A variation of Fitch’s Paradox is given, where no special rules of inference are assumed, only axioms. These axioms follow from the familiar assumptions which involve rules of inference. We show (by constructing a model) that by allowing that possibly the knower doesn’t know his own soundness (while still requiring he be sound), Fitch’s Paradox is avoided. Provided one is willing to admit that sound knowers may be ignorant of their own soundness, this might offer a way out (...) of the paradox. (shrink)
There is an argument (first presented by Fitch), which tries to show by formal means that the anti-realistic thesis that every truth might possibly be known, is equivalent to the unacceptable thesis that every truth is actually known (at some time in the past, present or future). First, the argument is presented and some proposals for the solution of Fitch'sParadox are briefly discussed. Then, by using Wehmeier's modal logic with subjunctive marks (S5*), it is shown how the (...) derivation can be blocked if one respects adequately the distinction between the indicative and the subjunctive mood. Essentially, this proposal amounts to the one by Edgington which was formulated with the help of the actuality-operator. Finally it is shown how the criticisms by Williamson against Edgington can be answered by the formulation of a new conception of possible knowledge that \alpha (thereby \alpha being in the indicative mood and thus referring to the actual world). This conception is based on the concept of same de re knowledge in different possible worlds. (shrink)
A number of authors have noted that the key steps in Fitch’s argument are not intuitionistically valid, and some have proposed this as a reason for an anti-realist to accept intuitionistic logic (e.g. Williamson 1982, 1988). This line of reasoning rests upon two assumptions. The first is that the premises of Fitch’s argument make sense from an anti-realist point of view – and in particular, that an anti-realist can and should maintain the principle that all truths are knowable. The second (...) is that we have some independent reason for thinking that classical logic is not appropriate in this area. This paper explores these two assumptions in the context of Michael Dummett’s version of anti-realism, with particular reference to the argument from indefinite extensibility developed at various points in Dummett’s writings (e.g. Dummett 1991 Ch. 24). -/- Dummett argues that certain concepts, the indefinitely extensible concepts, are such that we cannot form a clear and determinate conception of all the objects that fall under them. The most familiar examples of indefinitely extensible concepts are mathematical. Dummett discusses the concepts ordinal number, real number, and natural number, which are indefinitely extensible because any conception that one might form of their complete extension can be extended to a more inclusive conception (as, for example, in Cantor’s proof of the non-denumerability of the set of real numbers). This paper argues that the concept of a truth is indefinitely extensible. This gives a Dummettian anti-realist an independent motivation for rejecting the classical understanding of the quantifiers in this area. At the same time, however, it places in doubt the admissibility of the knowability principle, which seems to involve quantification over the “totality” of truths. As Dummett is at pains to point out (1991: 316), some sentences that purport to quantify over the extension of an indefinitely extensible concept plainly have a truth-value (we can truly say, for example, that every ordinal number has a successor, even though when we say that we are not quantifying over the set of all ordinals). But is the knowability principle one of these sentences? (shrink)
The paradox of knowability is a logical result suggesting that, necessarily, if all truths are knowable in principle then all truths are in fact known. The contrapositive of the result says, necessarily, if in fact there is an unknown truth, then there is a truth that couldn't possibly be known. More specifically, if p is a truth that is never known then it is unknowable that p is a truth that is never known. The proof has been used to (...) argue against versions of anti-realism committed to the thesis that all truths are knowable. For clearly there are unknown truths; individually and collectively we are non-omniscient. So, by the main result, it is false that all truths are knowable. The result has also been used to draw more general lessons about the limits of human knowledge. Still others have taken the proof to be fallacious, since it collapses an apparently moderate brand of anti-realism into an obviously implausible and naive idealism. (shrink)
The paper attempts to give a solution to the Fitch’s paradox though the strategy of the reformulation of the paradox in temporal logic, and a notion of knowledge which is a kind of ceteris paribus modality. An analogous solution has been offered in a different context to solve the problem of metaphysical determinism.
Recently predominant forms of anti-realism claim that all truths are knowable. We argue that in a logical explanation of the notion of knowability more attention should be paid to its epistemic part. Especially very useful in such explanation are notions of group knowledge. In this paper we examine mainly the notion of distributed knowability and show its effectiveness in the case of Fitch’s paradox. Proposed approach raised some philosophical questions to which we try to find responses. We also show (...) how we can combine our point of view on Fitch’s paradox with the others. Next we give an answer to the question: is distributed knowability factive? At the end, we present some details concerning a construction of anti-realist modal epistemic logic. (shrink)
Fitch’s paradox shows, from fairly innocent-looking assumptions, that if there are any unknown truths, then there are unknowable truths. This is generally thought to deliver a blow to antirealist positions that imply that all truths are knowable. The present paper argues that a probabilistic version of antirealism escapes Fitch’s result while still offering all that antirealists should care for.
This article shows that although Fitch’s paradox has been extremely widely studied, up to now no correct formalization of the problem has been proposed. The purpose of this article is to present the paradox front the viewpoint of combining logics. It is argued that the correct minimal logic to state the paradox is composed by a fusion of modal frames, and a fusion of modal languages and logics.
