Results for 'Ramsey's test'

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  1. Ramsey’s Test, Adams’ Thesis, and Left-Nested Conditionals.Richard Dietz & Igor Douven - 2010 - Review of Symbolic Logic 3 (3):467-484.
    Adams famously suggested that the acceptability of any indicative conditional whose antecedent and consequent are both factive sentences amounts to the subjective conditional probability of the consequent given the antecedent. The received view has it that this thesis offers an adequate partial explication of Ramsey’s test, which characterizes graded acceptability for conditionals in terms of hypothetical updates on the antecedent. Some results in van Fraassen may raise hope that this explicatory approach to Ramsey’s test is extendible to left-nested (...)
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  2.  63
    A Semantic-Modal View on Ramsey's Test.Alexandru Baltag & Sonja Smets - unknown
    We present a semantic analysis of the Ramsey test, pointing out its deep underlying flaw: the tension between the “static” nature of AGM revision (which was originally tailored for revision of only purely ontic beliefs, and can be applied to higher-order beliefs only if given a “backwards-looking” interpretation) and the fact that, semantically speaking, any Ramsey conditional must be a modal operator (more precisely, a dynamic-epistemic one). Thus, a belief about a Ramsey conditional is in fact a higher-order belief, (...)
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  3.  23
    McGee's Counterexample to the Ramsey Test.John Cantwell, Sten Lindström & Wlodek Rabinowicz - 2017 - Theoria 83 (2):154-168.
    Vann McGee has proposed a counterexample to the Ramsey Test. In the counterexample, a seemingly trustworthy source has testified that p and that if not-p, then q. If one subsequently learns not-p, then one has reason to doubt the trustworthiness of the source and so, the argument goes, one has reason to doubt the conditional asserted by the source. Since what one learns is that the antecedent of the conditional holds, these doubts are contrary to the Ramsey Test. (...)
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  4.  32
    In Defence of Ramsey's Test.D. H. Mellor - 2014 - Ratio 27 (3):356-361.
  5. Moore-Paradoxical Belief, Conscious Belief and the Epistemic Ramsey Test.John N. Williams - 2012 - Synthese 188 (2):231-246.
    Chalmers and Hájek argue that on an epistemic reading of Ramsey’s test for the rational acceptability of conditionals, it is faulty. They claim that applying the test to each of a certain pair of conditionals requires one to think that one is omniscient or infallible, unless one forms irrational Moore-paradoxical beliefs. I show that this claim is false. The epistemic Ramsey test is indeed faulty. Applying it requires that one think of anyone as all-believing and if one (...)
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  6.  9
    Difference-Making Conditionals and the Relevant Ramsey Test.Hans Rott - forthcoming - Review of Symbolic Logic:1-39.
    This paper explores conditionals expressing that the antecedent makes a difference for the consequent. A 'relevantised' version of the Ramsey Test for conditionals is employed in the context of the classical theory of belief revision. The idea of this test is that the antecedent is relevant to the consequent in the following sense: a conditional is accepted just in case (i) the consequent is accepted if the belief state is revised by the antecedent and (ii) the consequent fails (...)
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  7. New Surprises for the Ramsey Test.Malte Willer - 2010 - Synthese 176 (2):291 - 309.
    In contemporary discussions of the Ramsey Test for conditionals, it is commonly held that (i) supposing the antecedent of a conditional is adopting a potential state of full belief, and (ii) Modus Ponens is a valid rule of inference. I argue on the basis of Thomason Conditionals (such as ' If Sally is deceiving, I do not believe it') and Moore's Paradox that both claims are wrong. I then develop a double-indexed Update Semantics for conditionals which takes these two (...)
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  8.  69
    Belief Ascription and the Ramsey Test.Karolina Krzyżanowska - 2013 - Synthese 190 (1):21-36.
    In this paper, I analyse a finding by Riggs and colleagues that there is a close connection between people’s ability to reason with counterfactual conditionals and their capacity to attribute false beliefs to others. The result indicates that both processes may be governed by one cognitive mechanism, though false belief attribution seems to be slightly more cognitively demanding. Given that the common denominator for both processes is suggested to be a form of the Ramsey test, I investigate whether Stalnaker’s (...)
