but are really invalid. Arguments of the second type are at first more perplexing: given that acceptability is a matter of what people believe, it might seem that whatever appears to be endoxos must actually be endoxos . However, Aristotle probably has in mind arguments with premises that may at first glance seem to be acceptable but which, upon a moment’s reflection, we immediately realize we do not actually accept. Consider this example from Aristotle’s time:
This is transparently bad, but the problem is not that it is invalid: the problem is rather that the first premise, though superficially plausible, is false. In fact, anyone with a little ability to follow an argument will realize that at once upon seeing this very argument.
Aristotle’s study of sophistical arguments is contained in On Sophistical Refutations , which is actually a sort of appendix to the Topics .
To a remarkable extent, contemporary discussions of fallacies reproduce Aristotle’s own classifications. See Dorion 1995 for further discussion.
Two frequent themes of Aristotle’s account of science are (1) that the first principles of sciences are not demonstrable and (2) that there is no single universal science including all other sciences as its parts. “All things are not in a single genus”, he says, “and even if they were, all beings could not fall under the same principles” ( On Sophistical Refutations 11). Thus, it is exactly the universal applicability of dialectic that leads him to deny it the status of a science.
In Metaphysics IV (Γ), however, Aristotle takes what appears to be a different view. First, he argues that there is, in a way, a science that takes being as its genus (his name for it is “first philosophy”). Second, he argues that the principles of this science will be, in a way, the first principles of all (though he does not claim that the principles of other sciences can be demonstrated from them). Third, he identifies one of its first principles as the “most secure” of all principles: the principle of non-contradiction. As he states it,
It is impossible for the same thing to belong and not belong simultaneously to the same thing in the same respect ( Met. )
This is the most secure of all principles, Aristotle tells us, because “it is impossible to be in error about it”. Since it is a first principle, it cannot be demonstrated; those who think otherwise are “uneducated in analytics”. However, Aristotle then proceeds to give what he calls a “refutative demonstration” ( apodeixai elenktikôs ) of this principle.
Further discussion of this principle and Aristotle’s arguments concerning it belong to a treatment of his metaphysics (see Aristotle: Metaphysics ). However, it should be noted that: (1) these arguments draw on Aristotle’s views about logic to a greater extent than any treatise outside the logical works themselves; (2) in the logical works, the principle of non-contradiction is one of Aristotle’s favorite illustrations of the “common principles” ( koinai archai ) that underlie the art of dialectic.
See Aristotle’s Metaphysics , Aristotle on non-contradiction , Dancy 1975, and Code 1986 for further discussion.
The passage in Aristotle’s logical works which has received perhaps the most intense discussion in recent decades is On Interpretation 9, where Aristotle discusses the question whether every proposition about the future must be either true or false. Though something of a side issue in its context, the passage raises a problem of great importance to Aristotle’s near contemporaries (and perhaps contemporaries).
A contradiction ( antiphasis ) is a pair of propositions one of which asserts what the other denies. A major goal of On Interpretation is to discuss the thesis that, of every such contradiction, one member must be true and the other false. In the course of his discussion, Aristotle allows for some exceptions. One case is what he calls indefinite propositions such as “A man is walking”: nothing prevents both this proposition and “A man is not walking” being simultaneously true. This exception can be explained on relatively simple grounds.
A different exception arises for more complex reasons. Consider these two propositions:
It seems that exactly one of these must be true and the other false. But if (1) is now true, then there must be a sea-battle tomorrow, and there cannot fail to be a sea-battle tomorrow. The result, according to this puzzle, is that nothing is possible except what actually happens: there are no unactualized possibilities.
Such a conclusion is, as Aristotle is quick to note, a problem both for his own metaphysical views about potentialities and for the commonsense notion that some things are up to us. He therefore proposes another exception to the general thesis concerning contradictory pairs.
This much would probably be accepted by most interpreters. What the restriction is, however, and just what motivates it are matters of wide disagreement. It has been proposed, for instance, that Aristotle adopted, or at least flirted with, a three-valued logic for future propositions, or that he countenanced truth-value gaps, or that his solution includes still more abstruse reasoning. The literature is much too complex to summarize: see Anscombe, Hintikka, D. Frede, Whitaker, Waterlow.
Historically, at least, it is likely that Aristotle is responding to an argument originating with the Megarian philosophers. He ascribes the view that only that which happens is possible to the Megarians in Metaphysics IX (Θ). The puzzle with which he is concerned strongly recalls the “Master Argument” of Diodorus Cronus especially in certain further details. For instance, Aristotle imagines the statement about tomorrow’s sea battle having been uttered ten thousand years ago. If it was true, then its truth was a fact about the past; if the past is now unchangeable, then so is the truth value of that past utterance. This recalls the Master Argument’s premise that “what is past is necessary”. Diodorus Cronus was active a little after Aristotle, and he was certainly influenced by Megarian views, whether or not it is correct to call him a Megarian (David Sedley 1977 argues that he was instead a member of the Dialectical School which was in any event an offshoot of the Megarians; see Dorion 1995 and Döring 1989, Ebert 2008 and the article Dialectical School). It is therefore likely that Aristotle’s target here is some Megarian argument, perhaps a forerunner of Diodorus’ Master Argument.
