Individual differences and polysemy have rich literatures in cognitive linguistics, but little is said about the prospect of individual differences in polysemy. This article reports an investigation that sought to establish whether people vary in the senses of a polysemous word that they find meaningful, and to develop a novel methodology to study polysemy. The methodology combined established tools: sentence-sorting tasks, a rarely used statistical model of inter-participant agreement, and network visualisation. Two hundred and five English-speaking participants completed one of (...) twelve sentence-sorting tasks on two occasions, separated by a delay of two months. Participants varied in how similarly they sorted the sentences as compared to other participants, and mean agreement across all 24 tasks did not meet an established threshold of acceptable agreement. Between the two test phases, inter-participant agreement varied to a significant but trivial degree. Networks generated for each dataset varied in the degree to which they captured all participants’ responses. This variation correlated with inter-participant agreement. The data collectively suggest that word senses may be subject to individual differences, as is the case in other linguistic phenomena. The methodology proved replicable and has a promise as a useful tool for studying polysemy. (shrink)

John Worrall recently provided an account of epistemic structural realism, which explains the success of science by arguing for the correct mathematical structure of our theories. He accounts for the historical failures of science by pointing to bloated ontological interpretations of theoretical terms. In this paper I argue that Worrall’s account suffers from five serious problems. I also show that Pierre Cruse and David Papineau have developed a rival structural realism that solves all of the problems faced by Worrall. This (...) Ramsey-sentence realism is a significant advance in the debate, but still ultimately fails for its incomplete account of reference. (shrink)

1. Ramsey Sentences and the Function of Theoretical Concepts. In his famous paper “Theories,” Frank Ramsey introduced a technique of examining a scientific theory by means of certain propositions, dubbed later “Ramsey Sentences.” They are the results of what is often called Ramsey elimination. This prima facie elimination is often presented as a method of dispensing with theoretical concepts in scientific theorizing. The idea is this: Assume that we are given a finitely axiomatized scientific (...) theorywhere O1, O2, … are the primitive observation terms of and H1, H2, … its primitive theoretical terms. For simplicity, it will be assumed that is a first-order theory. Since it is finitely axiomatizable, we may think of it as having the form of a single complex proposition, i.e., the conjunction of all the axioms. What can then be done is to generalize existentially with respect to. The result is a sentence of the formIn, the theoretical terms H1, H2, … do not occur any longer. They have been replaced by the variables X1, X2, … bound to initial existential quantifiers. In this sense at least, Ramsey sentences do effect on elimination. Unlike, is not a first-order sentence but a second-order one. (shrink)

This paper defends scientific realism from the pessimistic meta-induction from past reference failure. It allows that a descriptive theory of reference implies that scientific terms characteristically fail of determinate reference. But it argues that a descriptive theory of reference also implies an equivalence between scientific theories and quantificational claims in the style of Ramsey. Since these quantificational claims do not use any of the referentially suspect scientific terms, they can be approximately true even when those terms fail to refer (...) determinately.Keywords: Science; Realism; Ramsey sentences; Approximate truth; Reference. (shrink)

Ramsey's device [2], for eliminating theoretical terms from a theory assumes that the theory has only finitely many axioms. Paul Berent [1], has recently suggested a modification of Ramsey's method that is designed to cover the infinite case. But, his modified method is quite unlike Ramsey's in that it involves an ascent from the original theory to a suitable metatheory. Thus, it is perhaps of some interest to note that there is an extension of Ramsey's method (...) that covers the infinite case and at the same time is much closer in spirit to his original suggestion. (shrink)

Ramsey argued that the best way to understand how the theoretical terms of a theory function is to picture them as existentially bound variables. We explore the ontological ramifications of Ramsey's idea by developing a new type of dynamic model-theoretical semantics, based on the concept of an experimental logic.

