problem solving vs theory

IR Theory: Problem-Solving Theory Versus Critical Theory?

Robert Cox began his canonical 1981 essay “Social Forces, States and World Orders: Beyond International Relations Theory” with the observation that it is “necessary and practical” for academic disciplines to “divide up the seamless web of the real social world”. We make these divisions, Cox wrote, in order to analyse the world and thus to produce practical knowledge of that world. It is not a stretch to suggest that the real social world of International Relations scholarship might also be approached as worthy of analysis and theory. Indeed, reflection on International Relations as theory appears in the field as part of the necessary and practical division of the complexity of the social and political world. Rare is the introduction to IR textbook that does not emphasize, and usually begin with, the “great (theoretical) debates” that have structured the field since it emerged as an academic discipline.

Thus theory itself has long and often been treated as an object for theoretical reflection in International Relations. Recently, we could point to both the founding of a specific section of the US-based International Studies Association dedicated to Theory – indeed, this section honoured Professor Cox at the ISA convention in Toronto in 2014 – as well as the special issue in September 2013 of the European Journal of International Relations on “ The End of IR Theory? ”, accompanied by a wide-ranging discussion of the papers collected there in the Duck of Minerva blog.

For some of the contributors to the special issue and to the debates on the symposium – and I hope I can be forgiven for making an impressionistic observation rather than an analytical one – it seems that the question mark at the end of “the end of IR theory?” was a sign of fatigue rather than a sense that the debates over theory needed to be renewed. Fatigue, in the sense of “are we still having this conversation?” or “haven’t we moved on yet?” Emblematic of this fatigue were the reflections of Professor Chris Brown in both his article in the EJIR and his contribution to the symposium . It’s not that Brown is hostile to theory; on the contrary, his contribution was a complaint that the critical theories that emerged in the 1980s had not fulfilled their potential and that problem-solving theory had contributed much more.

I disagree with his assessment of the status of critical theory, as do many of the contributors to the special issue and to the symposium, in particular with his claim that it has failed to live up to the promise it showed in the 1980s – but that’s a conversation for another time. What is most interesting here is how Brown takes up Cox’s analytical division of “critical theory” from “problem-solving theory”. Indeed, the trope of problem-solving versus critical theory is asserted quite often in discussions of the status of theory in IR: for example, in A. C. McKeil ; in Robert W. Murray ; or in Ali Diskaya , just to take a few examples appearing here in e-IR. It is this trope, along with Cox’s other oft-cited claim in the 1981 Millennium article that “theory is always for someone and for some purpose” (Cox 1981: 129) that have made his article canonical. Indeed, Cox’s categories of “critical” and “problem-solving” are now part of the very common-sense ordering of theory in IR.

It is therefore important to consider what Cox actually said about these categories. Problem-solving theory, first, “takes the world as it finds it, with the prevailing social and power relationships and the institutions into which they are organised, as the given framework for action. The general aim of problem-solving is to make these relationships and institutions work smoothly by dealing effectively with particular sources of trouble” (Cox 1981, 128-129). This definition, remember, follows Cox’s opening statements in the article about the importance of theory for the production of practical knowledge. Cox is often interpreted as elevating critical theory over problem solving theory – Brown takes him to do so, for example, in the symposium when he says Cox “compared ‘problem-solving’ theory unfavourably with ‘critical theory’” but I am not convinced that a careful reading of Cox’s article supports this (and Cox argues something similar ). In addition to signalling the importance of theory for practical knowledge, Cox explicitly notes, for example, how the analytical procedures he sees as defining problem-solving theory are the source of its strength. He takes issue with the idea that problem-solving theory is value-free and asserts that it is conservative (Cox 1981: 129-130) but this is as close to a normative assessment of problem-solving theory as Cox gets.

Critical theory, in contrast, is holistic where problem-solving theory is analytic. It “does not take institutions and social and power relations for granted but calls them into question by concerning itself with their origins and how and whether they might be in the process of changing. … Critical theory is directed to the social and political complex as a whole rather than to the separate parts” (Cox 1981: 129). Cox also allows that where problem-solving theory might be seen as conservative, critical theory might be seen as utopian: “Its aims are just as practical as those of problem-solving theory, but it approaches practice from a perspective with transcends that of the existing order. … Critical theory allows for a normative choice in favour of a social and political order different from the prevailing order, but it limits the range of choice to alternative orders which are feasible transformations of the existing world” (Cox 1981: 130).

I suspect that it is this holistic and utopian range for critical theory as asserted by Cox that leads Brown to identify critical theory with Quentin Skinner’s notion of Grand Theory and leads so many of the rest of us to assume that critical theory is posited as a superior theoretical approach to problem-solving theory. I’ve tried to show that Cox, at least, makes no explicit claims to that effect. Nevertheless, the categories Cox bequeathed to us seem to encourage us to turn this binary, critical versus problem-solving theory, into a hierarchy. Readers of International Relations theory instinctively want to read it as political theory – though as Rob Walker might remind us, this does not make us careful readers of political theory either. Perhaps we need to acknowledge that the theoretical choice presented by the binary critical theory-problem-solving theory is, at least, theory as engaged in a political contest.

Should Cox’s categories be preserved, critiqued, or abandoned? Would doing so lend a clearer (and practical) view of theory in the field? One way to extend the engagement with the practice of theory would be to read Cox’s categories alongside the other famous definition of critical theory, in Max Horkheimer’s essay “Traditional and Critical Theory” (Horkheimer 2014 [1937]). Though Cox did not explicitly cite Horkheimer, the latter’s efforts to distinguish critical theory from what he called “traditional theory” make him an obvious interlocutor. (There are, of course, many other serious contributions to the effort to situate theory socially and politically, from Bourdieu to Foucault, from Bruno Latour to Walter Mignolo. Many of these efforts are considered in the EJIR special issue and the Duck of Minerva symposium.) I focus on Horkheimer here in part due to the clear affinities between his approach and Cox’s and in part because Horkheimer, like Cox and as I would like to do, provides an explicit defence of the enterprise of critical theory.

While the scale of Horkheimer’s critique, engaged as he was with theory per se , is much grander than the stage Cox builds when he focuses on IR theory in the 1981 article, their accounts of “traditional” and “problem-solving” theory are remarkably similar. Cox notes how the power of problem-solving theory stems from its methodological “fixing” of the social and institutional parameters surrounding the variables it examines. For Horkheimer, this method, rooted in Descartes and predominant not only in social sciences but in science generally in his time, stems from the ability of the scholar to abstract him or herself from these social and institutional parameters in the production of theories and analyses. In other words, just as in any production process where a division of labour separates the subjective functions of planning, designing, interpreting, and analysing from the executive functions, traditional theory renders the world under study as objective and passive and the scientist an active, analysing subject.