I have argued that without an adequate solution to the knower paradoxFitch's Proof is- or at least ought to be-ineffective against verificationism. Of course, in order to follow my suggestion verificationists must maintain that there is currently no adequate solution to the knower paradox, and that the paradox continues to provide prima facie evidence of inconsistent knowledge. By my lights, any glimpse at the literature on paradoxes offers strong support for the first thesis, and any (...) honest, non-dogmatic reflection on the knower paradox provides strong support for the second. Whether verificationists want to go the route I've suggested is not for me todecide. As in the previous section my aim has been that of defending the mere viability of verificationism in the face of what many, many philosophers have taken to be its death-knell, namely Fitch's Proof. But, as the final objection makes clear, showing that verificationism can live in the face of Fitch's Proof is one thing; showing that it should live is another project. If nothing else, I hope that this papershows that verificationists still have a project to pursue; Fitch's Proof, contrary to popular opinion, need not bury verificationism.13. (shrink)
(T5) ϕ → ◊Kϕ |-- ϕ → Kϕ where ◊ is possibility, and ‘Kϕ’ is to be read as ϕ is known by someone at some time. Let us call the premise the knowability principle and the conclusion near-omniscience.2 Here is a way of formulating Fitch’s proof of (T5). Suppose the knowability principle is true. Then the following instance of it is true: (p & ~Kp) → ◊K(p & ~Kp). But the consequent is false, it is not possible to know (...) p & ~Kp. That is because the supposition that it is known is provably inconsistent.3 The inconsistency requires us to deny the possibility of the supposition, yielding ~◊K(p & ~Kp). This, together with the above instance of the knowability principle, entails ~(p & ~Kp), which is (classically) equivalent to p → Kp. Since p occurs in none of our undischarged assumptions, we may generalize to get near-omniscience, ϕ → Kϕ. QED. (shrink)
To save antirealism from Fitchs Paradox, Tennant has proposed to restrict the scope of the antirealist principle that all truths are knowable to truths that can be consistently assumed to be known. Although the proposal solves the paradox, it has been accused of doing so in an ad hoc manner. This paper argues that, first, for all Tennant has shown, the accusation is just; second, a restriction of the antirealist principle apparently weaker than Tennants yields a non-ad hoc (...) solution to Fitchs Paradox; and third, the alternative is only apparently weaker than, and even provably equivalent to, Tennants. It is thereby shown that the latter is not ad hoc after all. (shrink)
In this paper, I propose a solution to Fitch’s paradox that draws on ideas from Edgington (Mind 94:557–568, 1985), Rabinowicz and Segerberg (1994) and Kvanvig (Noûs 29:481–500, 1995). After examining the solution strategies of these authors, I will defend the view, initially proposed by Kvanvig, according to which the derivation of the paradox violates a crucial constraint on quantifier instantiation. The constraint states that non-rigid expressions cannot be substituted into modal positions. We will introduce a slightly modified syntax (...) and semantics that will help underline this point. Furthermore, we will prove results about the consistency of verificationism and the principle of non-omniscience by model-theoretical means. Namely, we prove there exists a model of these principles, and delineate certain constraints they pose on a structure in which they are true. (shrink)
A well-known proof by Alonzo Church, first published in 1963 by Frederic Fitch, purports to show that all truths are knowable only if all truths are known. This is the Paradox of Knowability. If we take it, quite plausibly, that we are not omniscient, the proof appears to undermine metaphysical doctrines committed to the knowability of truth, such as semantic anti-realism. Since its rediscovery by Hart and McGinn ( 1976), many solutions to the paradox have been offered. In (...) this article, we present a new proof to the effect that not all truths are knowable, which rests on different assumptions from those of the original argument published by Fitch. We highlight the general form of the knowability paradoxes, and argue that anti-realists who favour either an hierarchical or an intuitionistic approach to the Paradox of Knowability are confronted with a dilemma: they must either give up anti-realism or opt for a highly controversial interpretation of the principle that every truth is knowable. (shrink)
Curry's paradox, sometimes described as a general version of the better known Russell's paradox, has intrigued logicians for some time. This paper examines the paradox in a natural deduction setting and critically examines some proposed restrictions to the logic by Fitch and Prawitz. We then offer a tentative counterexample to a conjecture by Tennant proposing a criterion for what is to count as a genuine paradox.
We propose contractionless constructive logic which is obtained from Nelson's constructive logic by deleting contractions. We discuss the consistency of a naive set theory based on the proposed logic in relation to Curry's paradox. The philosophical significance of contractionless constructive logic is also argued in comparison with Fitch's and Prawitz's systems.
This paper contributes to an increasing literature strengthening the connection between epistemic logic and epistemology (Van Benthem, Hendricks). I give a survey of the most important applications of epistemic logic in epistemology. I show how it is used in the history of philosophy (Steiner's reconstruction of Descartes' sceptical argument), in solutions to Moore's paradox (Hintikka), in discussions about the relation between knowledge and belief (Lenzen) and in an alleged refutation of verificationism (Fitch) and I examine an early argument about (...) the (im)possibility of epistemic logic (Hocutt). Subsequently, I deal with interpretive questions about epistemic logic that, although implicitly, already appeared in the first section. I contend that a conception of epistemic logic as a theory of knowledge assertions is incoherent, and I argue that it does not make sense to adopt a normative interpretation of epistemic logic. Finally, I show ways to extend epistemic logic with other branches of philosophical logic so as to make it useful for some epistemological questions. Conditional logics and logics of public announcement are used to understand causal theories of knowledge and versions of reliabilism. Temporal logic helps understand some dynamic aspects of knowledge as well as the verificationist thesis. (shrink)
Fitch's basic logic is an untyped illative combinatory logic with unrestricted principles of abstraction effecting a type collapse between properties (or concepts) and individual elements of an abstract syntax. Fitch does not work axiomatically and the abstraction operation is not a primitive feature of the inductive clauses defining the logic. Fitch's proof that basic logic has unlimited abstraction is not clear and his proof contains a number of errors that have so far gone undetected. This paper corrects these (...) errors and presents a reasonably intuitive proof that Fitch's system K supports an implicit abstraction operation. Some general remarks on the philosophical significance of basic logic, especially with respect to neo-logicism, are offered, and the paper concludes that basic logic models a highly intensional form of logicism. (shrink)
Anti-realist epistemic conceptions of truth imply what is called the knowability principle: All truths are possibly known. The principle can be formalized in a bimodal propositional logic, with an alethic modality $${\diamondsuit}$$ and an epistemic modality $${\mathcal{K}}$$ , by the axiom scheme $${A \supset \diamondsuit \mathcal{K} A}$$ ( KP ). The use of classical logic and minimal assumptions about the two modalities lead to the paradoxical conclusion that all truths are known, $${A \supset \mathcal{K} A}$$ ( OP ). A Gentzen-style (...) reconstruction of the Church–Fitch paradox is presented following a labelled approach to sequent calculi. First, a cut-free system for classical (resp. intuitionistic) bimodal logic is introduced as the logical basis for the Church–Fitch paradox and the relationships between $${\mathcal {K}}$$ and $${\diamondsuit}$$ are taken into account. Afterwards, by exploiting the structural properties of the system, in particular cut elimination, the semantic frame conditions that correspond to KP are determined and added in the form of a block of nonlogical inference rules. Within this new system for classical and intuitionistic “knowability logic”, it is possible to give a satisfactory cut-free reconstruction of the Church–Fitch derivation and to confirm that OP is only classically derivable, but neither intuitionistically derivable nor intuitionistically admissible. Finally, it is shown that in classical knowability logic, the Church–Fitch derivation is nothing else but a fallacy and does not represent a real threat for anti-realism. (shrink)