Based on archival material from the Carnap and FeiglArchives, this paper re-examines Carnap's approach tothe issue of scientific realism in the 1950s and theearly 1960s. It focuses on Carnap's re-invention ofthe Ramsey-sentence approach to scientific theoriesand argues that Carnap wanted to entertain a genuineneutral stance in the realism-instrumentalism debate.Following Grover Maxwell, it claims that Carnap'sposition may be best understood as a version of`structural realism'. However, thus understood,Carnap's position faces the challenge that Newmanraised against Russell's structuralism: the claim thatthe knowledge (...) of the unobservable is limited to itspurely structural characteristics is eitheruninformative or unsustainable. (shrink)

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 mushroomed, there have been a number of different ways to read Ramsey’s views and to reconstruct Ramsey’s project. The second aim of the present paper is to discuss the most significant and controversial of this reconstruction, viz., structuralism. After some discussion of the problems of structuralism in the philosophy of science, as this was exemplified in Bertrand Russell’s and Grover Maxwell’s views and has re-appeared in Elie Zahar’s and John Worrall’s thought, I will argue that, for good reasons, Ramsey did not see his Ramsey-sentences as part of some sort of structuralist programme. I will close with an image of scientific theories that Ramsey might have found congenial. I will call it Ramseyan humility. (shrink)

In what is known as the “received view” analysis, logical positivism construed scientific theories TC as being axiomatized in first‐order predicate calculus using proper axioms T (the theoretical laws) and having distinct observational and theoretical vocabularies VO and VT which are related to each other via a dictionary of correspondence rules C (see theories). Prior to 1936 the correspondence rules were required to be equivalences between VT terms and simple or complex observational conditions expressible using just VO terms that provided (...) noncreative explicit definitions of the terms (see craig's theorem). The empirical content of the theory TC was identified with the set O of theorems which contained VO but not VT terms. (shrink)

We canvas a number of past uses of Ramsey sentences which have yielded disappointing results, and then consider three very interesting recent attempts to deploy them for a Ramseyan Dialetheist theory of truth, a modal account of laws and theories, and a criterion for the existence of factual properties. We think that once attention is given to the specific kinds of theories that Ramsey had in mind, it becomes evident that their Ramsey sentences are not (...) the best ways of presenting those theories. (shrink)

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 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 (...) class='Hi'>Ramsey’s views has mushroomed, there have been a number of different ways to read Ramsey’s views and to reconstruct Ramsey’s project. The second aim of the present paper is to discuss the most significant and controversial of this reconstruction, viz., structuralism. After some discussion of the problems of structuralism in the philosophy of science, as this was exemplified in Bertrand Russell’s and Grover Maxwell’s views and has re-appeared in Elie Zahar’s and John Worrall’s thought, I will argue that, for good reasons, Ramsey did not see his Ramsey-sentences as part of some sort of structuralist programme. I will close with an image of scientific theories that Ramsey might have found congenial. I will call it Ramseyan humility. (shrink)

F. P. Ramsey pointed out in Theories that the observational content of a theory expressed partly in non-observational terms is retained in the sentence resulting from existentially generalizing the conjunction of all sentences of the theory with respect to all nonobservational terms. Such terms are thus avoidable in principle, but only at the cost of forming a single "monolithic" sentence. This paper suggests that communication may be thought of as occurring not only by sentence but by clause, a (...) sentential formula closed except for a special kind of variable. Understanding such clauses requires incorporating them within the scope of one's own Ramsey sentence. Many concepts of deductive and inductive logic carry over without great change. But the concepts of truth and designation are extendible to clauses only in the sense that assertions involving them must, to be understood, in turn be construed as clauses and incorporated into the Ramsey sentence. The behavior of these extended concepts of truth and designation suggests an explication of coherence truth within a correspondence-truth framework. (shrink)

It is often thought that questions of reference are crucial in assessing scientific realism, construed as the view that successful theories are at least approximately true descriptions of the unobservable; realism is justified only if terms in empirically successful theories generally refer to genuinely existing entities or properties. In this paper this view is questioned. First, it is argued that there are good reasons to think that questions of realism are largely decided by convention and carry no epistemic significance. An (...) alternative conception of realism is then proposed, which focuses on the Ramsey sentences of scientific theories, constructed in the manner of David Lewis's 'How to define theoretical terms'. It is argued that because the Ramsey sentence of a theory preserves the epistemically significant part of the theory's content without generating commitments to any particular conclusions about reference, the realism issue is better addressed by asking whether Ramsey sentences of theories, rather than the theories themselves, are approximately true. (shrink)

