Search results for 'M. Timur Friedman' (try it on Scholar)

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  1. H. Friedman (1995). Sheard, M., See Friedman, H. Annals of Pure and Applied Logic 71:307.
     
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  2. Harvey Friedman, A Complete Theory of Everything: Satisfiability in the Universal Domain Harvey M. Friedman October 10, 1999 Friedman@Math.Ohio-State.Edu Www.Math.Ohio-State.Edu/~Friedman/. [REVIEW]
    Here we take the view that LPC(=) is applicable to structures whose domain is too large to be a set. This is not just a matter of class theory versus set theory, although it can be interpreted as such, and this interpretation is discussed briefly at the end.
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  3. Harvey Friedman, A Complete Theory of Everything: Satisfiability in the Universal Domain Harvey M. Friedman October 10, 1999 Friedman@Math.Ohio-State.Edu. [REVIEW]
    Here we take the view that LPC(=) is applicable to structures whose domain is too large to be a set. This is not just a matter of class theory versus set theory, although it can be interpreted as such, and this interpretation is discussed briefly at the end.
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  4.  42
    Edwina L. Rissland, David B. Skalak & M. Timur Friedman (1997). Evaluating a Legal Argument Program: The BankXX Experiments. [REVIEW] Artificial Intelligence and Law 5 (1-2):1-74.
    In this article we evaluate the BankXX program from several perspectives. BankXX is a case-based legal argument program that retrieves cases and other legal knowledge pertinent to a legal argument through a combination of heuristic search and knowledge-based indexing. The program is described in detail in a companion article in Artificial Intelligence and Law 4: 1--71, 1996. Three perspectives are used to evaluate BankXX:(1) classical information retrieval measures of precision and recall applied against a hand-coded baseline; (2) knowledge-representation and case-based (...)
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  5.  6
    Edwina L. Rissland, David B. Skalak & M. Timur Friedman (1996). BankXX: Supporting Legal Arguments Through Heuristic Retrieval. [REVIEW] Artificial Intelligence and Law 4 (1):1-71.
    The BankXX system models the process of perusing and gathering information for argument as a heuristic best-first search for relevant cases, theories, and other domain-specific information. As BankXX searches its heterogeneous and highly interconnected network of domain knowledge, information is incrementally analyzed and amalgamated into a dozen desirable ingredients for argument (called argument pieces), such as citations to cases, applications of legal theories, and references to prototypical factual scenarios. At the conclusion of the search, BankXX outputs the set of argument (...)
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  6. Harvey M. Friedman, Friedman@Math.Ohio-State.Edu.
    It has been accepted since the early part of the Century that there is no problem formalizing mathematics in standard formal systems of axiomatic set theory. Most people feel that they know as much as they ever want to know about how one can reduce natural numbers, integers, rationals, reals, and complex numbers to sets, and prove all of their basic properties. Furthermore, that this can continue through more and more complicated material, and that there is never a real problem.
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  7. Harvey Friedman, 4:00 P.M., F Sep 20.
    There are many familiar theorems whose proofs use methods which are in some appropriate sense substantially more "abstract" than its statement. Some particularly well known examples come from the use of complex variables in number theory. Sometimes such abstraction can be removed - for example by the "elementary proof of the prime number theorem" - and sometimes no appropriate removal is known. The interest in removing abstraction typically varies, with no agreed upon criteria for appropriateness. E.g., the removal might sacrifice (...)
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  8.  10
    Hannah Friedman (2011). Mining (A.M.) Hirt Imperial Mines and Quarries in the Roman World. Organizational Aspects 27 BC – AD 235. Pp. Xiv + 551, Maps. Oxford: Oxford University Press, 2010. Cased £80. ISBN: 978-0-19-957287-8. [REVIEW] The Classical Review 61 (02):612-613.
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  9.  1
    Sy D. Friedman (1992). Review: Donald A. Martin, A. S. Kechris, D. A. Martin, Y. N. Moschovakis, The Largest Countable This, That, and the Other; Alexander S. Kechris, Donald A. Martin, Robert M. Solovay, Introduction to $Q$-Theory; Steve Jackson, A. S. Kechris, D. A. Martin, J. R. Steel, AD and the Projective Ordinals. [REVIEW] Journal of Symbolic Logic 57 (1):262-264.