Fitch’s paradox of knowability is an apparently valid reasoning from the assumption (typical of semantic anti-realism) that every true proposition is knowable to the unacceptable conclusion that every true proposition is known. The paper develops a critical dialectic wrt one of the best motivated solutions to the paradox which have been proposed on behalf of semantic anti-realism—namely, the intuitionistic solution. The solution consists, on the one hand, in accepting the intuitionistically valid part of Fitch’s reasoning while, on the (...) other hand, exploiting the characteristic weakness of intuitionistic logic in order to preserve the consistency of such acceptance with the denial of omniscience. It is first remarked how the solution still commits one to acceptance of modal claims which are unwarranted even by the lights of standard intuitionistic semantics. A novel form of the paradox is then introduced, which focuses on infallibility rather than omniscience and derives, from semantic anti-realism and a highly plausible constraint on knowledge, that every believed proposition is not untrue. Because of the logical form of this conclusion, an analogue of the intuitionistic solution for the novel form of the paradox would require drawing the characteristic intuitionistic distinctions wrt decidable propositions, which cannot be done. Semantic anti-realism still intuitionistically entails the unacceptable conclusion that every believed (decidable) proposition is true. (shrink)
An interesting recent reply to the Paradox of Knowability is Neil Tennant's proposal: to restrict the anti-realist's knowability thesis to truths the knowing of which is logically consistent. However, this proposal is egregiously ad hoc unless motivated by something other than the wish to save anti-realism from embarrassment. We examine Tennant's argument that his restriction is motivated by parallel considerations in cases that are neutral with respect to debates about realism. We conclude that the cases are not neutral, nor (...) the considerations parallel. The failure of Tennant's argument provides an opportunity to reflect on, among other things, the nature of Moore's paradox, and the role of idealization in doxastic logic. (shrink)
The paradox of knowability and the debate about it are shortly presented. Some assumptions which appear more or less tacitly involved in its discussion are made explicit. They are embedded and integrated in a Russellian framework, where a formal paradox, very similar to the Russell-Myhill paradox, is derived. Its solution is provided within a Russellian formal logic introduced by A. Church. It follows that knowledge should be typed. Some relevant aspects of the typing of knowledge are pointed (...) out. (shrink)
I argue that Fitch’s ‘paradox of knowability’ presents no special problem for the epistemic anti-realist who believes that reality is epistemically accessible to us. For the claim which is the target of the argument (If p then it is possible to know p) is not a commitment of anti-realism. The epistemic anti-realist’s commitment is (or should be) to the recognizability of the states of affairs which render true propositions true, not to the knowability of the propositions themselves. A formal (...) apparatus for discussing the recognizability of states of affairs is offered, and other prima facie similar approaches to the paradox argument are reviewed. (shrink)
According to the “knowability thesis,” every truth is knowable. Fitch’s paradox refutes the knowability thesis by showing that if we are not omniscient, then not only are some truths not known, but there are some truths that are not knowable. In this paper, I propose a weakening of the knowability thesis (which I call the “conjunctive knowability thesis”) to the e:ect that for every truth p there is a collection of truths such that (i) each of them is knowable (...) and (ii) their conjunction is equivalent to p. I show that the conjunctive knowability thesis avoids triviality arguments against it, and that it fares very di:erently depending on another thesis connecting knowledge and possibility. If there are two propositions, inconsistent with one another, but both knowable, then the conjunctive knowability thesis is trivially true. On the other hand, if knowability entails truth, the conjunctive knowability thesis is coherent, but only if the logic of possibility is weak. (shrink)
This study continues the anti-realist’s quest for a principled way to avoid Fitch’s paradox. It is proposed that the Cartesian restriction on the anti-realist’s knowability principle ‘ϕ, therefore 3Kϕ’ should be formulated as a consistency requirement not on the premise ϕ of an application of the rule, but rather on the set of assumptions on which the relevant occurrence of ϕ depends. It is stressed, by reference to illustrative proofs, how important it is to have proofs in normal form (...) before applying the proposed restriction. A similar restriction is proposed for the converse inference, the so-called Rule of Factiveness ‘3Kϕ therefore ϕ’. The proposed restriction appears to block another Fitch-style derivation that uses the KK -thesis in order to get around.. (shrink)
This paper presents a generalized form of Fitch’s paradox of knowability, with the aim of showing that the questions it raises are not peculiar to the topics of knowledge, belief, or other epistemic notions. Drawing lessons from the generalization, the paper offers a solution to Fitch’s paradox that exploits an understanding of modal talk about what could be known in terms of capacities to know. It is argued that, in rare cases, one might have the capacity to know (...) that p even if it is metaphysically impossible for anyone to know that p , and that recognizing this fact provides the resources to solve Fitch’s paradox. (shrink)
In discussions of Fitch’s paradox, it is usually assumed without further argument that knowledge is factive, that if a subject knows that p, then p is true. It is argued that this common assumption is not as well-founded as it should be, and that there in fact are certain reasons to be suspicious of the unrestricted version of the factiveness claim. There are two kinds of reason for this suspicion. One is that unrestricted factiveness leads to paradoxes and unexpected (...) results, the other is that the usual arguments for factiveness are not as compelling as is commonly thought. There may in fact be some kinds of contexts, where factiveness doesn’t hold for knowledge—the usual arguments for factiveness don’t suffice to support the claim that knowledge is unrestrictedly factive. Perhaps all that can be shown is that knowledge is at times factive, or that it is default factive, as it were: this doesn’t show that there can’t be counterexamples, however. Certain aspects of knowledge without unrestricted factiveness are examined briefly. (shrink)
Nicholas Rescher, in The Limits of Science (1984), argued that: «perfected science is a mirage; complete knowledge a chimera» . He reached the above conclusion from a logical argument known as Fitch’s Paradox of Knowability. The argument, starting from the assumption that every truth is knowable, proves that every truth is also actually known and, given that some true propositions are not actually known, it concludes, by modus tollens, that there are unknowable truths. Prima facie, this argument seems to (...) seriously narrow our epistemic possibilities and to constitute a limit for knowledge (included scientific knowledge). Rescher’s above quoted conclusion follows the same sort of reasoning. Recently, Bernard Linsky exploited a possible way to block the argument employing a type-distinction of knowledge. If the Knowability paradox is blocked, then Rescher’s conclusion cannot be drawn. After an introduction to the paradox, we suggest, in our paper, a possible way of justifying a type-solution for it in the scientific field. A noteworthy point is that the effectiveness of this solution depends on the degree of reductionism adopted in science: the given solution is available only if we do not adopt a complete reductionism in science so that there is just one kind of scientific knowledge and, consequently, of scientific justification. Otherwise Rescher's argument still works. (shrink)