The major argument against Ramsey-style epistemic structural realism is the model-theoretic refinement of Newman’s objection against Russell, presented in Ketland : 409–424, 2004), where a technical result is interpreted as showing that the Ramsey-sentence approach collapses into instrumentalism. This paper addresses some questions raised by the application of model theory to the scientific realism debate. Firstly, I will suggest three different formal semantics for the positions in the debate. Then, some technicalities of Ketland’s result will be scrutinized in (...) light of comments by Zahar and Demopoulos. Finally, I will formalize Ketland’s argument by means of an intensional operator and focus on one problematic premise. The conclusion is that, with some adjustments, the Ramsey-sentence approach can represent an intermediate position between realism and instrumentalism, but the term “structuralism” does not suit it well. (shrink)

In "From Metaphysics to Ethics", Frank Jackson presents an impressively systematic conception of modal reality and its relation to our thought. His account of ethics is a test case for this conception. I will argue that Jackson's reasoning for his conclusions about ethics is unsound.

‘Epistemic structural realism’ (ESR) insists that all that we know of the world is its structure, and that the ‘nature’ of the underlying elements remains hidden. With structure represented via Ramsey sentences, the question arises as to how ‘hidden natures’ might also be represented. If the Ramsey sentence describes a class of realisers for the relevant theory, one way of answering this question is through the notion of multiple realisability. We explore this answer in the context of (...) the work of Carnap, Hintikka and Lewis. Both Carnap and Hintikka offer clear structuralist perspectives which, crucially, accommodate the openness inherent in theory change. Unfortunately there is little purchase for a viable form of realism in either case. Lewis’s approach, on the other hand, offers more scope for realism but, as we shall see, concerns arise as to whether a relevant form of structuralism can be maintained. In particular his thesis of Ramseyan humility undermines certain conceptions of scientific laws that the structural realist might naturally cleave to. Our overall conclusion is that the representational device of Ramsey sentence plus multiple realisability can accommodate either the structuralist or realist aspects of ESR but has difficulties capturing both. (shrink)

Functionalism has become one of the predominant theories in the philosophy of mind, with its many merits supposedly including its capacity for precise formulation. The most common method to express this precise formulation is by means of the modified Ramsey sentence. In this article, I will apply work from the field of the philosophy of science to functionalism for the first time, examining how Newman’s objection undermines the Ramsey sentence as a means of formalising functionalism. I will also (...) present a formal variation on Newman’s objection through mathematical induction. Together, these proofs suggest that functionalism formalised by the Ramsey sentence trivially reduces to a kind of behaviourism plus a cardinality constraint on the number of relations holding between mental-relevant behaviours. As most functionalists see functionalism as a distinct theory of mind from behaviourism, this suggests that the modified Ramsey sentence cannot form a satisfactory formalism for functionalism. (shrink)

Dogs display vast phenotypic diversity, including differences in height, skull shape, tail, etc. Yet, humans are almost always able to quickly recognize a dog, despite no single feature or group of features are critical to distinguish dogs from other objects/animals. In search of the mental activities leading human individuals to state “I see a dog”, we hypothesize that the brain might extract meaningful information from the environment using Ramsey sentences-like procedures. To turn the proposition “I see a dog” (...) in a Ramsey sentence, the term dog must be replaced by a long and complex assertion consisting only of observational terms, existential quantifiers and operational rules. The Ramsey sentence for “I see a dog” sounds: “There is at least an entity called dog which satisfies the following conditions: it is an animal, it has four legs, …, etc, …, and is something that I have in my sight”. We discuss the biological plausibility and the putative neural correlates of a Ramsey-like mechanism in the central nervous system. We accomplish a brain-inspired, theoretical neural architecture consisting of a parallel network that requires virtually no memory, is devoid of probabilistic choices and can analyze huge but finite amounts of unique visual details, combining them into a single conceptual output. In sum, Ramsey sentence stands for a versatile tool that can be used not just as a methodological device to cope with biophysical affairs, but also for a model to describe the real functioning of cognitive operations such as sensation and perception. (shrink)

In "From Metaphysics to Ethics", Frank Jackson presents an impressively systematic conception of modal reality and its relation to our thought. His account of ethics is a test case for this conception. I will argue that Jackson's reasoning for his conclusions about ethics is unsound.