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  10.  1
    Sy D. Friedman (1992). Martin Donald A.. The Largest Countable This, That, and the Other. Cabal Seminar 79–81, Proceedings, Caltech-UCLA Logic Seminar 1979–81, Edited by Kechris AS, Martin DA, and Moschovakis YN, Lecture Notes in Mathematics, Vol. 1019, Springer-Verlag, Berlin, Heidelberg, New York, and Tokyo, 1983, Pp. 97–106. Kechris Alexander S., Martin Donald A., and Solovay Robert M.. Introduction to Q-Theory. Cabal Seminar 79–81, Proceedings, Caltech-UCLA Logic Seminar 1979–81, Edited by Kechris AS, Martin DA, and .. [REVIEW] Journal of Symbolic Logic 57 (1):262-264.
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  11. S. D. Friedman, W. G. Handley, S. S. Wainer, A. Joyal, I. Moerdijk, L. Newelski, F. van Engelen & J. van Oosten (1994). Downey, R., Gasarch, W. And Moses, M., The Structure. Annals of Pure and Applied Logic 70:287.
     
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  12.  24
    Christina Starmans & Ori Friedman (2013). Taking 'Know' for an Answer: A Reply to Nagel, San Juan, and Mar. Cognition 129 (3):662-665.
    Nagel, San Juan, and Mar report an experiment investigating lay attributions of knowledge, belief, and justification. They suggest that, in keeping with the expectations of philosophers, but contra recent empirical findings [Starmans, C. & Friedman, O. (2012). The folk conception of knowledge. Cognition, 124, 272–283], laypeople consistently deny knowledge in Gettier cases, regardless of whether the beliefs are based on ‘apparent’ or ‘authentic’ evidence. In this reply, we point out that Nagel et al. employed a questioning method that biased (...)
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  13. Harvey Friedman, Ramsey Theory and Enormous Lower Bounds.
    by Harvey M. Friedman Department of Mathematics Ohio State University friedman@math.ohio-state.edu www.math.ohio-state.edu/~friedman/ April 5, 1997..
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  14. Harvey M. Friedman, Foundations of Mathematics: Past, Present, and Future.
    It turns out, time and time again, in order to make serious progress in f.o.m., we need to take actual reasoning and actual development into account at precisely the proper level. If we take these into account too much, then we are faced with information that is just too difficult to create an exact science around - at least at a given state of development of f.o.m. And if we take these into account too little, our findings will not have (...)
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  15.  5
    Harvey M. Friedman & Jeffry L. Hirst (1990). Weak Comparability of Well Orderings and Reverse Mathematics. Annals of Pure and Applied Logic 47 (1):11-29.
    Two countable well orderings are weakly comparable if there is an order preserving injection of one into the other. We say the well orderings are strongly comparable if the injection is an isomorphism between one ordering and an initial segment of the other. In [5], Friedman announced that the statement “any two countable well orderings are strongly comparable” is equivalent to ATR 0 . Simpson provides a detailed proof of this result in Chapter 5 of [13]. More recently, (...) has proved that the statement “any two countable well orderings are weakly comparable” is equivalent to ATR 0 . The main goal of this paper is to give a detailed exposition of this result. (shrink)
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  16.  11
    Sy-David Friedman & Radek Honzik (2012). Eastonʼs Theorem and Large Cardinals From the Optimal Hypothesis. Annals of Pure and Applied Logic 163 (12):1738-1747.
    The equiconsistency of a measurable cardinal with Mitchell order o=κ++ with a measurable cardinal such that 2κ=κ++ follows from the results by W. Mitchell [13] and M. Gitik [7]. These results were later generalized to measurable cardinals with 2κ larger than κ++ .In Friedman and Honzik [5], we formulated and proved Eastonʼs theorem [4] in a large cardinal setting, using slightly stronger hypotheses than the lower bounds identified by Mitchell and Gitik , for a suitable μ, instead of the (...)