Verificationism is the doctrine stating that all truths are knowable. Fitch’s knowability paradox, however, demonstrates that the verificationist claim (all truths are knowable) leads to “epistemic collapse”, i.e., everything which is true is (actually) known. The aim of this article is to investigate whether or not verificationism can be saved from the effects of Fitch’s paradox. First, I will examine different strategies used to resolve Fitch’s paradox, such as Edgington’s and Kvanvig’s modal strategy, Dummett’s and Tennant’s restriction (...) strategy, Beall’s paraconsistent strategy, and Williamson’s intuitionistic strategy. After considering these strategies I will propose a solution that remains within the scope of classical logic. This solution is based on the introduction of a truth operator. Though this solution avoids the shortcomings of the non-standard (intuitionistic) solution, it has its own problems. Truth, on this approach, is not closed under the rule of conjunction-introduction. I will conclude that verificationism is defensible, though only at a rather great expense. (shrink)
If proofs are nothing more than truth makers, then there is no force in the standard argument against classical logic (there is no guarantee that there is either a proof forA or a proof fornot A). The standard intuitionistic conception of a mathematical proof is stronger: there are epistemic constraints on proofs. But the idea that proofs must be recognizable as such by us, with our actual capacities, is incompatible with the standard intuitionistic explanations of the meanings of the logical (...) constants. Proofs are to be recognizable in principle, not necessarily in practice, as shown in section 1. Section 2 considers unknowable propositions of the kind involved in Fitch''s paradox:p and it will never be known thatp. It is argued that the intuitionist faces a dilemma: give up strongly entrenched common sense intuitions about such unknowable propositions, or give up verificationism. The third section considers one attempt to save intuitionism while partly giving up verificationism: keep the idea that a proposition is true iff there is a proof (verification) of it, and reject the idea that proofs must be recognizable in principle. It is argued that this move will have the effect that some standard reasons against classical semantics will be effective also against intuitionism. This is the case with Dummett''s meaning theoretical argument. At the same time the basic reason for regarding proofs as more than mere truth makers is lost. (shrink)
(PDF of penultimate draft; please don’t quote from or cite this version.) Forthcoming in Synthese. Generalizations of Fitch’s paradox of knowability motivate the thesis that in saying that a truth is knowable, or that it could be known, we do not mean that it is possible that it is known. Instead, I argue, claims about knowability express capacities to know. The paper concludes by explaining the requisite sense of “capacity” at work here, and by showing how the paradox (...) of knowability and its generalizations are solved. (shrink)
The naive anti-realist holds the following principle: (◊K) All truths are knowable. This unrestricted generalization (◊K), as is now well known, falls prey to Fitch’s Paradox (Fitch 1963: 38, Theorem 1). It can be used as the only suspect principle, alongside others that cannot be impugned, to prove quite generally, and constructively, that the set {p, ¬Kp} is inconsistent (Tennant 1997: 261). From this it would follow, intuitionistically, that any proposition that is never actually known to be true (by (...) anyone, at any time) is false; and it would follow, classically, that every truth is known (by someone, at some time). (shrink)
This paper adds temporal logic to public announcement logic (PAL) and dynamic epistemic logic (DEL). By adding a previous-time operator to PAL, we express in the language statements concerning the muddy children puzzle and sum and product. We also express a true statement that an agent’s beliefs about another agent’s knowledge flipped twice, and use a sound proof system to prove this statement. Adding a next-time operator to PAL, we provide formulas that express that belief revision does not take place (...) in PAL. We also discuss relationships between announcements and the new knowledge agents thus acquire; such relationships are related to learning and to Fitch’s paradox. We also show how inverse programs and hybrid logic each can be used to help determine whether or not an arbitrary structure represents the play of a game. We then add a past-time operator to DEL, and discuss the importance of adding yet another component to the language in order to prove completeness. (shrink)
A well-known open problem in epistemic logic is to give a syntactic characterization of the successful formulas. Semantically, a formula is successful if and only if for any pointed model where it is true, it remains true after deleting all points where the formula was false. The classic example of a formula that is not successful in this sense is the “Moore sentence” p ∧ ¬BOXp, read as “p is true but you do not know p.” Not only is the (...) Moore sentence unsuccessful, it is self-refuting, for it never remains true as described. We show that in logics of knowledge and belief for a single agent (extended by S5), Moorean phenomena are the source of all self-refutation; moreover, in logics for an introspective agent (extending KD45), Moorean phenomena are the source of all unsuccessfulness as well. This is a distinctive feature of such logics, for with a non-introspective agent or multiple agents, non-Moorean unsuccessful formulas appear. We also consider how successful and self-refuting formulas relate to the Cartesian and learnable formulas, which have been discussed in connection with Fitch’s “paradox of knowability.” We show that the Cartesian formulas are exactly the formulas that are not eventually self-refuting and that not all learnable formulas are successful. In an appendix, we give syntactic characterizations of the successful and the self-refuting formulas. (shrink)
Since its disc overy by Fitch, the paradox of knowability has been a thorn in the anti-realist's side. Recently both Dummett and Tennant have sought to relieve the anti-realist by restricting the applicability of the knowability principle -- the principle that all truths are knowable -- which has been viewed as both a cardinal doctrine of anti-realism and the assumption for reductio of Fitch's argument. In this paper it is argued that the paradox of knowability is a (...) peculiarly acute manifestation of a syndrome affecting anti-realism, against which Dummett's and Tennant's manoeuvres are not finally efficacious. The anti-realist can only cope with the syndrome by being much clearer about her notion of knowability. In fact, she'll have to offer an account which relativises the notion of knowability both to the world at which knowability is assessed and to the content of the proposition to which it is applied. This is not, however, merely an ad hoc manoeuvre to counter the problematic syndrome; rather it is just what we should expect from the anti-realist's intuitive use of the notion. A preliminary investigation indicates that there is no way of providing a general, systematic explanation of such a notion of knowability and thus an inherent restriction on the principle of knowability -- but one differing from those offered by either Dummett or Tennant -- is developed. (shrink)
The so-called knowability paradox results from Fitch's argument that if there are any unknown truths, then there are unknowable truths. This threatens recent versions of semantical antirealism, the central thesis of which is that truth is epistemic. When this is taken to mean that all truths are knowable, antirealism is thus committed to the conclusion that no truths are unknown. The correct antirealistic response to the paradox should be to deny that the fundamental thesis of the epistemic (...) nature of truth entails the knowability of all truths. Correctly understood, the antirealistic conditions on a proposition's truth do not require that the proposition possess a verification-procedure which, when executed under the given conditions, issues in an agent's recognition of truth, but merely that there be a verification-procedure which, under these conditions, takes the value true . The knowability paradox and the related idealism problem (that antirealism seems, but is not, committed to the necessary existence of an epistemic agent) draw attention to the fact that certain propositions, those that are about verification-procedures themselves, may under certain conditions take the value true despite their unperformability under these circumstances. Thus these propositions' procedures can only be performed when the propositions are false, and they gain the appearance of antirealistic impossibility (e.g., that there is an unknown truth). This differs from the unperformability that antirealists object to, pertaining merely to matters of execution rather than to the logical structure of the procedures themselves. The force of antirealism's notion of epistemic truth is piecemeal, rather than consisting in a blanket characterization of truth as knowable. (shrink)