In their conceptualisations of critical theory, however, Cox and Horkheimer differ slightly but in an important way. While both are concerned to defend theory as an approach to a dynamic and interconnected totality, Cox does not foreground the status of the theorist, while for Horkheimer the critical theorist must engage with theory as a productive process. Cox does take neorealism to task for neglecting the production process in the constitution of national interest (Cox 1981: 134-135) but Horkheimer goes further: it is not a matter of adding another parameter or variable to the theoretical enterprise; it is a matter of understanding the theoretical enterprise itself in relation to and as a part of a general production process and division of labour. When Cox wrote in 1981, the prevailing epistemology in IR and the epistemological commitment of problem-solving or traditional theory was realist: the world exists independently of our thoughts about it and the task of theory is to make thought adequate to reality. What Horkheimer shows is that there is no neat division between thought and reality that can justify the privileged position of the theorist in the social division of labour: our thoughts are part of reality, as real as the city you live in or the job you work at and they must be analysed as part of the general social division of labour and of social reproduction.

Thus the problem-solving theorist becomes a functionary in the maintenance of social order. The critical theorist must understand the role of theory in social reproduction in order to break down the divisions between theoretical reflection and the making of the world.

I am not suggesting that Horkheimer was right where Cox was wrong. Cox was certainly aware of the – explicit or implicit – political commitments of the theorist when he said, “theory is always for someone and for some purpose”. The question for me here is whether our common-sense taxonomy of International Relations theory as “problem-solving” or “critical” remains appropriate. Given how embedded it is in our ways of seeing ourselves and our field, and given that it can be quite useful for teaching theory, I don’t think it should necessarily be abandoned. Given the implicit, instinctual way IR theorists tend to treat the division as a contest, as in Chris Brown for whom problem-solving has produced better results than critical theory, I wonder if it would not be better to try to make the political stakes of that contest more evident.

For me, reading Cox with Horkheimer provides an interesting start on this task. The description of the first category as “problem-solving” or “traditional” points to a theoretical practice where expertise rules, where specialists take up their specific tasks and succeed or fail on the basis of how powerful their explanations are and the impact of their work. Cox and Horkheimer both acknowledge the importance of this approach in terms of method and results. And they both hint at the cost: politically, we might better describe this approach as technocratic theory . The enterprise is to uncover the timeless essences of things and relations and to keep things working by keeping them in their place.

The contrasting approach to theory, which Cox and Horkheimer both dub “critical theory”, seeks instead to enable the transformation of things. But critical theory is more than this, too; after all, as social constructivism suggests, the transformation of things is just the normal state of affairs as people make themselves and make their history. Critical theory does more: it disagrees . As Rancière suggests, it disrupts the order of the “distribution of the sensible.” Critical theory works by making visible the relationships and the things that International Relations refuses to recognise and qualify as relationships or things. It makes audible the voices of people not qualified to speak in International Relations. Against the technocratic barriers to international living and understandings, critical theory identifies the arbitrariness and artificiality of barriers and explains them in relation to their roles in the division of labour, social reproduction, or system maintenance. Politically, critical theory must be democratic theory – not a theory of democracy, posed externally to its object, but a theory that is democratic in its everyday practices. These are the political stakes in our theoretical choices.

Further Reading on E-International Relations

• Alienation and Marxism: An Alternative Starting Point for Critical IR Theory 
• The ‘Failure of Critical Theory’ as an Ideological Discourse
• Reflections on Critical Theory and Process Sociology
• Introducing Critical Theory in International Relations
• Why Is There No Minor International Theory?
• Rethinking Critical IR: Towards a Plurilogue of Cosmologies

Matt Davies lectures in International Political Economy at Newcastle University and is the Degree Programme Director for the MA in World Politics and Popular Culture . He is also a co-editor of the Popular Culture and World Politics book series , published by Routledge.

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In This Article Expand or collapse the "in this article" section Problem Solving and Decision Making

Introduction.

• General Approaches to Problem Solving
• Representational Accounts
• Problem Space and Search
• Working Memory and Problem Solving
• Domain-Specific Problem Solving
• The Rational Approach
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Problem Solving and Decision Making by Emily G. Nielsen , John Paul Minda LAST REVIEWED: 26 June 2019 LAST MODIFIED: 26 June 2019 DOI: 10.1093/obo/9780199828340-0246

Problem solving and decision making are both examples of complex, higher-order thinking. Both involve the assessment of the environment, the involvement of working memory or short-term memory, reliance on long term memory, effects of knowledge, and the application of heuristics to complete a behavior. A problem can be defined as an impasse or gap between a current state and a desired goal state. Problem solving is the set of cognitive operations that a person engages in to change the current state, to go beyond the impasse, and achieve a desired outcome. Problem solving involves the mental representation of the problem state and the manipulation of this representation in order to move closer to the goal. Problems can vary in complexity, abstraction, and how well defined (or not) the initial state and the goal state are. Research has generally approached problem solving by examining the behaviors and cognitive processes involved, and some work has examined problem solving using computational processes as well. Decision making is the process of selecting and choosing one action or behavior out of several alternatives. Like problem solving, decision making involves the coordination of memories and executive resources. Research on decision making has paid particular attention to the cognitive biases that account for suboptimal decisions and decisions that deviate from rationality. The current bibliography first outlines some general resources on the psychology of problem solving and decision making before examining each of these topics in detail. Specifically, this review covers cognitive, neuroscientific, and computational approaches to problem solving, as well as decision making models and cognitive heuristics and biases.

General Overviews

Current research in the area of problem solving and decision making is published in both general and specialized scientific journals. Theoretical and scholarly work is often summarized and developed in full-length books and chapter. These may focus on the subfields of problem solving and decision making or the larger field of thinking and higher-order cognition.

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Overview of the Problem-Solving Mental Process

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

• Identify the Problem
• Define the Problem
• Form a Strategy
• Organize Information
• Allocate Resources
• Monitor Progress
• Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

• Asking questions about the problem
• Breaking the problem down into smaller pieces
• Looking at the problem from different perspectives
• Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

• Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
• Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell​

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

Get Advice From The Verywell Mind Podcast

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You can become a better problem solving by:

• Practicing brainstorming and coming up with multiple potential solutions to problems
• Being open-minded and considering all possible options before making a decision
• Breaking down problems into smaller, more manageable pieces
• Asking for help when needed
• Researching different problem-solving techniques and trying out new ones
• Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors.  The Psychology of Problem Solving .  Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving .  Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

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Critical thinking and problem-solving, jump to: , what is critical thinking, characteristics of critical thinking, why teach critical thinking.