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  17.  1
    Harvey M. Friedman & Jeffry L. Hirst (1991). Reverse Mathematics and Homeomorphic Embeddings. Annals of Pure and Applied Logic 54 (3):229-253.
    Extrapolating from the work of Mahlo , one can prove that given any pair of countable closed totally bounded subsets of complete separable metric spaces, one subset can be homeomorphically embedded in the other. This sort of topological comparability is reminiscent of the statements concerning comparability of well orderings which Friedman has shown to be equivalent to ATR0 over the weak base system RCA0. The main result of this paper states that topological comparability is also equivalent to ATR0. In (...)
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  18. Lawrence J. Friedman & Anke M. Schreiber (2013). The Lives of Erich Fromm: Love's Prophet. Cup.
    Erich Fromm was a political activist, psychologist, psychoanalyst, philosopher, and one of the most important intellectuals of the twentieth century. Known for his theories of personality and political insight, Fromm dissected the sadomasochistic appeal of brutal dictators while also eloquently championing love--which, he insisted, was nothing if it did not involve joyful contact with others and humanity at large. Admired all over the world, Fromm continues to inspire with his message of universal brotherhood and quest for lasting peace. The first (...)
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  19. Lawrence J. Friedman & Anke M. Schreiber (2014). The Lives of Erich Fromm: Love's Prophet. Cup.
    Erich Fromm was a political activist, psychologist, psychoanalyst, philosopher, and one of the most important intellectuals of the twentieth century. Known for his theories of personality and political insight, Fromm dissected the sadomasochistic appeal of brutal dictators while also eloquently championing love--which, he insisted, was nothing if it did not involve joyful contact with others and humanity at large. Admired all over the world, Fromm continues to inspire with his message of universal brotherhood and quest for lasting peace. The first (...)
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  20. Alan M. Leslie, Ori Friedman & Tim P. German (2004). Core Mechanisms in ‘Theory of Mind’. Trends in Cognitive Sciences 8 (12):528-533.
    Our ability to understand the thoughts and feelings of other people does not initially develop as a theory but as a mechanism. The ‘ theory of mind ’ mechanism is part of the core architecture of the human brain, and is specialized for learning about mental states. Impaired development of this mechanism can have drastic effects on social learning, seen most strikingly in the autistic spectrum disorders. ToMM kick-starts belief–desire attribution but effective reasoning about belief contents depends on a process (...)
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  21. Harvey M. Friedman, The Upper Shift Kernel Theorems.
    We now fix A ⊆ Q. We study a fundamental class of digraphs associated with A, which we call the A-digraphs. An A,kdigraph is a digraph (Ak,E), where E is an order invariant subset of A2k in the following sense. For all x,y ∈ A2k, if x,y have the same order type then x ∈ E ↔ y ∈ E.
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  22. Harvey M. Friedman, Similar Subclasses.
    Reflection, in the sense of [Fr03a] and [Fr03b], is based on the idea that a category of classes has a subclass that is “similar” to the category. Here we present axiomatizations based on the idea that a category of classes that does not form a class has extensionally different subclasses that are “similar”. We present two such similarity principles, which are shown to interpret and be interpretable in certain set theories with large cardinal axioms.
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  23. Solomon Feferman, Harvey M. Friedman, Penelope Maddy & John R. Steel (2000). Does Mathematics Need New Axioms? Bulletin of Symbolic Logic 6 (4):401-446.
    Part of the ambiguity lies in the various points of view from which this question might be considered. The crudest di erence lies between the point of view of the working mathematician and that of the logician concerned with the foundations of mathematics. Now some of my fellow mathematical logicians might protest this distinction, since they consider themselves to be just more of those \working mathematicians". Certainly, modern logic has established itself as a very respectable branch of mathematics, and there (...)
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  24.  13
    Ori Friedman & Alan M. Leslie (2007). The Conceptual Underpinnings of Pretense: Pretending is Not ‘Behaving-as-If’. Cognition 105 (1):103-124.
    The ability to engage in and recognize pretend play begins around 18 months. A major challenge for theories of pretense is explaining how children are able to engage in pretense, and how they are able to recognize pretense in others. According to one major account, the metarepresentational theory, young children possess both production and recognition abilities because they possess the mental state concept, pretend. According to a more recent rival account, the Behavioral theory, young children are behaviorists about pretense, and (...)