This paper addresses an objection raised by Timothy Williamson to the ‘restriction strategy’ that I proposed, in The Taming of The True, in order to deal with the Fitch paradox. Williamson provides a new version of a Fitch-style argument that purports to show that even the restricted principle of knowability suffers the same fate as the unrestricted one. I show here that the new argument is fallacious. The source of the fallacy is a misunderstanding of the condition used in (...) stating the restricted knowability principle. I also rebut Williamson’s criticism of my argument for the claim that any proposition of the form ‘it is known that ϕ’ is decidable if ϕ is decidable. (shrink)
Reminiscences of Peter, by P. Oppenheim.--Natural kinds, by W. V. Quine.--Inductive independence and the paradoxes of confirmation, by J. Hintikka.--Partial entailment as a basis for inductive logic, by W. C. Salmon.--Are there non-deductive logics?, by W. Sellars.--Statistical explanation vs. statistical inference, by R. C. Jeffre--Newcomb's problem and two principles of choice, by R. Nozick.--The meaning of time, by A. Grünbaum.--Lawfulness as mind-dependent, by N. Rescher.--Events and their descriptions: some considerations, by J. Kim.--The individuation of events, by D. Davidson.--On properties, by (...) H. Putnam.--A method for avoiding the Curry paradox, by F. B. Fitch.--Publications (1934-1969) by Carl G. Hempel (p. [266]-270). (shrink)
First, some reminiscences. In the years 1973-80, when I was an undergraduate and then graduate student at Oxford, Michael Dummett’s formidable and creative philosophical presence made his arguments impossible to ignore. In consequence, one pole of discussion was always a form of anti-realism. It endorsed something like the replacement of truth-conditional semantics by verification-conditional semantics and of classical logic by intuitionistic logic, and the principle that all truths are knowable. It did not endorse the principle that all truths are known. (...) Nor did it mention the now celebrated argument, first published by Frederic Fitch (1963), that if all truths are knowable then all truths are known. (shrink)
In an attempt to improve upon Alexander Pruss’s work (2006, pp. 240-248), I (Weaver, 2012) have argued that if all purely contingent events could be caused and something like a Lewisian analysis of causation is true (per Lewis, 2004), then all purely contingent events have causes. I dubbed the derivation of the universality of causation the “Lewisian argument”. The Lewisian argument assumed not a few controversial metaphysical theses, particularly essentialism, an incommunicable-property view of essences (per Plantinga 2003), and the idea (...) that counterfactual dependence is necessary for causation. There are, of course, substantial objections to such theses. While I think a fight against objections to the Lewisian argument can be won, I develop, in what follows, a much more intuitive argument for the universality of causation which takes as its inspiration a result from Frederic Fitch’s work (1963) (with credit to who we now know was Alonzo Church (2009)) that if all truths are such that they are knowable, then (counter-intuitively) all truths are known. The resulting Church-Fitch proof for the universality of causation is preferable to the Lewisian argument since it rests upon far weaker formal and metaphysical assumptions than those of the Lewisian argument. (shrink)
We examine the question of which aspects of language are uniquely human and uniquely linguistic in light of recent suggestions by Hauser, Chomsky, and Fitch that the only such aspect is syntactic recursion, the rest of language being either specific to humans but not to language (e.g. words and concepts) or not specific to humans (e.g. speech perception). We find the hypothesis problematic. It ignores the many aspects of grammar that are not recursive, such as phonology, morphology, case, agreement, and (...) many properties of words. It is inconsistent with the anatomy and neural control of the human vocal tract. And it is weakened by experiments suggesting that speech perception cannot be reduced to primate audition, that word learning cannot be reduced to fact learning, and that at least one gene involved in speech and language was evolutionarily selected in the human lineage but is not specific to recursion. The recursion-only claim, we suggest, is motivated by Chomsky’s recent approach to syntax, the Minimalist Program, which de-emphasizes the same aspects of language. The approach, however, is sufficiently problematic that it cannot be used to support claims about evolution. We contest related arguments that language is not an adaptation, namely that it is “perfect,” non-redundant, unusable in any partial form, and badly designed for.. (shrink)
The intuitionistic conception of truth defended by Dummett, Martin Löf and Prawitz, according to which the notion of proof is conceptually prior1 to the notion of truth, is a particular version of the epistemic conception of truth. The paradox of knowability (first published by Frederic Fitch in 1963) has been described by many authors2 as an argument which threatens the epistemic, and the intuitionistic, conception of truth. In order to establish whether this is really so, one has to understand (...) what the epistemic conception of truth really is. So I shall start inpart I with a description of the matter at issue between theepistemic conception of truth and the opposite position, therealistic conception of truth. Inpart II I shall very briefly describe the paradox. Inpart III I shall try to answer the question which appears in the title of this paper: What can we learn from the paradox of knowability?. My conclusion will be that the paradox of knowability is not a refutation of the epistemic conception of truth, but helps us to better formulate (and understand) such a view. (shrink)
In a continuation of the conversation with Fitch, Chomsky, and Hauser on the evolution of language, we examine their defense of the claim that the uniquely human, language-specific part of the language faculty (the “narrow language faculty”) consists only of recursion, and that this part cannot be considered an adaptation to communication. We argue that their characterization of the narrow language faculty is problematic for many reasons, including its dichotomization of cognitive capacities into those that are utterly unique and those (...) that are identical to nonlinguistic or nonhuman capacities, omitting capacities that may have been substantially modified during human evolution. We also question their dichotomy of the current utility versus original function of a trait, which omits traits that are adaptations for current use, and their dichotomy of humans and animals, which conflates similarity due to common function and similarity due to inheritance from a recent common ancestor. We show that recursion, though absent from other animals’ communications systems, is found in visual cognition, hence cannot be the sole evolutionary development that granted language to humans. Finally, we note that despite Fitch et al.’s denial, their view of language evolution is tied to Chomsky’s conception of language itself, which identifies combinatorial productivity with a core of “narrow syntax.” An alternative conception, in which combinatoriality is spread across words and constructions, has both empirical advantages and greater evolutionary plausibility. q 2005 Elsevier B.V. All rights reserved. (shrink)
In a continuation of the conversation with Fitch, Chomsky, and Hauser on the evolution of language, we examine their defense of the claim that the uniquely human, language-specific part of the language faculty (the “narrow language faculty”) consists only of recursion, and that this part cannot be considered an adaptation to communication. We argue that their characterization of the narrow language faculty is problematic for many reasons, including its dichotomization of cognitive capacities into those that are utterly unique and those (...) that are identical to nonlinguistic or nonhuman capacities, omitting capacities that may have been substantially modified during human evolution. We also question their dichotomy of the current utility versus original function of a trait, which omits traits that are adaptations for current use, and their dichotomy of humans and animals, which conflates similarity due to common function and similarity due to inheritance from a recent common ancestor. We show that recursion, though absent from other animals’ communications systems, is found in visual cognition, hence cannot be the sole evolutionary development that granted language to humans. Finally, we note that despite Fitch et al.’s denial, their view of language evolution is tied to Chomsky’s conception of language itself, which identifies combinatorial productivity with a core of “narrow syntax.” An alternative conception, in which combinatoriality is spread across words and constructions, has both empirical advantages and greater evolutionary plausibility. q 2005 Elsevier B.V. All rights reserved. (shrink)