• Teaching Strategies to Help Promote Critical Thinking Skills

References and Resources

When examining the vast literature on critical thinking, various definitions of critical thinking emerge. Here are some samples:

• "Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action" (Scriven, 1996).
• "Most formal definitions characterize critical thinking as the intentional application of rational, higher order thinking skills, such as analysis, synthesis, problem recognition and problem solving, inference, and evaluation" (Angelo, 1995, p. 6).
• "Critical thinking is thinking that assesses itself" (Center for Critical Thinking, 1996b).
• "Critical thinking is the ability to think about one's thinking in such a way as 1. To recognize its strengths and weaknesses and, as a result, 2. To recast the thinking in improved form" (Center for Critical Thinking, 1996c).

Perhaps the simplest definition is offered by Beyer (1995) : "Critical thinking... means making reasoned judgments" (p. 8). Basically, Beyer sees critical thinking as using criteria to judge the quality of something, from cooking to a conclusion of a research paper. In essence, critical thinking is a disciplined manner of thought that a person uses to assess the validity of something (statements, news stories, arguments, research, etc.).

Back        

Wade (1995) identifies eight characteristics of critical thinking. Critical thinking involves asking questions, defining a problem, examining evidence, analyzing assumptions and biases, avoiding emotional reasoning, avoiding oversimplification, considering other interpretations, and tolerating ambiguity. Dealing with ambiguity is also seen by Strohm & Baukus (1995) as an essential part of critical thinking, "Ambiguity and doubt serve a critical-thinking function and are a necessary and even a productive part of the process" (p. 56).

Another characteristic of critical thinking identified by many sources is metacognition. Metacognition is thinking about one's own thinking. More specifically, "metacognition is being aware of one's thinking as one performs specific tasks and then using this awareness to control what one is doing" (Jones & Ratcliff, 1993, p. 10 ).

In the book, Critical Thinking, Beyer elaborately explains what he sees as essential aspects of critical thinking. These are:

• Dispositions: Critical thinkers are skeptical, open-minded, value fair-mindedness, respect evidence and reasoning, respect clarity and precision, look at different points of view, and will change positions when reason leads them to do so.
• Criteria: To think critically, must apply criteria. Need to have conditions that must be met for something to be judged as believable. Although the argument can be made that each subject area has different criteria, some standards apply to all subjects. "... an assertion must... be based on relevant, accurate facts; based on credible sources; precise; unbiased; free from logical fallacies; logically consistent; and strongly reasoned" (p. 12).
• Argument: Is a statement or proposition with supporting evidence. Critical thinking involves identifying, evaluating, and constructing arguments.
• Reasoning: The ability to infer a conclusion from one or multiple premises. To do so requires examining logical relationships among statements or data.
• Point of View: The way one views the world, which shapes one's construction of meaning. In a search for understanding, critical thinkers view phenomena from many different points of view.
• Procedures for Applying Criteria: Other types of thinking use a general procedure. Critical thinking makes use of many procedures. These procedures include asking questions, making judgments, and identifying assumptions.

Oliver & Utermohlen (1995) see students as too often being passive receptors of information. Through technology, the amount of information available today is massive. This information explosion is likely to continue in the future. Students need a guide to weed through the information and not just passively accept it. Students need to "develop and effectively apply critical thinking skills to their academic studies, to the complex problems that they will face, and to the critical choices they will be forced to make as a result of the information explosion and other rapid technological changes" (Oliver & Utermohlen, p. 1 ).

As mentioned in the section, Characteristics of Critical Thinking , critical thinking involves questioning. It is important to teach students how to ask good questions, to think critically, in order to continue the advancement of the very fields we are teaching. "Every field stays alive only to the extent that fresh questions are generated and taken seriously" (Center for Critical Thinking, 1996a ).

Beyer sees the teaching of critical thinking as important to the very state of our nation. He argues that to live successfully in a democracy, people must be able to think critically in order to make sound decisions about personal and civic affairs. If students learn to think critically, then they can use good thinking as the guide by which they live their lives.

Teaching Strategies to Help Promote Critical Thinking

The 1995, Volume 22, issue 1, of the journal, Teaching of Psychology , is devoted to the teaching critical thinking. Most of the strategies included in this section come from the various articles that compose this issue.