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  25. Harvey M. Friedman, Remarks On the Unknowable.
    The kind of unknowability I will discuss concerns the count of certain natural finite sets of objects. Even the situation with regard to our present strong formal systems is rather unclear. One can just profitably focus on that, putting aside issues of general unknowability.
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  26. Harvey M. Friedman, P01 INCOMPLETENESS: Finite Set Equations.
    Let R Õ [1,n]3k ¥ [1,n]k. We define R = {y Œ [1,n]k:($xŒA3)(R(x,y))}. We say that R is strictly dominating if and only if for all x,yŒ[1,n]k, if R(x,y) then max(x) < max(y).
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  27.  3
    Ori Friedman, Karen R. Neary, Corinna L. Burnstein & Alan M. Leslie (2010). Is Young Children’s Recognition of Pretense Metarepresentational or Merely Behavioral? Evidence From 2- and 3-Year-Olds’ Understanding of Pretend Sounds and Speech. [REVIEW] Cognition 115 (2):314-319.
  28. Harvey M. Friedman, Concept Calculus: Much Better Than.
    This is the initial publication on Concept Calculus, which establishes mutual interpretability between formal systems based on informal commonsense concepts and formal systems for mathematics through abstract set theory. Here we work with axioms for "better than" and "much better than", and the Zermelo and Zermelo Frankel axioms for set theory.
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  29. Harvey M. Friedman, Quadratic Axioms.
    We axiomatize EFA in strictly mathematical terms, involving only the ring operations, without extending the language by either exponentiation, finite sets of integers, or polynomials.
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  30. Harvey M. Friedman, Concrete Mathematical Incompleteness.
    there are mathematical statements that cannot be proved or refuted using the usual axioms and rules of inference of mathematics.
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  31. Harvey M. Friedman, Vigre Lectures.
    In mathematics, we back up our discoveries with rigorous deductive proofs. Mathematicians develop a keen instinctive sense of what makes a proof rigorous. In logic, we strive for a *theory* of rigorous proofs.
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  32. Harvey M. Friedman, Selection for Borel Relations.
    We present several selection theorems for Borel relations, involving only Borel sets and functions, all of which can be obtained as consequences of closely related theorems proved in [DSR 96,99,01,01X] involving coanalytic sets. The relevant proofs given there use substantial set theoretic methods, which were also shown to be necessary. We show that none of our Borel consequences can be proved without substantial set theoretic methods. The results are established for Baire space. We give equivalents of some of the main (...)
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  33.  9
    Ori Friedman & Alan M. Leslie (2004). A Developmental Shift in Processes Underlying Successful Belief‐Desire Reasoning. Cognitive Science 28 (6):963-977.
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  34. Harvey M. Friedman, Kernel Structure Theory.
    We have been recently engaged in this search, and have announced a long series of successively simpler and more convincing examples. See [Fr09-10].
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  35.  39
    M. Friedman (1998). On the Sociology of Scientific Knowledge and its Philosophical Agenda. Studies in History and Philosophy of Science Part A 29 (2):239-271.
  36. Harvey M. Friedman, Sentential Reflection.
    We present two forms of “sentential reflection”, which are shown to be mutually interpretable with Z2 and ZFC, respectively.
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  37. M. Friedman (forthcoming). Overcoming Metaphysics: Carnap and Heidegger. Origins of Logical Empiricism:45--79.
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  38. Harvey M. Friedman, Equational Representations.
    We begin by presenting the language L(N,℘N,℘℘N). This is the standard language for presenting third order sentences, using its intended interpretation.
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  39.  5
    Harvey M. Friedman, Stephen G. Simpson & Rick L. Smith (1983). Countable Algebra and Set Existence axioms11Research Partially Supported by NSF Grants MCS-79-23743, MCS-78-02558, and MCS 8107867. Simpson's Research Was Also Supported by an Alfred P. Sloan Research Fellowship. [REVIEW] Annals of Pure and Applied Logic 25 (2):141-181.