We examine the question of which aspects of language are uniquely human and uniquely linguistic in light of recent suggestions by Hauser, Chomsky, and Fitch that the only such aspect is syntactic recursion, the rest of language being either specific to humans but not to language (e.g. words and concepts) or not specific to humans (e.g. speech perception). We find the hypothesis problematic. It ignores the many aspects of grammar that are not recursive, such as phonology, morphology, case, agreement, and (...) many properties of words. It is inconsistent with the anatomy and neural control of the human vocal tract. And it is weakened by experiments suggesting that speech perception cannot be reduced to primate audition, that word learning cannot be reduced to fact learning, and that at least one gene involved in speech and language was evolutionarily selected in the human lineage but is not specific to recursion. The recursion-only claim, we suggest, is motivated by Chomsky’s recent approach to syntax, the Minimalist Program, which de-emphasizes the same aspects of language. The approach, however, is sufficiently problematic that it cannot be used to support claims about evolution. We contest related arguments that language is not an adaptation, namely that it is “perfect,” non-redundant, unusable in any partial form, and badly designed for.. (shrink)
Symlog is a system for learning symbolic logic by computer that allows students to interactively construct proofs in Fitch-style natural deduction. On request, Symlog can provide guidance and advice to help a student narrow the gap between goal theorem and premises. To effectively implement this capability, the program was equipped with a theorem prover that constructs proofs using the same methods and techniques the students are being taught. This paper discusses some of the aspects of the theorem prover's design, including (...) its set of proof-construction strategies, its unification algorithm as well as some of the tradeoffs between efficiency and pedagogy. (shrink)
The knowability paradox derives from a proof by Frederic Fitch in 1963. The proof purportedly shows that if all truths are knowable, it follows that all truths are known. Antirealists, wed as they are to the idea that truth is epistemic, feel threatened by the proof. For what better way to express the epistemic character of truth than to insist that all truths are knowable? Yet, if that insistence logically compels similar assent to some omniscience claim, antirealism is in (...) jeopardy. Response to the paradox has drifted toward a common theme, a theme I will argue is a non-starter in resolving the paradox. Seeing this point will also make clear the philosophical inadequacy of simply viewing the paradox as a refutation of a wide range of antirealisms. (shrink)
This paper considers two deflationary responses to the Fitch argument on behalf of the semantic anti-realistthat is, two responses which aim to evade the conclusion of that argument by, on a principled basis, weakening one of the principles essentially employed. The first deflationary approach that is consideredwhich proceeds by weakening the factivity principle for knowledgeis shown to be ultimately unpromising, but a second approachwhich proceeds by weakening the knowability principle that is at the heart of semantic anti-realismis shown to have (...) considerable prima facie appeal. It is then argued that some key objections that one might raise for this approach are on closer inspection ineffective. (shrink)
Metaphysics and language: Quine, W. V. O. On the individuation of attributes. Körner, S. On some relations between logic and metaphysics. Marcus, R. B. Does the principle of substitutivity rest on a mistake? Van Fraassen, B. C. Platonism's pyrrhic victory. Martin, R. M. On some prepositional relations. Kearns, J. T. Sentences and propositions.--Basic and combinatorial logic: Orgass, R. J. Extended basic logic and ordinal numbers. Curry, H. B. Representation of Markov algorithms by combinators.--Implication and consistency: Anderson, A. R. Fitch on (...) consistency. Belnap, N. D., Jr. Grammatical propaedeutic. Thomason, R. H. Decidability in the logic of conditionals. Myhill, J. Levels of implication.--Deontic, epistemic, and erotetic logic: Bacon, J. Belief as relative knowledge. Wu, K. J. Believing and disbelieving. Kordig, C. R. Relativized deontic modalities. Harrah, D. A system for erotetic sentences. (shrink)
Fitch’s argument purports to show that for any unknown truth, p , there is an unknowable truth, namely, that p is true and unknown; for a contradiction follows from the assumption that it is possible to know that p is true and unknown. In earlier work I argued that there is a sense in which it is possible to know that p is true and unknown, from a counterfactual perspective; that is, there can be possible, non-actual knowledge, of the actual (...) situation, that in that situation, p is true and unknown. Here I further elaborate that claim and respond to objections by Williamson, who argued that there cannot be non-trivial knowledge of this kind. I give conditions which suffice for such non-trivial counterfactual knowledge. (shrink)
The paper seeks a perfectly general argument regarding the non-contingent limits to any (human or non-human) knowledge. After expressing disappointment with the history of philosophy on this score, an argument is grounded in Fitch’s proof, which demonstrates the unknowability of some truths. The necessity of this unknowability is then defended by arguing for the necessity of Fitch’s premise—viz., there this is in fact some ignorance.
The general verificationist thesis says that What is true can be known or formally: φ → ◊Kφ VT Fitch's argument trivializes this principle. It uses a weak modal epistemic logic to show that VT collapses truth and knowledge, by taking a clever substitution instance for φ: P ∧ ¬KP → ◊ K(P ∧ ¬KP) Then we have the following chain of three conditionals (a) ◊ K(P ∧ ¬KP) → ◊ (KP ∧ K¬KP) in the minimal modal logic for the (...) knowledge operator K, (b) ◊ (KP ∧ K¬KP) → ◊ (KP ∧¬KP) in the modal logic T, and finally (c) ◊ (KP ∧¬KP) → ⊥ in the minimal modal logic for. (shrink)
The evolution of human language, and the kind of thought the communication of which requires it, raises considerable explanatory challenges. These systems of representation constitute a radical discontinuity in the natural world. Even species closely related to our own appear incapable of either thought or talk with the recursive structure, generalized systematicity, and task-domain neutrality that characterize human talk and the thought it expresses. W. Tecumseh Fitch’s proposal (2004, in press) that human language is descended from a sexually selected, prosodic (...) proto-language that approximated its syntactic complexity, and later acquired semantics thanks to kin selection for its use as a means of pedagogical transmission, has the promise of meeting these explanatory challenges. However, Fitch’s theory raises two problems of its own: (1) according to Boyd and Richerson (1996, Proc. Br. Acad. 88: 77–93), circumstances in which pedagogy is adaptive are inevitably rare in nature, and (2) it is unlikely that our non-discursive precursors had generally systematic, task-domain neutral thoughts to communicate to their offspring. I propose solutions to these problems. Pedagogy would be favored in a population where complex rituals dominated diverse aspects of life. Prosodic proto-language could emerge as the medium of pedagogic transmission. As this medium was used to teach a greater variety of tasks, it would become increasingly general and domain neutral. The presence and importance of such a system of communication in hominid populations could then drive, via Baldwinian mechanisms, the evolution of a kind of ‘thinking for speaking’ (Slobin 1991, Pragmatics 1: 7–25) characterized by recursive structure, generalized systematicity, and task-domain neutrality. (shrink)
Fitch showed that not every true proposition can be known in due time; in other words, that not every proposition is knowable. Moore showed that certain propositions cannot be consistently believed. A more recent dynamic phrasing of Moore-sentences is that not all propositions are known after their announcement, i.e., not every proposition is successful. Fitch's and Moore's results are related, as they equally apply to standard notions of knowledge and belief (S 5 and KD45, respectively). If we interpret ‘successful’ (...) as ‘known after its announcement’ and ‘knowable’ as ‘known after some announcement’, successful implies knowable. Knowable does not imply successful: there is a proposition ϕ that is not known after its announcement but there is another announcement after which ϕ is known. We show that all propositions are knowable in the more general sense that for each proposition, it can become known or its negation can become known. We can get to know whether it is true: ◊(Kϕ ∨ K¬ϕ). This result comes at a price. We cannot get to know whether the proposition was true. This restricts the philosophical relevance of interpreting ‘knowable’ as ‘known after an announcement’. (shrink)