In the literature over the Ramsey-sentence approach to structural realism, there is often debate over whether structural realists can legitimately restrict the range of the second-order quantifiers, in order to avoid the Newman problem. In this paper, I argue that even if they are allowed to, it won’t help: even if the Ramsey sentence is interpreted using such restricted quantifiers, it is still an implausible candidate to capture a theory’s structural content. To do so, I use the following (...) observation: if a Ramsey sentence did encode a theory’s structural content, then two theories would be structurally equivalent just in case they have logically equivalent Ramsey sentences. I then argue that this criterion for structural equivalence is implausible, even where frame or Henkin semantics are used. (shrink)

Frank Ramsey (1931) wrote: If two people are arguing 'if p will q?' and both are in doubt as to p, they are adding p hypothetically to their stock of knowledge and arguing on that basis about q. We can say that they are fixing their degrees of belief in q given p. Let us take the first sentence the way it is often taken, as proposing the following test for the acceptability of an indicative conditional: ‘If p then (...) q’ is acceptable to a subject S iff, were S to accept p and consider q, S would accept q. Now consider an indicative conditional of the form (1) If p, then I believe p. Suppose that you accept p and consider ‘I believe p’. To accept p while rejecting ‘I believe p’ is tantamount to accepting the Moore-paradoxical sentence ‘p and I do not believe p’, and so is irrational. To accept p while suspending judgment about ‘I believe p’ is irrational for similar reasons. So rationality requires that if you accept p and consider ‘I believe p’, you accept ‘I believe p’. (shrink)

Frank Ramsey writes: If two people are arguing ‘if p will q?’ and both are in doubt as to p, they are adding p hypothetically to their stock of knowledge and arguing on that basis about q. We can say that they are fixing their degrees of belief in q given p. (1931) Chalmers and Hájek write: Let us take the first sentence [of Ramsey] the way it is often taken, as proposing the following test for the acceptability (...) of an indicative conditional: ‘if p then q’ is acceptable to a subject S iff, were S to accept p and consider q, S would accept q. (shrink)

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 conditionals, that is, conditionals whose antecedent is itself conditional in form. We argue that this interpretation of van Fraassen’s results is to be rejected. Specifically, we provide an argument from material inadequacy against a generalization of Adams’ thesis for left-nested conditionals. (shrink)

This paper deals with Ramsey's theory of truth and its aim is twofold: on the one hand, it will explain what position about truth Ramsey actually defended, and, on the other hand, we will pursue Ramsey's insight in the 20th Century. When the name of Frank Ramsey is mentioned, one of the things that comes to mind is the theory of truth as redundancy. In the following pages we will argue that Ramsey never supported such (...) a theory, but rather an analysis of truth noticeably similar to the prosentential account. In fact, the very word "pro-sentence" appears for the first time in the 20th Century in Ramsey's unfinished work "The nature of truth," written around 1929. Besides, we will show that the prosentential account of truth is a neglected trend throughout the history of analytic philosophy, even though relevant analytic philosophers, such as Prior, Strawson, Williams, Grover, and Brandom, have endorsed it. (shrink)

In contemporary works on conditionals, the Ramsey test is a procedure for the evaluation of conditional sentences. There are several versions of the test, all inspired by a footnote by the British philosopher and mathematician Frank Ramsey, in his General Propositions and Causality. However, no study on Ramsey's own account of conditionals has been put forth so far. Furthermore, the footnote seems to cover indicative conditionals only, and this has led to the belief that no account (...) of counterfactuals can be found in Ramsey's work. In this paper, I recover Ramsey's account of counterfactuals and show that it is sketched in the footnote too. The result is a well-developed account of counterfactuals that resembles many contemporary ones. But Ramsey uses the same approach also for other types of conditionals, and this casts doubts on the current criteria for the classification of this type of sentences. (shrink)

The method of Ramsey sentences has been proposed for handling theoretical constructs within a scientific system. Essentially it consists of constructing a certain "monolithic" sentence for an entire theory. In this present paper several improvements are suggested which help to overcome some of the awkward features of the method. In particular we have here many Ramsey sentences rather than just one, each erstwhile primitive theoretical term giving rise to a Ramsey sentence. Such a sentence in (...) effect defines what we call a Ramsey constant. Using Ramsey constants, we attempt to improve the method in important logical and semantical respects. It is suggested also that such constants are of interest for the philosophy of mathematics. (shrink)