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  9.  29
    Becker, Ramsey, and Hi-World Semantics. Toward a Unified Account of Conditionals.Cheng-Chih Tsai - 2016 - Croatian Journal of Philosophy 16 (1):69-89.
    In Lowe (1995), instead of endorsing a Stalnaker/Lewis-style account of counterfactuals, E. J. Lowe claims that a variation of C. I. Lewis’s strict implication alone captures the essence of everyday conditionals and avoids the paradoxes of strict implication. However, Lowe’s approach fails to account for the validity of simple and straightforward arguments such as ‘if 2=3 then 2+1=3+1’, and Heylen & Horsten (2006) even claims that no variation of strict implication can successfully describe the logical behavior of natural language conditionals. (...)
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  10.  23
    Two Notions of Epistemic Validity-Epistemic Models for Ramsey's Conditionals.Horacio Arló Costa & Isaac Levi - 1996 - Synthese 109 (2):217-262.
    How to accept a conditional? F. P. Ramsey proposed the following test in . 'If A, then B' must be accepted with respect to the current epistemic state iff the minimal hypothetical change of it needed to accept A also requires accepting B. In this article we propose a formulation of , which unlike some of its predecessors, is compatible with our best theory of belief revision, the so-called AGM theory , chapters 1-5 for a survey). The new (...), which, we claim, encodes some of the crucial insights defended by F. P. Ramsey in , is used to study the conditionals epistemically validated by the AGM postulates. Our notion of validity is compared with the notion of negative validity used by Gärdenfors in . It is observed that the notions of PV and NV will in general differ and that when these differences arise it is the notion of PV that is preferable. Finally we compare our formulation of the Ramsey test with a previous formulation offered by Gärdenfors . We show that any attempt to interpret as delivering acceptance conditions for Ramsey's conditionals is doomed to failure. (shrink)
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  11.  50
    Ramsey's Tests.B. H. Slater - 2004 - Synthese 141 (3):431-444.
    This paper starts by criticising some olderaccounts of conditionals based on the so-called `Ramsey Test', and ends by proposing their replacement, in part with a material account, in part with a probabilistic account using epsilon terms. The combined replacement is in fact closer to Ramsey's ideas. But there is also a resemblance between the latter and a more recent account of conditionals, which relates some of them to causality. The comparison provides a basis for assessment of the proposed (...)
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  12. Indicative Conditionals Without Iterative Epistemology.Ben Holguín - forthcoming - Noûs.
    This paper argues that two widely accepted principles about the indicative conditional jointly presuppose the falsity of one of the most prominent arguments against epistemological iteration principles. The first principle about the indicative conditional, which has close ties both to the Ramsey test and the “or-to-if” inference, says that knowing a material conditional suffices for knowing the corresponding indicative. The second principle says that conditional contradictions cannot be true when their antecedents are epistemically possible. Taken together, these principles entail (...)
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  13.  25
    On the Ramsey Test Analysis of ‘Because’.Holger Andreas & Mario Günther - 2019 - Erkenntnis 84 (6):1229-1262.
    The well-known formal semantics of conditionals due to Stalnaker Studies in logical theory, Blackwell, Oxford, 1968), Lewis, and Gärdenfors The logic and 1140 epistemology of scientific change, North-Holland, Amsterdam, 1978, Knowledge in flux, MIT Press, Cambridge, 1988) all fail to distinguish between trivially and nontrivially true indicative conditionals. This problem has been addressed by Rott :345–370, 1986) in terms of a strengthened Ramsey Test. In this paper, we refine Rott’s strengthened Ramsey Test and the corresponding analysis of explanatory (...)
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  14.  47
    Defending the Ramsey Test: What is Wrong with Preservation?B. Hill - 2012 - Mind 121 (481):131-146.
    In ‘A Defence of the Ramsey Test’, Richard Bradley makes a case for not concluding from the famous impossibility results regarding the Ramsey Test — the thesis that a rational agent believes a conditional if he would believe the consequent upon learning the antecedent — that the thesis is false. He lays the blame instead on one of the other premisses in these results, namely the Preservation condition. In this paper, we explore how this condition can be weakened (...)