• CATS (Classroom Assessment Techniques): Angelo stresses the use of ongoing classroom assessment as a way to monitor and facilitate students' critical thinking. An example of a CAT is to ask students to write a "Minute Paper" responding to questions such as "What was the most important thing you learned in today's class? What question related to this session remains uppermost in your mind?" The teacher selects some of the papers and prepares responses for the next class meeting.
• Cooperative Learning Strategies: Cooper (1995) argues that putting students in group learning situations is the best way to foster critical thinking. "In properly structured cooperative learning environments, students perform more of the active, critical thinking with continuous support and feedback from other students and the teacher" (p. 8).
• Case Study /Discussion Method: McDade (1995) describes this method as the teacher presenting a case (or story) to the class without a conclusion. Using prepared questions, the teacher then leads students through a discussion, allowing students to construct a conclusion for the case.
• Using Questions: King (1995) identifies ways of using questions in the classroom:
• Reciprocal Peer Questioning: Following lecture, the teacher displays a list of question stems (such as, "What are the strengths and weaknesses of...). Students must write questions about the lecture material. In small groups, the students ask each other the questions. Then, the whole class discusses some of the questions from each small group.
• Reader's Questions: Require students to write questions on assigned reading and turn them in at the beginning of class. Select a few of the questions as the impetus for class discussion.
• Conference Style Learning: The teacher does not "teach" the class in the sense of lecturing. The teacher is a facilitator of a conference. Students must thoroughly read all required material before class. Assigned readings should be in the zone of proximal development. That is, readings should be able to be understood by students, but also challenging. The class consists of the students asking questions of each other and discussing these questions. The teacher does not remain passive, but rather, helps "direct and mold discussions by posing strategic questions and helping students build on each others' ideas" (Underwood & Wald, 1995, p. 18 ).
• Use Writing Assignments: Wade sees the use of writing as fundamental to developing critical thinking skills. "With written assignments, an instructor can encourage the development of dialectic reasoning by requiring students to argue both [or more] sides of an issue" (p. 24).
• Written dialogues: Give students written dialogues to analyze. In small groups, students must identify the different viewpoints of each participant in the dialogue. Must look for biases, presence or exclusion of important evidence, alternative interpretations, misstatement of facts, and errors in reasoning. Each group must decide which view is the most reasonable. After coming to a conclusion, each group acts out their dialogue and explains their analysis of it.
• Spontaneous Group Dialogue: One group of students are assigned roles to play in a discussion (such as leader, information giver, opinion seeker, and disagreer). Four observer groups are formed with the functions of determining what roles are being played by whom, identifying biases and errors in thinking, evaluating reasoning skills, and examining ethical implications of the content.
• Ambiguity: Strohm & Baukus advocate producing much ambiguity in the classroom. Don't give students clear cut material. Give them conflicting information that they must think their way through.
• Angelo, T. A. (1995). Beginning the dialogue: Thoughts on promoting critical thinking: Classroom assessment for critical thinking. Teaching of Psychology, 22(1), 6-7.
• Beyer, B. K. (1995). Critical thinking. Bloomington, IN: Phi Delta Kappa Educational Foundation.
• Center for Critical Thinking (1996a). The role of questions in thinking, teaching, and learning. [On-line]. Available HTTP: http://www.criticalthinking.org/University/univlibrary/library.nclk
• Center for Critical Thinking (1996b). Structures for student self-assessment. [On-line]. Available HTTP: http://www.criticalthinking.org/University/univclass/trc.nclk
• Center for Critical Thinking (1996c). Three definitions of critical thinking [On-line]. Available HTTP: http://www.criticalthinking.org/University/univlibrary/library.nclk
• Cooper, J. L. (1995). Cooperative learning and critical thinking. Teaching of Psychology, 22(1), 7-8.
• Jones, E. A. & Ratcliff, G. (1993). Critical thinking skills for college students. National Center on Postsecondary Teaching, Learning, and Assessment, University Park, PA. (Eric Document Reproduction Services No. ED 358 772)
• King, A. (1995). Designing the instructional process to enhance critical thinking across the curriculum: Inquiring minds really do want to know: Using questioning to teach critical thinking. Teaching of Psychology, 22 (1) , 13-17.
• McDade, S. A. (1995). Case study pedagogy to advance critical thinking. Teaching Psychology, 22(1), 9-10.
• Oliver, H. & Utermohlen, R. (1995). An innovative teaching strategy: Using critical thinking to give students a guide to the future.(Eric Document Reproduction Services No. 389 702)
• Robertson, J. F. & Rane-Szostak, D. (1996). Using dialogues to develop critical thinking skills: A practical approach. Journal of Adolescent & Adult Literacy, 39(7), 552-556.
• Scriven, M. & Paul, R. (1996). Defining critical thinking: A draft statement for the National Council for Excellence in Critical Thinking. [On-line]. Available HTTP: http://www.criticalthinking.org/University/univlibrary/library.nclk
• Strohm, S. M., & Baukus, R. A. (1995). Strategies for fostering critical thinking skills. Journalism and Mass Communication Educator, 50 (1), 55-62.
• Underwood, M. K., & Wald, R. L. (1995). Conference-style learning: A method for fostering critical thinking with heart. Teaching Psychology, 22(1), 17-21.
• Wade, C. (1995). Using writing to develop and assess critical thinking. Teaching of Psychology, 22(1), 24-28.

Other Reading

• Bean, J. C. (1996). Engaging ideas: The professor's guide to integrating writing, critical thinking, & active learning in the classroom. Jossey-Bass.
• Bernstein, D. A. (1995). A negotiation model for teaching critical thinking. Teaching of Psychology, 22(1), 22-24.
• Carlson, E. R. (1995). Evaluating the credibility of sources. A missing link in the teaching of critical thinking. Teaching of Psychology, 22(1), 39-41.
• Facione, P. A., Sanchez, C. A., Facione, N. C., & Gainen, J. (1995). The disposition toward critical thinking. The Journal of General Education, 44(1), 1-25.
• Halpern, D. F., & Nummedal, S. G. (1995). Closing thoughts about helping students improve how they think. Teaching of Psychology, 22(1), 82-83.
• Isbell, D. (1995). Teaching writing and research as inseparable: A faculty-librarian teaching team. Reference Services Review, 23(4), 51-62.
• Jones, J. M. & Safrit, R. D. (1994). Developing critical thinking skills in adult learners through innovative distance learning. Paper presented at the International Conference on the practice of adult education and social development. Jinan, China. (Eric Document Reproduction Services No. ED 373 159)
• Sanchez, M. A. (1995). Using critical-thinking principles as a guide to college-level instruction. Teaching of Psychology, 22(1), 72-74.
• Spicer, K. L. & Hanks, W. E. (1995). Multiple measures of critical thinking skills and predisposition in assessment of critical thinking. Paper presented at the annual meeting of the Speech Communication Association, San Antonio, TX. (Eric Document Reproduction Services No. ED 391 185)
• Terenzini, P. T., Springer, L., Pascarella, E. T., & Nora, A. (1995). Influences affecting the development of students' critical thinking skills. Research in Higher Education, 36(1), 23-39.

On the Internet

• Carr, K. S. (1990). How can we teach critical thinking. Eric Digest. [On-line]. Available HTTP: http://ericps.ed.uiuc.edu/eece/pubs/digests/1990/carr90.html
• The Center for Critical Thinking (1996). Home Page. Available HTTP: http://www.criticalthinking.org/University/
• Ennis, Bob (No date). Critical thinking. [On-line], April 4, 1997. Available HTTP: http://www.cof.orst.edu/cof/teach/for442/ct.htm
• Montclair State University (1995). Curriculum resource center. Critical thinking resources: An annotated bibliography. [On-line]. Available HTTP: http://www.montclair.edu/Pages/CRC/Bibliographies/CriticalThinking.html
• No author, No date. Critical Thinking is ... [On-line], April 4, 1997. Available HTTP: http://library.usask.ca/ustudy/critical/
• Sheridan, Marcia (No date). Internet education topics hotlink page. [On-line], April 4, 1997. Available HTTP: http://sun1.iusb.edu/~msherida/topics/critical.html

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Theory vs problems in modern math

Quick background: I'm a fourth year undergraduate entering graduate school next year. I am trying to identify areas of mathematical research in which there tends to be more emphasis on developing new theory as opposed to solving problems which can be formulated in terms of established theory.