Some of the most interesting recent work in philosophy of language and metaphysics is focused on questions about propositions, the abstract, truth-bearing contents of sentences and beliefs. The aim of this guide is to give instructors and students a road map for some significant work on propositions since the mid-1990s. This work falls roughly into two areas: challenges to the existence of propositions and theories about the nature and structure of propositions. The former includes both a widely discussed puzzle about (...) propositional designators as well as direct and indirect arguments against the existence of propositions. The latter is dominated by what is currently the central debate about the metaphysics of propositions, i.e. whether they are structured, composite entities or unstructured ontological simples. This issue has eclipsed older debates about whether propositions can be identified with sets of possible worlds or other kinds of sentence intensions. Author Recommends 1. Soames, Scott. 'Direct Reference, Propositional Attitudes, and Semantic Content.' Philosophical Topics 15 (1987): 47–87. Reprinted in Propositions and Attitudes . Eds. N. Salmon and S. Soames. Oxford: Oxford University Press, 1988. 197–239. Essential groundwork for more recent work on propositions. Soames gives a careful and exacting presentation of the case against identifying propositions with sets of possible worlds or other truth-supporting circumstances. Also contains a detailed statement of the Russellian conception of propositions on which propositions are ordered sets of objects, properties and relations. 2. King, Jeffrey. 'Designating Propositions.' The Philosophical Review 111 (2002): 341–71. Sometimes substituting a definite description for a corresponding 'that'-clause can lead to bizarre changes in truth-conditions: compare 'Bill fears that Hillary will be president' with 'Bill fears the proposition that Hillary will be president'. This puzzle about propositional designators threatens the relational analysis of propositional attitude reports, the view that 'believes' expresses a relation to the proposition designated by its 'that'-clause, and thereby poses an indirect threat to the existence of propositions. King's solution posits an ambiguity in verbs like 'fear' that embed both 'that'-clauses and definite descriptions. 3. Jubien, Michael. 'Propositions and the Objects of Thought.' Philosophical Studies 104 (2001): 47–62. A direct attack on the existence of propositions. Jubien deploys an analogue of the problem that Paul Benacerraf raised for set-theoretical reductions of numbers against metaphysical reductions of propositions. Just as numbers can be reduced to sets in many different ways, any reduction of propositions brings with it equally good variants, thus making any such reduction arbitrary and unmotivated. The only alternative is to treat propositions as abstract metaphysical primitives. As Jubien argues, however, abstract primitive entities are incapable of doing what propositions must do, i.e. represent objects and states of affairs on their own, without the input of thinking subjects. The upshot is the propositions cannot be reduced and they cannot be primitive, and so they must not exist. 4. Hanks, Peter. 'How Wittgenstein Defeated Russell's Multiple Relation Theory of Judgment.' Synthese 154 (2007): 121–46. Scepticism about propositions has recently led some philosophers, Jubien included, to resuscitate Russell's multiple relation theory of judgment, the idea that judgment is a many-place relation to objects, properties and relations. This paper explains why Russell himself abandoned that theory, and why the theory is still refuted by an objection due to Wittgenstein. 5. Hofweber, Thomas. 'Inexpressible Properties and Propositions.' Oxford Studies in Metaphysics . 2 vols. Ed. D. Zimmerman. Oxford: Oxford University Press, 2006. 155–206. An indirect attack on the existence of propositions. Hofweber argues that sentences like 'Bill believes something that Hillary asserted' do not commit us to the existence of propositions. His view is that propositional quantification is an instance of what he calls 'internal' or 'inferential role' quantification, a kind of quantification that carries no ontological implications. 6. Schiffer, Stephen. The Things We Mean . Oxford: Oxford University Press, 2003. esp. chs 1–2. Schiffer defends his theory of pleonastic propositions, on which propositions are unstructured, have no parts, and are very finely grained. 7. Bealer, George. 'Propositions.' Mind 107 (1998): 1–32. Bealer defends his algebraic theory of propositions, which, like Schiffer's pleonastic account, treats propositions as unstructured metaphysical simples. 8. King, Jeffrey. The Nature of and Structure of Content . Oxford: Oxford University Press, 2007. The best developed current theory of the structure in structured propositions. King identifies propositions with certain kinds of facts in which objects, properties and relations are bound together by amalgams of syntactic and semantic relations. 9. Hanks, Peter. 'Recent Work on Propositions.' Philosophy Compass 4 (2009): 1–18. A survey of work on propositions since the mid-1990s that complements this teaching and learning guide. Contains responses to Jubien's and Hofweber's arguments against propositions and critical discussions of Schiffer's pleonastic propositions and King's theory of propositional structure. Online Resources 1. http://plato.stanford.edu/entries/propositions/ Propositions (Matthew McGrath) 2. http://plato.stanford.edu/entries/propositions-structured/ Structured Propositions (Jeffrey King) 3. http://plato.stanford.edu/entries/propositions-singular/ Singular Propositions (Greg Fitch) Sample Partial Syllabus The following partial syllabus can be used as a unit on recent work on propositions in graduate level courses in philosophy of language or metaphysics. Week 1: A Substitution Puzzle About Propositional Designators King, Jeffrey. 'Designating Propositions'. Moltmann, Friederike. 'Propositional Attitudes Without Propositions.' Synthese 135 (2003): 77–118. Week 2: The Benacerraf Problem and Propositional Representation Benacerraf, Paul. 'What Numbers Could Not Be.' Philosophical Review 74 (1965): 47–73. Jubien, Michael. 'Propositions and the Objects of Thought.' Week 3: Propositional Quantification Hofweber, Thomas. 'Inexpressible Properties and Propositions'. Hofweber, Thomas. 'A Puzzle about Ontology.' Noûs 39 (2005): 256–83. Week 4: Schiffer on Pleonastic Propositions Schiffer, Stephen. 'Language-Created Language-Independent Entities.' Philosophical Topics 24 (1996): 149–67. Schiffer, Stephen. The Things We Mean , chs 1–2. Week 5: King on Structured Propositions King, Jeffrey. 'Structured Propositions and Complex Predicates.' Noûs , 29 (1995): 516–35. King, Jeffrey. The Nature and Structure of Content , chs 1–3. Focus Questions 1. Why does identifying propositions with sentence intensions, e.g. sets of possible worlds, 'require the attitudes to have a particular sort of closure under logical consequence, which they clearly don't have' (Mark Richard)? 2. How does the difference between (a) and (b) pose a threat to the existence of propositions? (a) Bill fears that Hillary will be president. (b) Bill fears the proposition that Hillary will be president. 3. What is the Benacerraf problem for metaphysical reductions of propositions? 4. Why must a proposition represent 'on its own cuff' (Michael Jubien)? Why is this a problem for the view that propositions are primitive abstract entities? 5. What does it mean to say that propositions are structured ? Give two different accounts of what propositional structure might be. (shrink)
Church and Fitch have argued that from the verificationationist thesis “for every proposition, if this proposition is true, then it is possible to know it” we can derive that for every truth there is someone who knows that truth. Moreover, Humberstone has shown that from the latter proposition we can derive that someone knows every truth, hence that there is an omniscient being. In his article “Omnificence”, John Bigelow adapted these arguments in order to argue that from the assumption "every (...) contingent proposition is such that if it is true something brought it about that it is true" we can derive that there is an omnificent being: a being that brings it about that every true contingent proposition is true. In my reply to his article, I show that Bigelow’s argument is flawed because there is some formal property that the knowledge operator has but that the bringing about operator lacks. This is the property of distributing over conjunctions. I explain why what brings it about that some conjunctive proposition is true need not bring it about that its conjuncts are true. (shrink)