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  15.  1
    On the Ramsey Test Analysis of ‘Because’.Holger Andreas & Mario Günther - 2019 - Erkenntnis 84 (6):1229-1262.
    The well-known formal semantics of conditionals due to Stalnaker Studies in logical theory, Blackwell, Oxford, 1968), Lewis, and Gärdenfors The logic and 1140 epistemology of scientific change, North-Holland, Amsterdam, 1978, Knowledge in flux, MIT Press, Cambridge, 1988) all fail to distinguish between trivially and nontrivially true indicative conditionals. This problem has been addressed by Rott :345–370, 1986) in terms of a strengthened Ramsey Test. In this paper, we refine Rott’s strengthened Ramsey Test and the corresponding analysis of explanatory (...)
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  16. On the Strength of Ramsey's Theorem for Pairs.Peter A. Cholak, Carl G. Jockusch & Theodore A. Slaman - 2001 - Journal of Symbolic Logic 66 (1):1-55.
    We study the proof-theoretic strength and effective content of the infinite form of Ramsey's theorem for pairs. Let RT n k denote Ramsey's theorem for k-colorings of n-element sets, and let RT $^n_{ denote (∀ k)RT n k . Our main result on computability is: For any n ≥ 2 and any computable (recursive) k-coloring of the n-element sets of natural numbers, there is an infinite homogeneous set X with X'' ≤ T 0 (n) . Let IΣ n (...)
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  17.  34
    Ramsey's Theorem for Pairs and Provably Recursive Functions.Alexander Kreuzer & Ulrich Kohlenbach - 2009 - Notre Dame Journal of Formal Logic 50 (4):427-444.
    This paper addresses the strength of Ramsey's theorem for pairs ($RT^2_2$) over a weak base theory from the perspective of 'proof mining'. Let $RT^{2-}_2$ denote Ramsey's theorem for pairs where the coloring is given by an explicit term involving only numeric variables. We add this principle to a weak base theory that includes weak König's Lemma and a substantial amount of $\Sigma^0_1$-induction (enough to prove the totality of all primitive recursive functions but not of all primitive recursive functionals). (...)
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  18.  18
    Term Extraction and Ramsey's Theorem for Pairs.Alexander P. Kreuzer & Ulrich Kohlenbach - 2012 - Journal of Symbolic Logic 77 (3):853-895.
    In this paper we study with proof-theoretic methods the function(al) s provably recursive relative to Ramsey's theorem for pairs and the cohesive principle (COH). Our main result on COH is that the type 2 functional provably recursive from $RCA_0 + COH + \Pi _1^0 - CP$ are primitive recursive. This also provides a uniform method to extract bounds from proofs that use these principles. As a consequence we obtain a new proof of the fact that $WKL_0 + \Pi _1^0 (...)
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  19.  17
    Stable Ramsey's Theorem and Measure.Damir D. Dzhafarov - 2011 - Notre Dame Journal of Formal Logic 52 (1):95-112.
    The stable Ramsey's theorem for pairs has been the subject of numerous investigations in mathematical logic. We introduce a weaker form of it by restricting from the class of all stable colorings to subclasses of it that are nonnull in a certain effective measure-theoretic sense. We show that the sets that can compute infinite homogeneous sets for nonnull many computable stable colorings and the sets that can compute infinite homogeneous sets for all computable stable colorings agree below $\emptyset'$ but (...)
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  20.  20
    Ramsey’s Theorem and König’s Lemma.T. E. Forster & J. K. Truss - 2007 - Archive for Mathematical Logic 46 (1):37-42.
    We consider the relation between versions of Ramsey’s Theorem and König’s Infinity Lemma, in the absence of the axiom of choice.
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  21.  47
    Belief Revision, Non-Monotonic Reasoning, and the Ramsey Test.Charles B. Cross - 1990 - In Kyburg Henry E., Loui Ronald P. & Carlson Greg N. (eds.), Knowledge Representation and Defeasible Reasoning. Kluwer Academic Publishers. pp. 223--244.