The problem of computational complexity of semantics for some natural language constructions – considered in [M. Mostowski, D. Wojtyniak 2004] – motivates an interest in complexity of Ramsey quantifiers in finite models. In general a sentence with a Ramsey quantifier R of the following form Rx, yH(x, y) is interpreted as ∃A(A is big relatively to the universe ∧A2 ⊆ H). In the paper cited the problem of the complexity of the Hintikka sentence is reduced to the problem (...) of computational complexity of the Ramsey quantifier for which the phrase “A is big relatively to the universe” is interpreted as containing at least one representative of each equivalence class, for some given equvalence relation. In this work we consider quantifiers Rf, for which “A is big relatively to the universe” means “card(A) > f (n), where n is the size of the universe”. Following [Blass, Gurevich 1986] we call R mighty if Rx, yH(x, y) defines N P – complete class of finite models. Similarly we say that Rf is N P –hard if the corresponding class is N P –hard. We prove the following theorems. (shrink)

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 (...) formulas. We also show that Ramsey's Theorem for Pairs is strong enough to prove some sentences in first order arithmetic which are not provable within . In particular, Ramsey's Theorem for Pairs is not conservative over for -sentences. (shrink)

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 (...) some other weak conditions, on pain of triviality incompatible with the following principle, which was there called the preservation criterion: (P) If a proposition B is accepted in a given state of belief K and the proposition A is consistent with the beliefs in K, then B is still accepted in the minimal change of K needed to accept A. (RT) provides a necessary and sufficient criterion for when a 'positive' conditional should be included in a belief state, but it does not say anything about when the negation of a conditional sentence should be accepted. A very natural candidate for this purpose is the following negative Ramsey test: (NRT) Accept the negation of a proposition of the form "if A, then C" in a consistent state of belief K, if and only if the minimal change of K needed to accept A does not require accepting C. This note shows that (NRT) leads to triviality results even in the absence of additional conditions like (P). (shrink)

We prove that any proof of a [Formula: see text] sentence in the theory [Formula: see text] can be translated into a proof in [Formula: see text] at the cost of a polynomial increase in size. In fact, the proof in [Formula: see text] can be obtained by a polynomial-time algorithm. On the other hand, [Formula: see text] has nonelementary speedup over the weaker base theory [Formula: see text] for proofs of [Formula: see text] sentences. We also show that (...) for [Formula: see text], proofs of [Formula: see text] sentences in [Formula: see text] can be translated into proofs in [Formula: see text] at a polynomial cost in size. Moreover, the [Formula: see text]-conservativity of [Formula: see text] over [Formula: see text] can be proved in [Formula: see text], a fragment of bounded arithmetic corresponding to polynomial-time computation. For [Formula: see text], this answers a question of Clote, Hájek and Paris. (shrink)

Frank Plumpton Ramsey, Cambridge mathematician and philosopher, was one of the most brilliant people of his generation. He lived in an extraordinarily stimulating milieu, surrounded by figures such as Russell, Whitehead, Keynes, Moore, and Wittgenstein. Ramsey's highly original papers on the foundations of mathematics, probability, economics, philosophy of science and the theory of knowledge were very influential in the 20th century and are still widely discussed in the 21st. Perhaps two of Ramsey's achievements outshine all the rest. (...) One is his treatment of the theoretical terms of scientific theories and the other is his deflationary account of truth. In 'Theories' he showed that, for any theory, it is always possible to offer an empirically equivalent one that does not contain theoretical terms by re-expressing it in what later became known as 'Ramsey sentences'. His account of truth was rediscovered in the 1960s and is now known as the 'prosentential' theory of truth. This collection of eleven new papers, specially written to commemorate his centenary, answers a crying need for more secondary literature on Frank Ramsey. Nearly all the aspects of Ramsey's work are examined: his logic, philosophy of mind, philosophy of science, metaphysics, epistemology, pragmatism, economics, and the mutual influences between Ramsey and Wittgenstein. The book will be eagerly welcomed by those working in many branches of analytic philosophy and beyond. (shrink)

The influential proposal that the analytical component of a theory is captured by its ‘Carnap sentence’ is critically scrutinized. A counterexample which makes the suggestion problematic is presented.

This article is a defense of frank ramsey's thesis that there is a symmetry between the logical roles of subjects and predicates in subject-Predicate sentences against recent objections.