Let me give two examples:

(Example 1) Suppose an analyst wants to study a particular PDE. In most cases, the PDE (which probably arose from phsyics or geometry) has been known for a long time. Moreover, the function spaces ($L^2, H^2,$ ect) which are usually used in formulating PDE problems have also been defined for the better part of a century. Now, there is a gigantic amount of room for innovation in modern PDE theory for developing new techniques . However, the basic questions (well posedness, unique continuation, ect) would have been intelligible sixty years ago.

(Example 2) A huge area of research in modern topology is the study of smooth 4-manifolds. The holy grail is the smooth 4-d Poincaré conjecture. Here again, there are incredibly sophisticated and beautiful tools being developed to answer questions about 4-manifolds. But the questions themselves are quite old. Fundamentally, we are trying to understand objects (namely smooth manifolds) whose definition has unchanged for the better part of a century.

My questions are:

A1 (Main question): Are there some areas of mathematics whose guiding questions would not be intelligible in terms of the theory we knew 20 years ago?

A2 (More subjective question): What are some areas where new theory is being developed as we speak, or where there seems to be a great need for new theory?

Remark: All mathematicians (at least all the one's I've spoken to) agree that good theory arises from good problems. However, I do get the feeling that some areas leave more room for theory than others, hence my question!

• soft-question
• math-history

• $\begingroup$ I'm having trouble understanding what you mean by "new theory", since it seems that under any reasonable definition the answer is "all areas of mathematics are in the need for new theory". For instance, would you consider that the fact that all elliptic curves over $\mathbb Q$ are modular "old theory" since one of the guiding questions (Fermat's Last Theorem) was intelligible to mathematics centuries ago? What about Connes' approach to the Riemann hypothesis (an old question) in terms of operator algebras? $\endgroup$ –  Santiago Canez Commented Apr 25, 2014 at 18:07
• $\begingroup$ I guess it's a little bit like the distinction between lemma and theorem (not always obvious of course). Although I don't know very much about FLT, I gather that one of the remarkable things about the proof is that it relied on a lot of modern theory, and generated theory of its own. But I don't think this is true in general. I can think of plenty of problems whose resolution requires the introduction of remarkable techniques, but which did not generate a new class of mathematical objects worthy of intrinsic study. In fact, I would say that in some fields (like PDEs) this is the norm. $\endgroup$ –  user142700 Commented Apr 25, 2014 at 18:18

2 Answers 2

Tropical algebraic geometry is being developed as we speak though I can't vouch for any "great need" as you put it.

Mirror symmetry almost certainly fits the bill; it didn't exist as a subject until the 1990's. More generally, my sense is that symplectic geometry/topology is developing theory quite rapidly.

But I don't think I understand your Example 2. Sure, much of the motivation behind $4$-manifold theory comes from classical questions. But many of these classical questions are quite hard, hence the need for sophisticated technology (as you mention).

All of this is to say that many of the "guiding questions" today are about these new invariants themselves, and likely would not be understood 20 (okay, maybe 30) years ago. In other words, my sense is that questions about these invariants have largely replaced classical questions in terms of what is actually done day-to-day.

If anything, it seems to me (a complete beginner) that new invariants are being proposed or discovered quite rapidly, and it seems like there's still a lot of space for new ones.

• $\begingroup$ Thanks for the answer. I think you make a good point regarding example 2. $\endgroup$ –  user142700 Commented Apr 30, 2014 at 5:13

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IR Theory: Problem-Solving Theory Versus Critical Theory?

• Post author By Matt Davies
• Post date 01/10/2014
• No Comments on IR Theory: Problem-Solving Theory Versus Critical Theory?

This article was originally published by E-International Relations on 19 September 2014.

Robert Cox began his canonical 1981 essay “Social Forces, States and World Orders: Beyond International Relations Theory” with the observation that it is “necessary and practical” for academic disciplines to “divide up the seamless web of the real social world”. We make these divisions, Cox wrote, in order to analyse the world and thus to produce practical knowledge of that world. It is not a stretch to suggest that the real social world of International Relations scholarship might also be approached as worthy of analysis and theory. Indeed, reflection on International Relations as theory appears in the field as part of the necessary and practical division of the complexity of the social and political world. Rare is the introduction to IR textbook that does not emphasize, and usually begin with, the “great (theoretical) debates” that have structured the field since it emerged as an academic discipline.

Thus theory itself has long and often been treated as an object for theoretical reflection in International Relations. Recently, we could point to both the founding of a specific section of the US-based International Studies Association dedicated to Theory – indeed, this section honoured Professor Cox at the ISA convention in Toronto in 2014 – as well as the special issue in September 2013 of the European Journal of International Relations on “The End of IR Theory?”, accompanied by a wide-ranging discussion of the papers collected there in the Duck of Minerva blog.

For some of the contributors to the special issue and to the debates on the symposium – and I hope I can be forgiven for making an impressionistic observation rather than an analytical one – it seems that the question mark at the end of “the end of IR theory?” was a sign of fatigue rather than a sense that the debates over theory needed to be renewed. Fatigue, in the sense of “are we still having this conversation?” or “haven’t we moved on yet?” Emblematic of this fatigue were the reflections of Professor Chris Brown in both his article in the EJIR and his contribution to the symposium. It’s not that Brown is hostile to theory; on the contrary, his contribution was a complaint that the critical theories that emerged in the 1980s had not fulfilled their potential and that problem-solving theory had contributed much more.

I disagree with his assessment of the status of critical theory, as do many of the contributors to the special issue and to the symposium, in particular with his claim that it has failed to live up to the promise it showed in the 1980s – but that’s a conversation for another time. What is most interesting here is how Brown takes up Cox’s analytical division of “critical theory” from “problem-solving theory”. Indeed, the trope of problem-solving versus critical theory is asserted quite often in discussions of the status of theory in IR: for example, in A. C. McKeil; in Robert W. Murray; or in Ali Diskaya, just to take a few examples appearing here in e-IR. It is this trope, along with Cox’s other oft-cited claim in the 1981 Millennium article that “theory is always for someone and for some purpose” (Cox 1981: 129) that have made his article canonical. Indeed, Cox’s categories of “critical” and “problem-solving” are now part of the very common-sense ordering of theory in IR.