    Peter Gärdenfors has proved (Philosophical Review, 1986) that the Ramsey rule and the methodologically conservative Preservation principle are incompatible given innocuous-looking background assumptions about belief revision. Gärdenfors gives up the Ramsey rule; I argue for preserving the Ramsey rule and interpret Gärdenfors's theorem as showing that no rational belief-reviser can avoid reasoning nonmonotonically. I argue against the Preservation principle and show that counterexamples to it always involve nonmonotonic reasoning. I then construct a new formal model of belief revision that does (...)
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  22.  26
    Reverse Mathematics and a Ramsey-Type König's Lemma.Stephen Flood - 2012 - Journal of Symbolic Logic 77 (4):1272-1280.
    In this paper, we propose a weak regularity principle which is similar to both weak König's lemma and Ramsey's theorem. We begin by studying the computational strength of this principle in the context of reverse mathematics. We then analyze different ways of generalizing this principle.
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  23.  55
    Reapproaching Ramsey: Conditionals and Iterated Belief Change in the Spirit of AGM.Hans Rott - 2011 - Journal of Philosophical Logic 40 (2):155-191.
    According to the Ramsey Test, conditionals reflect changes of beliefs: α > β is accepted in a belief state iff β is accepted in the minimal revision of it that is necessary to accommodate α. Since Gärdenfors’s seminal paper of 1986, a series of impossibility theorems (“triviality theorems”) has seemed to show that the Ramsey test is not a viable analysis of conditionals if it is combined with AGM-type belief revision models. I argue that it is possible to (...)
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  24.  20
    On the Strength of Ramsey's Theorem Without S1-Induction.Keita Yokoyama - 2013 - Mathematical Logic Quarterly 59 (1-2):108-111.
    In this paper, we show that equation image is a equation image-conservative extension of BΣ1 + exp, thus it does not imply IΣ1.
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  25. Ramsey's Principle Re-Situated.Jérôme Dokic & Pascal Engel - 2004 - In Hallvard Lillehammer & D. H. Mellor (eds.), Ramsey's Legacy. Oxford University Press.
    This paper is about Ramsey's Principle, according to which a belief's truth-conditions are those that guarantee the success of an action based on that belief whatever the underlying motivating desires. Some philosophers have argued that the Principle should be rejected because it leads to the apparently implausible consequence that any failure of action is the result of some false belief on the agent's part. There is a gap between action and success that cannot be bridged by the agent's cognitive (...)
     
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  26.  14
    Ramsey's Legacies on Conditionals and Truth.Dorothy Edgington - 2005 - In Hallvard Lillehammer & D. H. Mellor (eds.), Ramsey's Legacy. Oxford University Press.
    Book synopsis: The Cambridge philosopher Frank Ramsey died tragically young, but had already established himself as one of the most brilliant minds of the twentieth century. Besides groundbreaking work in philosophy, particularly in logic, language, and metaphysics, he created modern decision theory and made substantial contributions to mathematics and economics. In these original essays, written to commemorate the centenary of Ramsey's birth, a distinguished international team of contributors offer fresh perspectives on his work and show how relevant it is (...)
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  27.  47
    For the Sake of the Argument: Ramsey Test Conditionals, Inductive Inference and Nonmonotonic Reasoning.Isaac Levi - 1996 - Cambridge University Press.
    This book by one of the world's foremost philosophers in the fields of epistemology and logic offers an account of suppositional reasoning relevant to practical deliberation, explanation, prediction and hypothesis testing. Suppositions made 'for the sake of argument' sometimes conflict with our beliefs, and when they do, some beliefs are rejected and others retained. Thanks to such belief contravention, adding content to a supposition can undermine conclusions reached without it. Subversion can also arise because suppositional reasoning is ampliative. These two (...)
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  28. On the Ramsey Test Without Triviality.Hannes Leitgeb - 2010 - Notre Dame Journal of Formal Logic 51 (1):21-54.
    We present a way of classifying the logically possible ways out of Gärdenfors' inconsistency or triviality result on belief revision with conditionals. For one of these ways—conditionals which are not descriptive but which only have an inferential role as being given by the Ramsey test—we determine which of the assumptions in three different versions of Gärdenfors' theorem turn out to be false. This is done by constructing ranked models in which such Ramsey-test conditionals are evaluated and which are (...)