We investigate the question “To what extent can random reals be used as a tool to establish number theoretic facts?” Let $\text{2-\textit{RAN\/}}$ be the principle that for every real $X$ there is a real $R$ which is 2-random relative to $X$. In Section 2, we observe that the arguments of Csima and Mileti [3] can be implemented in the base theory $\text{\textit{RCA}}_0$ and so $\text{\textit{RCA}}_0+\text{2-\textit{RAN\/}}$ implies the Rainbow Ramsey Theorem. In Section 3, we show that the Rainbow Ramsey (...) Theorem is not conservative over $\text{\textit{RCA}}_0$ for arithmetic sentences. Thus, from the Csima—Mileti fact that the existence of random reals has infinitary-combinatorial consequences we can conclude that $\text{2-\textit{RAN\/}}$ has non-trivial arithmetic consequences. In Section 4, we show that $\text{2-\textit{RAN\/}}$ is conservative over $\text{\textit{RCA}}_0+\text{\textit{B\/}$\,\Sigma$}_2$ for $\Pi^1_1$-sentences. Thus, the set of first-order consequences of $\text{2-\textit{RAN\/}}$ is strictly stronger than $P^-+I\Sigma_1$ and no stronger than $P^-+\text{\textit{B\/}$\,\Sigma$}_2$. (shrink)

Modal logic has been applied in many different areas, as reasoning about time, knowledge and belief, necessity and possibility, to mention only some examples. In the present paper, an attempt is made to use modal logic to account for the semantics of theoretical sentences in scientific language. Theoretical sentences have been studied extensively since the work of Ramsey and Carnap. The present attempt at a modal analysis is motivated by there being several intended interpretations of the theoretical (...) terms once these terms are introduced through the axioms of a theory. (shrink)

Cheryl Misak offers a strikingly new view of the development of philosophy in the twentieth century. Pragmatism, the home-grown philosophy of America, thinks of truth not as a static relation between a sentence and the believer-independent world, but rather, a belief that works. The founders of pragmatism, Peirce and James, developed this idea in more and less objective ways. The standard story of the reception of American pragmatism in England is that Russell and Moore savaged James's theory, and that pragmatism (...) has never fully recovered. An alternative, and underappreciated, story is told here. The brilliant Cambridge mathematician, philosopher and economist, Frank Ramsey, was in the mid-1920s heavily influenced by the almost-unheard-of Peirce and was developing a pragmatist position of great promise. He then transmitted that pragmatism to his friend Wittgenstein, although had Ramsey lived past the age of 26 to see what Wittgenstein did with that position, Ramsey would not have liked what he saw. (shrink)

As is well-known, the Bernays-Schönfinkel-Ramsey class of all prenex ∃*∀* -sentences which are valid in classical first-order logic is decidable. This paper paves the way to an analogous result which the authors deem to hold when the only available predicate symbols are ∈ and =, no constants or function symbols are present, and one moves inside a (rather generic) Set Theory whose axioms yield the well-foundedness of membership and the existence of infinite sets. Here semi-decidability of the satisfiability (...) problem for the BSR class is proved by following a purely semantic approach, the remaining part of the decidability result being postponed to a forthcoming paper. (shrink)

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 (...) that they generate in other systems. In addition to standard Ramsey test conditionals, a more general variant of epistemic conditionals is defined, representing statements of the form ”if the belief state is changed to satisfy condition A then it will satisfy condition B”. An axiomatic characterization of such descriptor conditionals is presented. It is related in intricate ways to the KLM postulates for cumulative reasoning. (shrink)

The Ramsey-sentence H* of any hypothesis H is shown to be a synthetic proposition containing mathematics as a finite component. Far from being quasi-tautological, H* proves to have as much physical content as H itself.

We show that a theory of autonomous iterated Ramseyness based on second order arithmetic (SOA) is proof-theoretically equivalent to ${\Pi^1_2}$ -comprehension. The property of Ramsey is defined as follows. Let X be a set of real numbers, i.e. a set of infinite sets of natural numbers. We call a set H of natural numbers homogeneous for X if either all infinite subsets of H are in X or all infinite subsets of H are not in X. X has the (...) property of Ramsey if there exists a set which is homogeneous for X. The property of Ramsey is considered in reverse mathematics to compare the strength of subsystems of SOA. To characterize the system of ${\Pi^1_2}$ -comprehension in terms of Ramseyness we introduce a system of autonomous iterated Ramseyness, called R-calculus. We augment the language of SOA with additional set terms (called R-terms) ${R\vec{x}X\phi(\vec{x},X)}$ for each first order formula ${\phi(\vec{x},X)}$ (where φ may contain further R-terms). The R-calculus is a system which comprises comprehension for all first order formulas (which may contain R-terms or other set parameters) and defining axioms for the R-terms which claim that for each ${\vec{x}}$ , we can remove finitely many elements from the set ${R\vec{x}X\phi(\vec{x},X)}$ such that the remaining set is homogeneous for ${\{{X}{\phi(\vec{x},X)\}}}$ . We show that the R-calculus proves the same ${\Pi^1_1}$ -sentences as the system of ${\Pi^1_2}$ -comprehension. (shrink)