It is therefore important to consider what Cox actually said about these categories. Problem-solving theory, first, “takes the world as it finds it, with the prevailing social and power relationships and the institutions into which they are organised, as the given framework for action. The general aim of problem-solving is to make these relationships and institutions work smoothly by dealing effectively with particular sources of trouble” (Cox 1981, 128-129). This definition, remember, follows Cox’s opening statements in the article about the importance of theory for the production of practical knowledge. Cox is often interpreted as elevating critical theory over problem solving theory – Brown takes him to do so, for example, in the symposium when he says Cox “compared ‘problem-solving’ theory unfavourably with ‘critical theory’” but I am not convinced that a careful reading of Cox’s article supports this (and Cox argues something similar). In addition to signalling the importance of theory for practical knowledge, Cox explicitly notes, for example, how the analytical procedures he sees as defining problem-solving theory are the source of its strength. He takes issue with the idea that problem-solving theory is value-free and asserts that it is conservative (Cox 1981: 129-130) but this is as close to a normative assessment of problem-solving theory as Cox gets.

Critical theory, in contrast, is holistic where problem-solving theory is analytic. It “does not take institutions and social and power relations for granted but calls them into question by concerning itself with their origins and how and whether they might be in the process of changing. … Critical theory is directed to the social and political complex as a whole rather than to the separate parts” (Cox 1981: 129). Cox also allows that where problem-solving theory might be seen as conservative, critical theory might be seen as utopian: “Its aims are just as practical as those of problem-solving theory, but it approaches practice from a perspective with transcends that of the existing order. … Critical theory allows for a normative choice in favour of a social and political order different from the prevailing order, but it limits the range of choice to alternative orders which are feasible transformations of the existing world” (Cox 1981: 130).

I suspect that it is this holistic and utopian range for critical theory as asserted by Cox that leads Brown to identify critical theory with Quentin Skinner’s notion of Grand Theory and leads so many of the rest of us to assume that critical theory is posited as a superior theoretical approach to problem-solving theory. I’ve tried to show that Cox, at least, makes no explicit claims to that effect. Nevertheless, the categories Cox bequeathed to us seem to encourage us to turn this binary, critical versus problem-solving theory, into a hierarchy. Readers of International Relations theory instinctively want to read it as political theory – though as Rob Walker might remind us, this does not make us careful readers of political theory either. Perhaps we need to acknowledge that the theoretical choice presented by the binary critical theory-problem-solving theory is, at least, theory as engaged in a political contest.

Should Cox’s categories be preserved, critiqued, or abandoned? Would doing so lend a clearer (and practical) view of theory in the field? One way to extend the engagement with the practice of theory would be to read Cox’s categories alongside the other famous definition of critical theory, in Max Horkheimer’s essay “Traditional and Critical Theory” (Horkheimer 2014 [1937]). Though Cox did not explicitly cite Horkheimer, the latter’s efforts to distinguish critical theory from what he called “traditional theory” make him an obvious interlocutor. (There are, of course, many other serious contributions to the effort to situate theory socially and politically, from Bourdieu to Foucault, from Bruno Latour to Walter Mignolo. Many of these efforts are considered in the EJIR special issue and the Duck of Minerva symposium.) I focus on Horkheimer here in part due to the clear affinities between his approach and Cox’s and in part because Horkheimer, like Cox and as I would like to do, provides an explicit defence of the enterprise of critical theory.

While the scale of Horkheimer’s critique, engaged as he was with theory per se, is much grander than the stage Cox builds when he focuses on IR theory in the 1981 article, their accounts of “traditional” and “problem-solving” theory are remarkably similar. Cox notes how the power of problem-solving theory stems from its methodological “fixing” of the social and institutional parameters surrounding the variables it examines. For Horkheimer, this method, rooted in Descartes and predominant not only in social sciences but in science generally in his time, stems from the ability of the scholar to abstract him or herself from these social and institutional parameters in the production of theories and analyses. In other words, just as in any production process where a division of labour separates the subjective functions of planning, designing, interpreting, and analysing from the executive functions, traditional theory renders the world under study as objective and passive and the scientist an active, analysing subject.

In their conceptualisations of critical theory, however, Cox and Horkheimer differ slightly but in an important way. While both are concerned to defend theory as an approach to a dynamic and interconnected totality, Cox does not foreground the status of the theorist, while for Horkheimer the critical theorist must engage with theory as a productive process. Cox does take neorealism to task for neglecting the production process in the constitution of national interest (Cox 1981: 134-135) but Horkheimer goes further: it is not a matter of adding another parameter or variable to the theoretical enterprise; it is a matter of understanding the theoretical enterprise itself in relation to and as a part of a general production process and division of labour. When Cox wrote in 1981, the prevailing epistemology in IR and the epistemological commitment of problem-solving or traditional theory was realist: the world exists independently of our thoughts about it and the task of theory is to make thought adequate to reality. What Horkheimer shows is that there is no neat division between thought and reality that can justify the privileged position of the theorist in the social division of labour: our thoughts are part of reality, as real as the city you live in or the job you work at and they must be analysed as part of the general social division of labour and of social reproduction.

Thus the problem-solving theorist becomes a functionary in the maintenance of social order. The critical theorist must understand the role of theory in social reproduction in order to break down the divisions between theoretical reflection and the making of the world.

I am not suggesting that Horkheimer was right where Cox was wrong. Cox was certainly aware of the – explicit or implicit – political commitments of the theorist when he said, “theory is always for someone and for some purpose”. The question for me here is whether our common-sense taxonomy of International Relations theory as “problem-solving” or “critical” remains appropriate. Given how embedded it is in our ways of seeing ourselves and our field, and given that it can be quite useful for teaching theory, I don’t think it should necessarily be abandoned. Given the implicit, instinctual way IR theorists tend to treat the division as a contest, as in Chris Brown for whom problem-solving has produced better results than critical theory, I wonder if it would not be better to try to make the political stakes of that contest more evident.

For me, reading Cox with Horkheimer provides an interesting start on this task. The description of the first category as “problem-solving” or “traditional” points to a theoretical practice where expertise rules, where specialists take up their specific tasks and succeed or fail on the basis of how powerful their explanations are and the impact of their work. Cox and Horkheimer both acknowledge the importance of this approach in terms of method and results. And they both hint at the cost: politically, we might better describe this approach as technocratic theory. The enterprise is to uncover the timeless essences of things and relations and to keep things working by keeping them in their place.