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  29. Against the Ramsey Test.A. Morton - 2004 - Analysis 64 (4):294-299.
    I argue against the Ramsey test connecting indicative conditionals with conditional probability, by means of examples in which conditional probability is high but the conditional is intuitively implausible. At the end of the paper, I connect these issues to patterns of belief revision.
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  30.  27
    Iterated Descriptor Revision and the Logic of Ramsey Test Conditionals.Sven Hansson - 2016 - Journal of Philosophical Logic 45 (4):429-450.
    Two of the major problems in AGM-style belief revision, namely the difficulties in accounting for iterated change and for Ramsey test conditionals, have satisfactory solutions in descriptor revision. In descriptor revision, the input is a metalinguistic sentence specifying the success condition of the operation. The choice mechanism selects one of the potential outcomes in which the success condition is satisfied. Iteration of this operation is unproblematic. Ramsey test conditionals can be introduced without giving rise to the paradoxical results (...)
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  31. The Negative Ramsey Test.Peter Gärdenfors, Sten Lindström, Michael Morreau & Wlodek Rabinowicz - 1991 - In André Fuhrmann & Michael Morreau (eds.), The Logic of Theory Change. Springer.
    The so called Ramsey test is a semantic recipe for determining whether a conditional proposition is acceptable in a given state of belief. Informally, it can be formulated as follows: (RT) Accept a proposition of the form "if A, then C" in a state of belief K, if and only if the minimal change of K needed to accept A also requires accepting C. In Gärdenfors (1986) it was shown that the Ramsey test is, in the context of (...)
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  32.  39
    Conditional Belief and the Ramsey Test.Scott Sturgeon - 2002 - Royal Institute of Philosophy Supplement 51:215-232.
    Consider the frame S believes that—. Fill it with a conditional, say If you eat an Apple, you'll drink a Coke. what makes the result true? More generally, what facts are marked by instances of S believes ? In a sense the answer is obious: beliefs are so marked. Yet that bromide leads directly to competing schools of thought. And the reason is simple. Common-sense thinks of belief two ways. Sometimes it sees it as a three-part affair. When so viewed (...)
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  33.  63
    Ramsey’s Theorem for Trees: The Polarized Tree Theorem and Notions of Stability. [REVIEW]Damir D. Dzhafarov, Jeffry L. Hirst & Tamara J. Lakins - 2010 - Archive for Mathematical Logic 49 (3):399-415.
    We formulate a polarized version of Ramsey’s theorem for trees. For those exponents greater than 2, both the reverse mathematics and the computability theory associated with this theorem parallel that of its linear analog. For pairs, the situation is more complex. In particular, there are many reasonable notions of stability in the tree setting, complicating the analysis of the related results.
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  34.  49
    Ramsey's Foundations Extended to Desirabilities.Jordan Howard Sobel - 1998 - Theory and Decision 44 (3):231-278.
    In his Truth and Probability (1926), Frank Ramsey provides foundations for measures of degrees of belief in propositions and preferences for worlds. Nonquantitative conditions on preferences for worlds, and gambles for worlds and certain near-worlds, are formulated which he says insure that a subject's preferences for worlds are represented by numbers, world values. Numbers, for his degrees of belief in propositions, probabilities, are then defined in terms of his world values. Ramsey does not also propose definitions of desirabilities for propositions, (...)
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  35. Nils-Eric Sahlin, Ed., Ramsey's Ontology. [REVIEW]Matteo Morganti - 2005 - Philosophy in Review 25 (5):380-382.
    Review of a collection of papers on the ontological aspects of Ramsey's work.
     
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  36.  50
    Conditionals and Conditional Thinking.Andrea Manfrinati, Pierdaniele Giaretta & Paolo Cherubini - 2008 - Mind and Society 7 (1):21-34.
    In this paper, we claim that the problem of conditionals should be dealt with by carefully distinguishing between thinking conditional propositions and conditional thinking, i.e. thinking on the basis of some supposition. This distinction deserves further investigation, if we are to make sense of some old and new experimental data concerning the understanding and the assertion of conditional sentences. Here we will argue that some of these data seem to refute the mental models theory of conditional reasoning, setting the ground (...)