The well-known argument of Frederick Fitch, purporting to show that verificationism (= Truth implies knowability) entails the absurd conclusion that all the truths are known, has been disarmed by Dorothy Edgington''s suggestion that the proper formulation of verificationism presupposes that we make use of anactuality operator along with the standardly invoked epistemic and modal operators. According to her interpretation of verificationism, the actual truth of a proposition implies that it could be known in some possible situation that the proposition holds (...) in theactual situation. Thus, suppose that our object language contains the operatorA — it is actually the case that ... — with the following truth condition: vA iff w0, wherew 0 stands for the designated world of the model — the actual world. Then we can formalize the verificationist claim as follows. (shrink)
In answering “No” to his question “Does the descriptivist/antidescriptivist debate have any philosophical significance [beyond semantics]?” Lowe gives what at first sounds like an exciting answer to an interesting question – until one identifies his reason. That reason is the belief – now widely shared -- that a decisive resolution of this semantic debate would not allow one, using only secure non-philosophical knowledge, to establish interesting metaphysical principles, beyond philosophical doubt. Though this belief is widespread, the idea that its truth (...) would show the semantics of modality to have no significance for metaphysics (or other areas of philosophy) is preposterous, and, as far as I know, the sole possession of Professor Lowe. Are we to suppose that for any area of philosophy A, and any debated question Q in A, the resolution of Q has no significance for any other part B of philosophy, unless that resolution, absent all other philosophical principles, is sufficient (together with secure non-philosophical knowledge) to establish interesting positions in B, beyond philosophical doubt? It is hard to imagine anyone agreeing with that. Lowe’s failure to find the philosophical significance of semantic anti-descriptivism comes from looking in the wrong place. Its importance lies in expanding the range of metaphysical hypotheses to be taken seriously, not in limiting debate by proving metaphysical theorems from nonmetaphysical premises. The unraveling of Quine’s attack on the intelligibility of essentialism is a case in point. That attack, which distorted discussion of the subject from 1943 until well into the sixties, was based on faulty semantic premises about modality, singular terms, and quantification. Particular troublesome were Quine’s identification of necessity with analyticity, and his implicitly descriptivist conception of singular terms. It was recognized early on – by Smullyan, Fitch, Marcus, Follesdal, and the young Kripke, among others – that the availability of nondescriptive terms would blunt the attack. However, it wasn’t until Naming and Necessity that this line of thought came together in a decisive.... (shrink)
In [7] I produced natural derivation systems, including demonstration of soundness and completeness, for each of the logics described in the first edition of Priest, An Introduction to Non-Classical Logic [3]. The first edition of Priest’s book is Part I of the second edition. Eventually, I hope to complete the project, providing natural derivation systems for the quantified versions in Part II. In the meantime, without including parts for soundness and completeness, this document simply extends the previous paper to account (...) for additions and changes in the first part of the new edition. Thus, as before, I provide an alternative or supplement to the semantic tableaux of his text. Some of the derivation systems may also be of interest in their own right. They are all Fitch-style systems on the model of [1, 6], and many other places. Though a classical system is presented for chapter 1, prior acquaintance with some such system is assumed. Associated goaldirected derivation strategies are discussed extensively in [6, chapter 6]. Except that some chapters are collapsed, there are sections for each chapter in the first part of Priest’s book, with an additional section on four-valued relevant logic. In each case, (i) the language is briefly described and key semantic definitions stated, and (ii) the derivation system is presented with a few examples given. For those with interest, demonstration of soundness and completeness should be straightforward given background and strategy from the published paper. (shrink)
There is some very limited evidence for a role of estrogens in human psychosexual masculinization; its interpretation is uncertain. Fitch & Denenberg's demonstration of a role for estrogens in the behavioral feminization of nonhuman mammals implicitly suggests an answer to a riddle posed by the syndrome of congenital adrenal hyperplasia in women.
I discuss Fitch & Denenberg's argument that no correction for brain size is needed when assessing callosal size. Morphometric criteria may not be sufficient to determine whether corrections are needed. Functional studies of callosal transfer will ultimately specify whether corrections for size are necessary in each case.
Data do exist to support the fact that the corpus callosum is relatively larger in women than in men. The corpus callosum is an integral part of the brain, and contrary to Fitch & Denenberg's examples of “pseudostatistics,” is not an extrinsic structure when determining its relative size.
Indirect routes by which gonadal hormones influence sexual differentiation are considered. In rats, differentiation may depend on the way in which the mother responds to the hormonal condition of her pups, and this has implications for the interpretation of the data for humans. Interaction between gonadal hormones and light experience in chicks is compared with the mammalian systems covered in Fitch & Denenberg's review.
I suggest that most discussions of intentional systems have overlooked an important aspect of living organisms: the intrinsic goal-directedness inherent in the behaviour of living eukaryotic cells. This goal directedness is nicely displayed by a normal cell’s ability to rearrange its own local material structure in response to damage, nutrient distribution or other aspects of its individual experience. While at a vastly simpler level than intentionality at the human cognitive level, I propose that this basic capacity of living things provides (...) a necessary building block for cognition and high-order intentionality, because the neurons that make up vertebrate brains, like most cells in our body, embody such capacities. I provisionally dub the capacities in question “nano-intentionality”: a microscopic form of “aboutness”. The form of intrinsic intentionality I propose is thoroughly materialistic, fully compatible with known biological facts, and derived non-mysteriously through evolution. Crucially, these capacities are not shared by any existing computers or computer components, and thus provide a clear, empirically-based distinction between brains and currently existing artificial information processing systems. I suggest that an appreciation of this aspect of living matter provides a potential route out of what may otherwise appear to be a hopeless philosophical quagmire confronting information-processing models of the mind. (shrink)
Explaining the transition from a signed to a spoken protolanguage is a major problem for all gestural theories. I suggest that Arbib's improved “beyond the mirror” hypothesis still leaves this core problem unsolved, and that Darwin's model of musical protolanguage provides a more compelling solution. Second, although I support Arbib's analytic theory of language origin, his claim that this transition is purely cultural seems unlikely, given its early, robust development in children.
Millikan's account of substance concepts fails to do away with features. Her approach simply moves the suite of relevant features into an encapsulated module. The crux of the problem for scientists studying human infants and nonhuman animals is to determine how individuals reidentify objects and events in the world.
Seneca was a man of many facets: statesman, dramatist, philosopher, prose stylist. His life was marked by extremes of fortune - extremes that are reflected in much of his writing, and in the vicissitudes of his reputation in later centuries. This volume brings together some outstanding essays written about him over the past four decades, and illustrates the diversity of approaches by which modern critics have attempted to understand this multifaceted figure. Just as Seneca's writings often reflect his times, so (...) current critical approaches often reflect issues in contemporary thought and society. Several of the essays have been revised by their authors for this volume, and two of them are translated for the first time. A new introduction places the articles within the context of recent academic thought and criticism. All Latin has been translated. (shrink)