How to cite this entry . Preview the PDF version of this entry at the Friends of the SEP Society . Look up topics and thinkers related to this entry at the Internet Philosophy Ontology Project (InPhO). Enhanced bibliography for this entry at PhilPapers , with links to its database.
[Please contact the author with suggestions.]
Aristotle, General Topics: aesthetics | Aristotle, General Topics: metaphysics | Aristotle, General Topics: rhetoric | Aristotle, Special Topics: mathematics | Aristotle, Special Topics: on non-contradiction | -->Chrysippus --> | Diodorus Cronus | future contingents | logic: ancient | logic: relevance | -->Megaric School --> | square of opposition | Stoicism
I am indebted to Alan Code, Marc Cohen, and Theodor Ebert for helpful criticisms of earlier versions of this article. I thank Franz Fritsche, Nikolai Biryukov, Ralph E. Kenyon, Johann Dirry, Ben Greenberg, Hasan Masoud, Marc Michael Hämmerling, James Whitely, and [email protected] for calling my attention to errors.
Copyright © 2022 by Robin Smith < rasmith @ tamu . edu >
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I'm looking for the word as stated by the title?
E.g. "Hey imagine if cats actually had 9 lives. Cats would have a bigger population than humans. "
"But they don't."
"I know but in the context that they actually did have 9 lives".
What word should replace in the context ? Basis,premise,conjecture??
It might be called assumption :
something taken for granted; a supposition: a correct assumption.
a proposition antecedently supposed or proved as a basis of argument or inference;
or presupposition :
presuppose : to require as an antecedent in logic or fact
2) - If you'd had [had had] more luck, you'd have been [would have been] rich [past perfect + past conditional]
In Logic , these examples are called: Hypothesis Contrary to Fact, counterfactual fallacy, speculative fallacy, "what if" fallacy. Please see the link. fallacy
At the bottom of the Wikipedia page, there is further consideration of these propositions (utterances or statements).
Contrary-to-Fact
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Since the first man walked this earth, we have been trying to understand why everything is the way it is. Why do things work the way they do? What happens if you put this with that? Humans have always been determined to learn and understand everything they can. As a result, the knowledge that beings have acquired and the patterns in subjects have come to be facts. These facts show the definite ways that objects, persons, and events function. After studying, one can determine results and learn to comprehend things that happen every day such as choices made and their outcomes.
But what if the alternative would have been selected? Can one identify what the outcome for that selection would have been? In other words, can we determine the “ifs” and “maybes” through the knowledge we have acquired? Hypothesis contrary to fact, the fallacy, questions claims made with certainty about what would have happened if a past event or condition would have been different from what is actually was. Fallacies are errors in logical reasoning, or when an arguments language is wrong or vague.
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However, many of these errors aren’t determined in the argument until they are analyzed because they appear to “look good”. There are numerous types of fallacies: informal fallacies, formal fallacies, fallacies of ambiguity, fallacies of presumption, and fallacies of relevance. There are ways to think about these fallacies: speculatively, analytically/critically, and normatively. Under hypothesis contrary to fact, hypothetical situations are treated as facts although it is a poorly supported claim.
An example of this fallacy is “If my dad hadn’t won the lottery ticket, my parents would have been divorced” or “If I had bitten into that jawbreaker, my tooth would have fallen out”. In both of these examples, an alternate outcome is being determined through supposition s through the use of prior knowledge and experience. For example, perhaps the person’s parents were fighting over financial issues and the lottery resolved their disputes. Also, the person possibly has already bitten into a jaw breaker and there tooth had fallen out.
These hypothetical situations are concluded through prior experiences but are they enough to assume what did not happen? Does one need to experience everything in order to understand? Regardless of how much knowledge one has it is impossible to determine what might have happened, however knowledge does help assess the possible outcomes and there likelihood of occurring through prior knowledge and experience. But one here can easily detect the fallacy’s inconsistency; there will never be enough evidence to see what may have happened because there is never any way of knowing.
A soccer athlete might argue that if he were to kick the ball he would score a goal because he’s never missed in his life but if he never shoots how can one really know if he would have made it? Maybe there was a strong breeze or maybe he tripped before kicking the ball or someone interfered with his shot. Yes, the soccer player probably wouldn’t miss the goal but there is no way of actually identifying if the statement is true hence why it is a speculative fallacy. Speculative fallacies are guesses or hypotheses. It deals with implications and the consequences of things such as “what are the consequences of thinking in a certain way”.