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  37.  11
    Ramsey's Pragmatic Approach to Truth and Belief.Monika Gruber - 2017 - Theoria 83 (3):225-248.
    In spite of his tragically short life, Ramsey made extensive contributions in the fields of mathematics, logic, economics and philosophy. In this article we focus on Ramsey's investigations into the notions of belief and judgement, their truth conditions and probability theory. We show that the central role given by Ramsey to belief and action together with his pragmatism allows for a new interpretation of the theories of truth and probability, paving the way for a modern decision theory.
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  38.  51
    On Ramsey's 'Silly Delusion' Regarding Tractatus 5.53.Kai Wehmeier - 2009 - In Giuseppe Primiero & Shahid Rahman (eds.), Acts of Knowledge: History, Philosophy and Logic. College Publications.
    We investigate a variant of the variable convention proposed at Tractatus 5.53ff for the purpose of eliminating the identity sign from logical notation. The variant in question is what Hintikka has called the strongly exclusive interpretation of the variables, and turns out to be what Ramsey initially (and erroneously) took to be Wittgenstein's intended method. We provide a tableau calculus for this identity-free logic, together with soundness and completeness proofs, as well as a proof of mutual interpretability with first-order logic (...)
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  39.  9
    Ramsey's Record: Wittgenstein on Infinity and Generalization.S. J. Methven - forthcoming - British Journal for the History of Philosophy:1-18.
    There is, in the Ramsey Archive at the Hillman Library of the University of Pittsburgh, a note, written in 1929, in Ramsey's hand and mostly in German, consisting of twenty paragraphs the contents...
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  40.  62
    Ramsey's Cognitivism: Truth, Ethics, and the Meaning of Life. Misak - 2015 - Transactions of the Charles S. Peirce Society 51 (4):463.
    In 1925, the 22 year old Frank Ramsey read a provocative paper to the Apostles titled “On There Being No Discussable Subject”. Many of the papers presented to this ‘Cambridge Conversazione Society’ were not terribly serious, and most have left minimal trace. But after Ramsey died in 1930 just shy of his 27th birthday, this paper was pulled from his manuscript remains by Richard Braithwaite, and printed in the posthumously-published The Foundations of Mathematics, under the title “Epilogue”. A snappy passage (...)
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  41.  45
    What is Squiggle? Ramsey on Wittgenstein's Theory of Judgement.Peter M. Sullivan - 2005 - In Hallvard Lillehammer & D. H. Mellor (eds.), Ramsey's Legacy. Oxford University Press.
    At the age of 20, and fresh from his undergraduate studies in mathematics, Ramsey set about writing what would be his first substantial publication, his 1923 Critical Notice of Wittgenstein’s Tractatus. It is hard for modern students of that book, who negotiate its obscurities with generations of previous commentary to serve as guides, to appreciate the task Ramsey confronted; and, to the extent that one can appreciate it, it is hard not to feel intimidated by the brilliance of his success. (...)
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  42.  31
    Combinatorial Principles Weaker Than Ramsey's Theorem for Pairs.Denis R. Hirschfeldt & Richard A. Shore - 2007 - Journal of Symbolic Logic 72 (1):171-206.
    We investigate the complexity of various combinatorial theorems about linear and partial orders, from the points of view of computability theory and reverse mathematics. We focus in particular on the principles ADS (Ascending or Descending Sequence), which states that every infinite linear order has either an infinite descending sequence or an infinite ascending sequence, and CAC (Chain-AntiChain), which states that every infinite partial order has either an infinite chain or an infinite antichain. It is well-known that Ramsey's Theorem for (...)
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  43.  6
    Separating Principles Below Ramsey's Theorem for Pairs.Manuel Lerman, Reed Solomon & Henry Towsner - 2013 - Journal of Mathematical Logic 13 (2):1350007.