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  40. Harvey M. Friedman, Remarks On GÖDel Phenomena and the Field of Reals.
    A lot of the well known impact of the Gödel phenomena is in the form of painful messages telling us that certain major mathematical programs cannot be completed as intended. This aspect of Gödel – the delivery of bad news –is not welcomed, and defensive measures are now in place.
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  41. Harvey M. Friedman, Transfer Principles in Set Theory.
    1. Transfer principles from N to On. A. Mahlo cardinals. B. Weakly compact cardinals. C. Ineffable cardinals. D. Ramsey cardinals. E. Ineffably Ramsey cardinals. F. Subtle cardinals. G. From N to (...))
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  42. Harvey M. Friedman, Finite Phase Transitions.
    This topic has been discussed earlier on the FOM email list in various guises. The common theme is: big numbers and long sequences associated with mathematical objects. See..
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  43. Harvey M. Friedman, Adjacent Ramsey Theory.
    Let k ≥ 2 and f:Nk Æ [1,k] and n ≥ 1 be such that there is no x1 < ... < xk+1 £ n such that f(x1,...,xk) = f(x1,...,xk+1). Then we want to find g:Nk+1 Æ [1,3] such that there is no x1 < ... < xk+2 £ n such that g(x1,...,xk+1) = g(x2,...,xk+2). This reducees adjacent Ramsey in k dimensions with k colors to adjacent Ramsey in k+1 dimensions with 3 colors.
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  44. Michael Friedman, Robert DiSalle, J. D. Trout, Shaun Nichols, Maralee Harrell, Clark Glymour, Carl G. Wagner, Kent W. Staley, Jesús P. Zamora Bonilla & Frederick M. Kronz (2002). 10. Interpreting Quantum Field Theory Interpreting Quantum Field Theory (Pp. 348-378). Philosophy of Science 69 (2).
     
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  45. Harvey M. Friedman, From Russell's Paradox To.
    Russell’s way out of his paradox via the impredicative theory of types has roughly the same logical power as Zermelo set theory - which supplanted it as a far more flexible and workable axiomatic foundation for mathematics. We discuss some new formalisms that are conceptually close to Russell, yet simpler, and have the same logical power as higher set theory - as represented by the far more powerful Zermelo-Frankel set theory and beyond. END.
     
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  46. Harvey M. Friedman, Philosophy 532 Philosophical Problems in Logic Lecture 1 9/25/02.
    This is widely accepted, inside and outside philosophy, but one can spend an entire career clarifying, justifying, and amplifying on this statement. Certainly a graduate student career.
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  47. Harvey M. Friedman, What Are These Three Aspects?
    Provide a formal system that is a conservative extension of PA for Π02 sentences, and even a conservative extension of HA, that supports the worry free smooth development of constructive analysis in the style of Errett Bishop.
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  48. Harvey M. Friedman, Boolean Relation Theory.
    BRT is always based on a choice of BRT setting. A BRT setting is a pair (V,K), where V is an interesting family of multivariate functions. K is an interesting family of sets. In this talk, we will only consider V,K, where V is an interesting family of multivariate functions from N into N. K is an interesting family of subsets of N.
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  49. Harvey M. Friedman, Introduction.
    The use of x[y,z,w] rather than the more usual y Πx has many advantages for this work. One of them is that we have found a convenient way to eliminate any need for axiom schemes. All axioms considered are single sentences with clear meaning. (In one case only, the axiom is a conjunction of a manageable finite number of sentences).
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  50.  57
    J. Earman & M. Friedman (1973). The Meaning and Status of Newton's Law of Inertia and the Nature of Gravitational Forces. Philosophy of Science 40 (3):329-359.
    A four dimensional approach to Newtonian physics is used to distinguish between a number of different structures for Newtonian space-time and a number of different formulations of Newtonian gravitational theory. This in turn makes possible an in-depth study of the meaning and status of Newton's Law of Inertia and a detailed comparison of the Newtonian and Einsteinian versions of the Law of Inertia and the Newtonian and Einsteinian treatments of gravitational forces. Various claims about the status of Newton's Law of (...)
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