For example, hypothesis contrary to fact can often be misinterpreted in a situation or a person may be “misjudged” for its use which may lead to serious consequences. Max might say about his enemy “if he would have touched me I would have killed him”. This could be misinterpreted in two ways; one, in a literal sense and people would be concerned, or two that he is an aggressive person. However, this is usually not the case. Like all other fallacies, hypothesis contrary to fact is taken lightly and can be “innocent fun”.
One usually uses it when teasing someone else saying “if you had one more cookie you would have exploded” or “if you had a few more drinks he would have been good looking”. It is often used by people because it is a different form of expressing what they are trying to convey. Sometimes it is used to help exaggerate a situation such as the cookies one or the drinks one for a sense of humor. These fallacies are usually not taken literally and become a form of expressing themselves for the person using them by asserting what would have happened if what had happened had not happened.
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Cause to the contrary defective notice.
The first circumstances where the aggrieved person can say that the chargee fails to meet the conditions to seek the order for sale is when the statutory notice of demand served was defective or improper. The notice can be said to be defective when the chargee included default interest which was more than the prescribed
Animal welfare
Norman led Jennie into the laboratory and had her sit on a metal table near the windows. She sat quietly while Norman fitted her with a helmet containing electrial monitors and couplings for attaching the helmet to other devices. She was watching people walking across the lawn. When Norman finished, she had to lie down
Critical Thinking Skills
Yes, it is true that the fallacy of complex question is one of the fallacies of presumption. Complex question is also known as many questions, loaded question or presupposition. Complex question is firstly logical fallacy belonging to the fallacy of presumption. This fallacy is committed when a person asks a question presupposing something unproven and
Common sense
One would thin that as we become more sophisticated in our technology, we would also become more sophisticated in our thinking. This is not really the case, and our everyday life reflects this fact, in looking at critical thinking and arguments in daily life. In this essay we will examine three fallacies that exist
It is likely that some would read Max Schulman’s essay entitled “Love Is a Fallacy,” and view it as ‘anti-women. ’ Others would be just as likely to see it as ‘anti-men. ’ Objectively speaking, neither view is entirely correct. This is because, equally strong arguments can be made for both cases. A more accurate conclusion
The idea of a man's desire is both fascinating and powerful, particularly in car industry advertisements. Whether in magazines or on television, we are exposed to ads promoting various products and services. Companies often employ fallacies to influence people's decision-making, making it challenging to discern the creator's intended message. Fallacy in advertisement can be an effective
Unreliable Narrator From the perspective of how figures of speech help to characterize in Love is a Fallacy An unreliable narrator is a narrator whose credibility has been seriouly compromised in fictions (as implemented in literature, film, theatre, etc). It is a narrator whose account of events appears to be faulty, misleadingly biased, or otherwise
American Dream
The American dream that one can become something from nothing is the main reason why America is the fastest growing country. It is often seen as a melting pot encompassing many different religions and nationalities. People move to America with dreams of becoming wealthy, but many of the ideologies that have existed within the country
Critical Thinking
Chapter 1: The Science of Psychology Chapter one of our text begins by discussing psuedoscience, or as the authors call it "psychobabble". Basically they discuss how it is common that people are often misled by false psychology in our culture and quite often in the media. The authors compare and contrast true psychological practices with psuedopsychology,
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Real World Examples. 1. Sports Scenario: Imagine a basketball fan saying, "If Michael Jordan had not retired in 1993, the Chicago Bulls would have won eight consecutive NBA championships instead of six." This statement is an example of a hypothesis contrary to fact. It assumes a hypothetical scenario where Jordan didn't retire and then predicts ...
Everybody Should Exercise. "' Dicto Simpliciter means an argument based on an unqualified generalization. For example: 'Exercise is good. Therefore everybody should exercise.'. "'I agree,' said Polly earnestly. 'I mean exercise is wonderful. I mean it builds the body and everything.'. "'Polly,' I said gently. 'The argument is a fallacy.
The fallacy of Hypothesis Contrary to Fact appears to follow the same general pattern of reasoning, but it does not. In the fallacy of Hypothesis Contrary to Fact, the conclusion is a hypothetical statement, while the premiss is a statement of fact. We are inferring a connection between an antecendent and a consequent from the fact stated in ...
Here in this article, we will learn about the examples of logical fallacies that we may face in our daily life. Fallacy Examples in Real Life. 1. The Straw Man Fallacy. Example of the Straw-man Fallacy. 2. The Ad Hominem Fallacy. Example of Ad Hominem Fallacy. 3.