    In recent years, there has been a substantial amount of work in reverse mathematics concerning natural mathematical principles that are provable from RT, Ramsey's Theorem for Pairs. These principles tend to fall outside of the "big five" systems of reverse mathematics and a complicated picture of subsystems below RT has emerged. In this paper, we answer two open questions concerning these subsystems, specifically that ADS is not equivalent to CAC and that EM is not equivalent to RT.
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  44. The Polarized Ramsey’s Theorem.Damir D. Dzhafarov & Jeffry L. Hirst - 2009 - Archive for Mathematical Logic 48 (2):141-157.
    We study the effective and proof-theoretic content of the polarized Ramsey’s theorem, a variant of Ramsey’s theorem obtained by relaxing the definition of homogeneous set. Our investigation yields a new characterization of Ramsey’s theorem in all exponents, and produces several combinatorial principles which, modulo bounding for ${\Sigma^0_2}$ formulas, lie (possibly not strictly) between Ramsey’s theorem for pairs and the stable Ramsey’s theorem for pairs.
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  45.  44
    On the Strength of Ramsey's Theorem.David Seetapun & Theodore A. Slaman - 1995 - Notre Dame Journal of Formal Logic 36 (4):570-582.
    We show that, for every partition F of the pairs of natural numbers and for every set C, if C is not recursive in F then there is an infinite set H, such that H is homogeneous for F and C is not recursive in H. We conclude that the formal statement of Ramsey's Theorem for Pairs is not strong enough to prove , the comprehension scheme for arithmetical formulas, within the base theory , the comprehension scheme for recursive (...)
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  46.  41
    Ramsey's Theorem and Cone Avoidance.Damir Dzhafarov & Carl Jockusch Jr - 2009 - Journal of Symbolic Logic 74 (2):557 - 578.
    It was shown by Cholak, Jockusch, and Slaman that every computable 2-coloring of pairs admits an infinite low₂ homogeneous set H. We answer a question of the same authors by showing that H may be chosen to satisfy in addition $C\,\not \leqslant _T \,H$ , where C is a given noncomputable set. This is shown by analyzing a new and simplified proof of Seetapun's cone avoidance theorem for Ramsey's theorem. We then extend the result to show that every computable (...)
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  47. Ramsey’s Ramsey-Sentences.Stathis Psillos - 2004 - Vienna Circle Institute Yearbook 12:67-90.
    In the present paper I want to do two things. First, I want to discuss Ramsey’s own views of Ramsey-sentences. This, it seems to me, is an important issue not just (or mainly) because of its historical interest. It has a deep philosophical significance. Addressing it will enable us to see what Ramsey’s lasting contribution in the philosophy of science was as well as what its relevance to today’s problems is. Since the 1950s, where the interest in Ramsey’s views has (...)
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    Ramsey's Legacy.Hallvard Lillehammer & D. H. Mellor (eds.) - 2005 - Oxford University Press.
    The Cambridge philosopher Frank Ramsey died tragically young, but had already established himself as one of the most brilliant minds of the twentieth century. Besides groundbreaking work in philosophy, particularly in logic, language, and metaphysics, he created modern decision theory and made substantial contributions to mathematics and economics. In these original essays, written to commemorate the centenary of Ramsey's birth, a distinguished international team of contributors offer fresh perspectives on his work and show how relevant it is to present-day (...)
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  49. The Ramsey Test Revisited.Sten Lindström & Wlodek Rabinowicz - 1995 - In G. Crocco, L. Fariñas del Cerro & A. Herzig (eds.), Conditionals: From Philosophy to Computer Science. Oxford University Press. pp. 131-182.
  50.  20
    Reverse Mathematics and Ramsey's Property for Trees.Jared Corduan, Marcia J. Groszek & Joseph R. Mileti - 2010 - Journal of Symbolic Logic 75 (3):945-954.
    We show, relative to the base theory RCA₀: A nontrivial tree satisfies Ramsey's Theorem only if it is biembeddable with the complete binary tree. There is a class of partial orderings for which Ramsey's Theorem for pairs is equivalent to ACA₀. Ramsey's Theorem for singletons for the complete binary tree is stronger than $B\sum_{2}^{0}$ , hence stronger than Ramsey's Theorem for singletons for ω. These results lead to extensions of results, or answers to questions, of Chubb, (...)
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