The contrasting approach to theory, which Cox and Horkheimer both dub “critical theory”, seeks instead to enable the transformation of things. But critical theory is more than this, too; after all, as social constructivism suggests, the transformation of things is just the normal state of affairs as people make themselves and make their history. Critical theory does more: it disagrees. As Rancière suggests, it disrupts the order of the “distribution of the sensible.” Critical theory works by making visible the relationships and the things that International Relations refuses to recognise and qualify as relationships or things. It makes audible the voices of people not qualified to speak in International Relations. Against the technocratic barriers to international living and understandings, critical theory identifies the arbitrariness and artificiality of barriers and explains them in relation to their roles in the division of labour, social reproduction, or system maintenance. Politically, critical theory must be democratic theory – not a theory of democracy, posed externally to its object, but a theory that is democratic in its everyday practices. These are the political stakes in our theoretical choices.

Matt Davies lectures in International Political Economy at Newcastle University and is the Degree Programme Director for the MA in World Politics and Popular Culture . He is also a co-editor of the Popular Culture and World Politics book series , published by Routledge.

• Tags Neorealism , Liberalism , International Relations , History , Realism

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Theory learning vs problem solving

What do you like more? In school we barely studied any theory, mostly just solved problems to prepare for exams. So it was like 5% theory, 95% practice. In University it's the complete opposite. Like 70% theory, 30% practice. I didn't enjoy such a system at school too much, since you don't learn a lot. But now I kind of miss it. I hope that math research is something like 30% theory, 70% practice. So what do you guys enjoy more?

Screen Rant

Deadpool & spider-man theory makes a dream mcu movie a bigger deal than deadpool & wolverine.

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I've Been Waiting 5 Years For A Deadpool & Spider-Man Movie, Please Make It Happen Marvel

How michael keaton’s vulture moved to sony’s spider-man villain universe finally explained, it's not too late for sony's spider-man universe to flourish after venom 3.

• After Deadpool & Wolverine , Ryan Reynolds' Deadpool could team up with another powerful Marvel hero for a new adventure.
• Deadpool & Wolverine director Shawn Levy wants to bring Deadpool and Spider-Man together in the MCU.
• A new MCU theory suggests Deadpool and Spider-Man could embark on a multiversal journey into Sony's Spider-Man Universe.

Following the release of Marvel Studios' Deadpool & Wolverine , a new MCU theory teams up Deadpool and Spider-Man for an even bigger multiverse adventure. Fox's Deadpool and Deadpool 2 established Ryan Reynolds as one of the most popular fixtures of the X-Men franchise, but also cemented Deadpool as a lone wolf. Since he previously had little connection to the wider world of the X-Men, it's possible Deadpool may stay separate from the MCU's other heroes after his debut in 2024's upcoming Deadpool & Wolverine , but Shawn Levy might have other plans.

Deadpool & Wolverine will mark Reynolds' permanent move from Fox's X-Men franchise to the MCU proper. This creates the opportunity for Deadpool to cross paths with other notable heroes in his future Marvel Studios adventures , perhaps adapting some of his most exciting and explosive team-up storylines from Marvel Comics. This could include teaming up the Merc with a Mouth with everyone's favorite Friendly Neighborhood superhero, which a new MCU theory claims could branch out into another faltering Marvel franchise.

10 MCU Heroes We Can't Wait To See Meet Deadpool (& Why)

Deadpool & Wolverine will introduce Deadpool into the Marvel Cinematic Universe, meaning he will inevitably be meeting some of Marvel's other heroes.

Shawn Levy Wants To Direct A Deadpool & Spider-Man Team-Up Movie In The MCU

Deadpool & spider-man have fought together many times in marvel comics.

Even though Deadpool & Wolverine director Shawn Levy hasn't yet been confirmed to be returning to helm another Marvel Studios project, this is very likely , considering Deadpool & Wolverine is expected to be one of the MCU's most successful movies ever. If Levy does return, he already has an idea of which hero he'd want to introduce to Deadpool next, as he revealed to Total Film (via GamesRadar ) that he'd "love to see Deadpool and Spidey." Deadpool and Spider-Man embarked on many adventures together in Marvel Comics, so this grouping is a real possibility.

The thing about Deadpool is I think he makes everything more interesting because of his audacity. But, boy, I'd sure love to see Deadpool and Spidey. That's a movie I'd love to make. I feel like Tom Holland would run circles around everyone else.

Although they had met on several previous occasions, Marvel Comics' Spider-Man/Deadpool , which ran between 2016 and 2019, could form the basis of a Deadpool and Spider-Man MCU team-up story . This series saw Deadpool and Spider-Man fight Life Model Decoys, journey to Weirdworld, battle the Chameleon, and save the entire Marvel Universe in an epic finale that would fit perfectly in the MCU's Multiverse Saga. There is a huge amount of potential in bringing Deadpool and Spider-Man together in the MCU , and one theory may have worked out the best storyline for the unlikely pair.

Shawn Levy recently shared his interest in a Spider-Man/Deadpool crossover, and it's exactly what I'd love to see after 2024's Deadpool & Wolverine.

Deadpool & Spider-Man Can Continue Deadpool & Wolverine’s Multiverse Themes

Deadpool & wolverine bridges the gap between the mcu & fox's x-men universe.

Trailers for Deadpool & Wolverine have proven that the upcoming movie will be a cameo-filled exploration of Fox's now-defunct X-Men franchise, bringing iconic mutant characters into the MCU for one final adventure. Reynolds' Deadpool and Hugh Jackman's Wolverine will find themselves in the Void at the End of Time, first seen in Loki season 1 , and have been rumored to be embarking on an adventure throughout various MCU timelines. These themes could continue in a possible Deadpool and Spider-Man team-up project, according to a theory posed by Reddit user Ok-Ingenuity9833 .

Instead of focusing again on Fox's X-Men franchise, the Reddit theory posits that Deadpool and Spider-Man could instead explore Sony's Spider-Man Universe . Sony's Marvel franchise kicked off with Venom in 2018, and has introduced a variety of Spider-Man-related characters from Marvel Comics, without actually debuting its own version of the wall-crawler. The franchise has crossed over with the MCU already, thanks to Tom Hardy's appearance in Spider-Man: No Way Home , but a Deadpool and Spider-Man movie could take this one step further.

Tom Holland’s Spider-Man Can Finally Meet His SSU Villains In Deadpool & Spider-Man

Spider-man hasn't met any of his adversaries from sony's spider-man universe yet.

There is speculation that Holland's Spider-Man will battle Venom in his MCU future.

