https://link.springer.com/content/pdf/10.2307%2F3343168.pdf

Development as Freedom

It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology. Here “reduced” means, roughly speaking, that the first problem can be solved deterministically in polynomial time provided an oracle is available for solving the second. From this notion of reducible, polynomial degrees of difficulty are defined, and it is shown that the problem of determining tautologyhood has the same polynomial degree as the problem of determining whether the first of two given graphs is isomorphic to a subgraph of the second. Other examples are discussed. A method of measuring the complexity of proof procedures for the predicate calculus is introduced and discussed.

http://4mhz.de/download.php?file=Cook1971_A4.pdf

The complexity of theorem-proving procedures

The purpose of this article is to examine how the field of mixed methods currently is being defined. The authors asked many of the current leaders in mixed methods research how they define mixed methods research. The authors provide the leaders' definitions and discuss the content found as they searched for the criteria of demarcation. The authors provide a current answer to the question, What is mixed methods research? They also briefly summarize the recent history of mixed methods and list several issues that need additional work as the field continues to advance. They argue that mixed methods research is one of the three major “research paradigms” (quantitative research, qualitative research, and mixed methods research). The authors hope this article will contribute to the ongoing dialogue about how mixed methods research is defined and conceptualized by its practitioners.

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Toward a Definition of Mixed Methods Research

Evolutionary psychology is one of many biologically informed approaches to the study of human behavior. Along with cognitive psychologists, evolutionary psychologists propose that much, if not all, of our behavior can be explained by appeal to internal psychological mechanisms. What distinguishes evolutionary psychologists from many cognitive psychologists is the proposal that the relevant internal mechanisms are adaptations—products of natural selection—that helped our ancestors get around the world, survive and reproduce. To understand the central claims of evolutionary psychology we require an understanding of some key concepts in evolutionary biology, cognitive psychology, philosophy of science and philosophy of mind. Philosophers are interested in evolutionary psychology for a number of reasons. For philosophers of science —mostly philosophers of biology—evolutionary psychology provides a critical target. There is a broad consensus among philosophers of science that evolutionary psychology is a deeply flawed enterprise. For philosophers of mind and cognitive science evolutionary psychology has been a source of empirical hypotheses about cognitive architecture and specific components of that architecture. Philosophers of mind are also critical of evolutionary psychology but their criticisms are not as all-encompassing as those presented by philosophers of biology. Evolutionary psychology is also invoked by philosophers interested in moral psychology both as a source of empirical hypotheses and as a critical target.

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Stanford Encyclopedia of Philosophy

Companies are increasingly asked to provide innovative solutions to deep-seated problems of human misery, even as economic theory instructs managers to focus on maximizing their shareholders' wealt

Misery Loves Companies: Rethinking Social Initiatives by Business:

The hope that mathematical methods employed in the investigation of formal logic would lead to purely computational methods for obtaining mathematical theorems goes back to Leibniz and has been revived by Peano around the turn of the century and by Hilbert's school in the 1920's. Hilbert, noting that all of classical mathematics could be formalized within quantification theory, declared that the problem of finding an algorithm for determining whether or not a given formula of quantification theory is valid was the central problem of mathematical logic. And indeed, at one time it seemed as if investigations of this “decision” problem were on the verge of success. However, it was shown by Church and by Turing that such an algorithm can not exist. This result led to considerable pessimism regarding the possibility of using modern digital computers in deciding significant mathematical questions. However, recently there has been a revival of interest in the whole question. Specifically, it has been realized that while no decision procedure exists for quantification theory there are many proof procedures available—that is, uniform procedures which will ultimately locate a proof for any formula of quantification theory which is valid but which will usually involve seeking “forever” in the case of a formula which is not valid—and that some of these proof procedures could well turn out to be feasible for use with modern computing machinery.Hao Wang [9] and P. C. Gilmore [3] have each produced working programs which employ proof procedures in quantification theory. Gilmore's program employs a form of a basic theorem of mathematical logic due to Herbrand, and Wang's makes use of a formulation of quantification theory related to those studied by Gentzen. However, both programs encounter decisive difficulties with any but the simplest formulas of quantification theory, in connection with methods of doing propositional calculus. Wang's program, because of its use of Gentzen-like methods, involves exponentiation on the total number of truth-functional connectives, whereas Gilmore's program, using normal forms, involves exponentiation on the number of clauses present. Both methods are superior in many cases to truth table methods which involve exponentiation on the total number of variables present, and represent important initial contributions, but both run into difficulty with some fairly simple examples.In the present paper, a uniform proof procedure for quantification theory is given which is feasible for use with some rather complicated formulas and which does not ordinarily lead to exponentiation. The superiority of the present procedure over those previously available is indicated in part by the fact that a formula on which Gilmore's routine for the IBM 704 causes the machine to computer for 21 minutes without obtaining a result was worked successfully by hand computation using the present method in 30 minutes. Cf. §6, below.It should be mentioned that, before it can be hoped to employ proof procedures for quantification theory in obtaining proofs of theorems belonging to “genuine” mathematics, finite axiomatizations, which are “short,” must be obtained for various branches of mathematics. This last question will not be pursued further here; cf., however, Davis and Putnam [2], where one solution to this problem is given for ele

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A Computing Procedure for Quantification Theory

Hilary Putnam deals in this book with some of the most fundamental persistent problems in philosophy: the nature of truth, knowledge and rationality. His aim is to break down the fixed categories of thought which have always appeared to define and constrain the permissible solutions to these problems.

Reason, truth, and history

Introduction 1. Language and philosophy 2. The analytic and synthetic 3. Do true assertions correspond to reality? 4. Some issues in the theory of grammar 5. The 'innateness hypothesis' and explanatory models in linguistics 6. How not to talk about meaning 7. Review of The concept of a person 8. Is semantics possible? 9. The refutation of conventionalism 10. Reply to Gerald Massey 11. Explanation and reference 12. The meaning of 'meaning' 13. Language and reality 14. Philosophy and our mental life 15. Dreaming and 'depth grammar' 16. Brains and behaviour 17. Other minds 18. Minds and machines 19. Robots: machines or artificially created life? 20. The mental life of some machines 21. The nature of mental states 22. Logical positivism and the philosophy of mind Bibliography Index.

Mind, language, and reality

Although it is on occasion important and useful to distinguish between factual claims and value judgments, the distinction becomes, Hilary Putnam argues, positively harmful when identified with a dichotomy between the objective and the purely "subjective." Lively, concise, and wise, his book prepares the way for a renewed mutual fruition of philosophy and the social sciences.

The Collapse of the Fact/Value Dichotomy and Other Essays

Preface 1. Brains in a vat 2. A problem about reference 3. Two philosophical perspectives 4. Mind and body 5. Two conceptions of rationality 6. Fact and value 7. Reason and history 8. The impact of science on modern conceptions of rationality 9. Values, facts and cognition Appendix Index.

Hilary Putnam

Papers

A Computing Procedure for Quantification Theory

Reason, truth, and history

Mind, language, and reality

The Collapse of the Fact/Value Dichotomy and Other Essays

Reason, Truth and History.