Most causal discovery algorithms in the literature exploit an assumption usually referred to as the Causal Faithfulness or Stability Condition. In this paper, we highlight two components of the condition used in constraint-based algorithms, which we call “Adjacency-Faithfulness” and “Orientation- Faithfulness.” We point out that assuming Adjacency-Faithfulness is true, it is possible to test the validity of Orientation- Faithfulness. Motivated by this observation, we explore the consequence of making only the Adjacency-Faithfulness assumption. We show that the familiar PC algorithm has (...) to be modified to be correct under the weaker, Adjacency-Faithfulness assumption. The modified algorithm, called Conservative PC (CPC), checks whether Orientation- Faithfulness holds in the orientation phase, and if not, avoids drawing certain causal conclusions the PC algorithm would draw. Howtion: ever, if the stronger, standard causal Faith-. (shrink)

The analytic/synthetic distinction can be conceived from two points of view: from within or from without; from the perspective of one's own language or from the perspective of the language of others. From without, the central question is which sentences of a foreign language are to be classified as analytic. From within, by contrast, the question concerning the synthetic and the analytic acquires a normative dimension: which sentences am I not permitted to reject—if I want to avoid talking (...) nonsense? Both perspectives on analytic sentences do not mutually exclude but supplement and illuminate each other. In "Two Dogmas", Quine's criticism of the analytic/synthetic distinction comes from within, whereas in Word and Object, Quine repeats his earlier criticism from without. His criticism is directed against Carnap's views on our understanding of theoretical terms. I challenge Quine's criticism in both of its versions and provide two definitions for analyticity that are immune to Quine's arguments. Using the first of these definitions (the one from without) I try to show how it is possible to distinguish (genuine) belief revision from linguistic change—even in case of a scientific revolution. (shrink)

A Christian ethicist discusses such problems as organ transplants, caring for the terminally ill, and defining death.

Deweyan pedagogy seeks to promotes growth, characterized as an increased sensitivity, responsiveness, and ability to participate in an environment. Growth, Dewey says, is fostered by the development of habits that enable further habit formation. Unfortunately, humans have their own habitual ways of encountering other species, which often do not support growth. In this article, I briefly review some common conceptions of learning and the process of habit-formation to scope out the landscape of a more responsible and responsive approach to taking (...) growth seriously. What emerges is a reflexive biosemiotics that has humans explicitly concerned with the in situ emergence of new signification in themselves and in other organisms. This requires we take a pedagogical stance in our attitudes and practices towards other species, which we can enrich with insights derived from re-interpreting traditional empirical studies. By freeing the habit-forming process from confining stereotype, a biological pedagogy can enable a more fluid and creative biosphere, unencumbered to explore unfolding possibilities in semiotic space. (shrink)

I consider the case of the “simplest” living beings—bacteria—and examine how their embodied activity constitutes an organism/environment interaction, out of which emerges the possibility of learning from an environment. I suggest that this mutual co-emergence of organism and environment implies a panbiotic educational interaction that is at once the condition for, and achievement of, all living beings. Learning and being learned from are entangled in varied ways throughout the biosphere. Education is not an exclusively human project, it is part of (...) the ancient evolutionary process of elaborating and diversifying the relational possibilities inherent in metabolism that has brought forth our diverse and flourishing world.ed from context, “education” appears as a set of ways in which humans actively engage and take responsibility for the learning outcomes of relationships with each other. Insofar as we consider this distinction absolute rather than a performed construct to be assessed by its consequences, we blind ourselves to the educative dimension of other species as well as our many miseducative engagements with them. If learning processes are inherent and constitutive of ecological communities, education theorists should devote their pedagogical sensitivities and insights to the crucial challenge of developing educative sustainable human–nature relations. (shrink)