One of the biggest criticisms of Sony's Spider-Man Universe is that the titular web-slinger hasn't come to blows with any of the villains introduced in the franchise. Deadpool and Spider-Man traveling to the SSU in a future MCU movie would, thankfully, change this. Tom Holland's Spider-Man could finally face off against Eddie Brock's Venom and Morbius the Living Vampire, and could cross paths with Cassandra Webb and the other Spider-Women introduced in Madame Web . This would not only create an exciting adventure for Deadpool and Spider-Man, but also benefit the SSU itself.

There is speculation that Holland's Spider-Man will battle Venom in his MCU future , particularly since a piece of the symbiote was left in the MCU in Spider-Man: No Way Home . However, it seems this wouldn't be Tom Hardy's popular version of the villain-turned-antihero, but a multiversal Deadpool and Spider-Man movie could rectify this missed opportunity. Shawn Levy's dream MCU movie could even bring Spider-Man back into opposition with Michael Keaton's Vulture , who controversially found himself in the SSU in Morbius' post-credits scene.

We finally have a reason as to why Michael Keaton's Vulture bizarrely came to Sony's Spider-Man universe from the MCU (as seen in the Morbius movie).

Deadpool & Spider-Man Can Solve Major Problems With Sony’s Spider-Man Universe

Sony's spider-man universe has produced its fair share of disappointments.

A huge problem with Sony's Spider-Man Universe is that iconic Marvel villains have become antiheroes.

While the Venom franchise has been popular, Sony's other Marvel movies have been major box office disappointments. Of course, this could mean Marvel Studios would prefer to avoid tying the likes of Morbius and Madame Web into the MCU's Spider-Man timeline . However, connecting the faltering SSU more closely to the MCU could help to deliver stronger interpretations of its characters , and doing this in a Deadpool and Spider-Man team-up movie would give Reynolds' Merc with a Mouth the chance to make jokes about the state of the SSU directly.

A huge problem with Sony's Spider-Man Universe is that iconic Marvel villains have become antiheroes, most notably Venom and Kraven the Hunter. Introducing Spider-Man on a multiversal journey into the franchise would give these characters the chance to be much more menacing , and finally fill their duties as outright villains. Introducing Deadpool and Spider-Man into the SSU, albeit briefly, could also expand Spider-Man's knowledge of his own existence, as he'd be introduced to more spider-like heroes, including Madame Web's Julia Cornwall, Mattie Franklin, and Anya Corazon .

Venom: The Last Dance will be Tom Hardy's final solo movie as Eddie Brock; however, there is still hope for Sony's Spider-Man Universe.

If Deadpool and Spider-Man do join forces in the MCU, it's likely this will take place after the conclusion of the Multiverse Saga. This means the multiverse may no longer be a vehicle the pair could use for their story, though Deadpool's upcoming experiences with the Time Variance Authority could grant him special privileges. Sony Pictures may also have an issue with Deadpool poking fun at its divisive Marvel franchise , so it's unclear whether this story could actually unfold after Deadpool & Wolverine , no matter how entertaining it could be.​​​​​​​

Deadpool & Wolverine

A sequel to the highly successful Deadpool and Deadpool 2 starring Ryan Reynolds as the Merc with a Mouth. The third film will be the first film in the franchise to be developed under the Marvel Studios banner following Disney's acquisition of 20th Century Fox. Ryan Reynolds is returning to play the character, alongside Hugh Jackman, reprising his Wolverine role in the Marvel Cinematic Universe for the first time. 

Cooperative control of marine vehicles using the receding horizon concept and consensus theory

• Published: 28 June 2024

Cite this article

• Alexis Zakartchouk Jr. 1 &
• Helio Mitio Morishita 1  

This paper envisages the use of the receding horizon concept to deal with the path following control problem of marine vehicles, deployed in cooperative mode. In this way, the system comprises a Lyapunov-based model predictive control to guide the vehicle along the desired path, and a moving horizon estimator to provide noise attenuated estimates of the states required by the control. It also comprises a consensus-based cooperative controller to solve the collective formation control problem. The performance of the whole system is assessed through numerical simulation, considering three vehicles operating in cooperative mode along a 2D path. The results exhibit the efficacy of both controllers, evidencing the quality of the outputs supplied by the estimator.

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Consensus in multi-agent systems: a review

Trajectory Tracking Control of Fixed-Wing Hybrid Aerial Underwater Vehicle Subject to Wind and Wave Disturbances

3D Formation Control of Multiple Cooperating Autonomous Agents via Leader-Follower Strategy

Due to solving online a non-convex optimization problem.

Originally conceived to solve the individual motion control problem.

Estimates which present a reduced level of noise if compared with the original associated measurements (attenuation/filtering).

The coefficients are defined according to SNAME ( 1950 ).

For notation simplicity, the associated matrices will kept the previous notation.

For notation simplicity, the time dependency is dropped in the incoming formulation.

From a reference controller.

For the sake of simplicity, the ocean current’s speed components were already taken related to \(\{I\}\) , as indicated by their associated sub-indexes.

\(\varvec{\delta } = \begin{bmatrix} \delta&0 \end{bmatrix}^T\) with \(\delta \) being an arbitrarily small negative constant, introduced to incorporate the angular velocity r in the reference controller error dynamics formulation (Vanni et al. 2008 ).

Eventually, providing also estimates of position, heading angle and speeds for the ocean current state observer.

For the sake of simplicity, the arrival cost was not considered in the cost function.

Conceived under the premises of constant and irrotational ocean current.

Continuous communication is a costly and unnecessary practice. Particularly for underwater applications, it is even unfeasible due to the aforementioned technical issues.

This topology is modeled using Graph Theory.

For that reason, the synchronization state \(\gamma \) was chosen as the angular speed ( \(u^i/R_i\) ), as indicated in Fig.  4 .

In the path figures, the vehicle’s position/heading is represented by a filled arrow and the trajectories by dashed lines. For the path zoomed figure, the vehicles’ predicted positions are represented by red asterisks and their associated boundaries are represented by blue circles. The scale of the arrows was adjusted case by case, according to the figure’s objective and characteristic.

In this figure, the angular speeds were already converted into linear speeds.

For the sake of visualization clarity, only the first 50 s are presented.

Such as actuators and time-varying attack angular velocity dynamics.

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Zakartchouk, A., Morishita, H.M. Cooperative control of marine vehicles using the receding horizon concept and consensus theory. J. Ocean Eng. Mar. Energy (2024). https://doi.org/10.1007/s40722-024-00334-0

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Received : 07 July 2023

Accepted : 31 May 2024

Published : 28 June 2024

DOI : https://doi.org/10.1007/s40722-024-00334-0

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