Here are common fallacies of relevance: 1. Ad hominem attack. An ad hominem, or personal, attack is a form of rhetoric that criticizes or praises the person making an argument instead of the actual argument. It tries to reason that someone's claim is factual or wrong based on the person's reputation instead of the facts they present.
For example, the claim, "If only you had learned how to play the piano as a child, you would be a concert pianist today" is untenable; there's no way to guarantee that they would have continued playing throughout their life, have the talent and skill to perform at a professional level, or would not suffer a serious injury that would ...
Hypothesis Contrary to Fact- arguing from something that might have happened, but didn't ... Not necessarily an exact example of this fallacy, but it does show that interviewers can manipulate ... fire him because his life will be terrible and he won't be able to get another job, it's a fallacy. The fact is
Perhaps the listener had an abusive home-life or school-life, suffered from a chemical imbalance leading to depression and paranoia, or made a bad choice in his companions. ... Hypothesis Contrary to Fact ... but it is simply useless when it comes to actually proving anything about the real world. A common example is the idea that one "owes ...
Definition and explanation. Counterfactual reasoning means thinking about alternative possibilities for past or future events: what might happen/ have happened if…? In other words, you imagine the consequences of something that is contrary to what actually happened or will have happened ("counter to the facts"). For instance, "if Lee Harvey ...
Alternative names []. argumentum ad speculum; hypothesis contrary to fact "what if" wouldchuck; Form [] P1: A causes B. P2: A is true. C1: Therefore, B is true. C2 (fallacious): Therefore, if-counterfactual A was false, then-counterfactual B would be false. Or even more egregiously: P1: A is true. P2: B is true. C: Therefore, if-counterfactual A was false, then-counterfactual B would be false.
This entry will follow this widely used terminology to avoid confusion. However, this usage also promotes a confusion worth dispelling. Counterfactuals are not really conditionals with contrary-to-fact antecedents. For example can be used as part of an argument that the antecedent is true (Anderson 1951): (2)
(This claim dismisses opposition by saying poverty is just a fact of life.) Broad generalizations take some cases and apply them to every case. A similar fallacy is the hasty conclusion, which leaps over intervening steps of logic. The news is full of cases of husbands abusing wives. All domestic violence is committed by men.
What's the Difference Between a Fact, a Hypothesis ...
Hypothesis contrary to fact (argumentum ad speculum): asserting that, if hypothetically X had occurred, Y would have been the result. Sunk cost fallacy: continuing with a task or project because of what has been invested already, without considering the future costs of continuing and the diminishing benefits; See also references on logical ...
Hypothesis Contrary to Fact. A Hypothesis Contrary to Fact is, simply, speculation without concrete evidence. It is an argument that, under different circumstances or historical events, the present or the future would certainly look a certain way. For example, "if you had gotten a job in finance, you'd be making loads of money right now."
False Analogy: the two objects or events being compared are relevantly dissimilar. Slothful Induction: the conclusion of a strong inductive argument is denied despite the evidence to the contrary. Fallacy of Exclusion: evidence which would change the outcome of an inductive argument is excluded from consideration.
Definition. The term "counterfactual" was coined by philosopher Nelson Goodman (1947) to capture Roderick Chisholm's more convoluted locution "contrary-to-fact" (Chisholm 1946). "Counterfactual" was initially used in reference to conditional statements with false antecedents such as "If kangaroos had no tails, they would topple ...
Both situations are imaginary. Neither one is a fact. A past hypothetical situation (imaginary, did not happen, or is contrary to fact) influences a present or future hypothetical situation. This is actually a combination of a Class Three Conditional and a Class Two Conditional. Form: If + past perfect tense, would or could + verb stem. Examples:
Hypothesis Contrary to Fact Fallacy by Olivia Ingram on Prezi. Blog. Aug. 21, 2024. Creating engaging teacher presentations: tips, ideas, and tools. Aug. 20, 2024. How to use AI in the classroom. July 25, 2024. Sales pitch presentation: creating impact with Prezi.
5. The Syllogistic. Aristotle's most famous achievement as logician is his theory of inference, traditionally called the syllogistic (though not by Aristotle). That theory is in fact the theory of inferences of a very specific sort: inferences with two premises, each of which is a categorical sentence, having exactly one term in common, and having as conclusion a categorical sentence the ...
In Grammar, this is an IF-clause used in a condition contrary to fact: There are two basic cases:. 1) - If you had lots of money, you would be rich. [simple past + conditional] - If you were sane, you would not do that. [please not: were in the first or third person singular is called "subjunctive" here in English]
Under hypothesis contrary to fact, hypothetical situations are treated as facts although it is a poorly supported claim. An example of this fallacy is "If my dad hadn't won the lottery ticket, my parents would have been divorced" or "If I had bitten into that jawbreaker, my tooth would have fallen out". In both of these examples, an ...