A conception of pragmatics distinguishes pragmatics from semantics proper in terms of indexicality: semantics is conceived as the quest for a truth definition for languages without indexical expressions; pragmatics is conceived as a quest for a truth definition for languages with indexical expressions. I argue that indexicality is not a feature that can be used to capture anything like what Morris and Carnap had in mind.
In an earlier paper Sayward argued that a speaker could not make an assertion by uttering a sentence of form “p, but I believe not-p” given that the speaker spoke honestly and literally. Robert Imlay criticized some things said in that earlier paper. This paper responds to those criticisms.
Conversational implicatures are easy to grasp for the most part. But it is another matter to give a rational reconstruction of how they are grasped. We argue that Grice's attempt to do this fails. We distinguish two sorts of cases: (1) those in which we grasp the implicature by asking ourselves what would the speaker have to believe given that what he said is such as is required by the talk exchange; (2) those in which we grasp the implicature by (...) asking ourselves why it is that what the speaker said is so obviously not such as is required by the talk exchange. We argue that Grice's account does not fit those cases falling under (2). (shrink)
Psychological egoism says that a purposive action is self-interested in a certain sense. The trick is to say in what sense. On the one hand, the psychological egoist wants to avoid a thesis that can be falsified by trivial examples. On the other hand, what is wanted is a thesis that lacks vacuity. The paper’s purpose is to arrive at such a thesis and show that it is a reasonable guess with empirical content.
Fundamental to Quine’s philosophy of logic is the thesis that substitutional quantification does not express existence. This paper considers the content of this claim and the reasons for thinking it is true.
In ANARCY, STATE AND UTOPIA Robert Nozick says that the fundamental question of political philosophy, one that precedes questions about how the state should be organized, is whether there should be any state at all. In the first part of his book he attempts to justify the state. We argue that he is not successful.
[David Charles] Aristotle, it appears, sometimes identifies well-being (eudaimonia) with one activity (intellectual contemplation), sometimes with several, including ethical virtue. I argue that this appearance is misleading. In the Nicomachean Ethics, intellectual contemplation is the central case of human well-being, but is not identical with it. Ethically virtuous activity is included in human well-being because it is an analogue of intellectual contemplation. This structure allows Aristotle to hold that while ethically virtuous activity is valuable in its own right, the (...) best life available for humans is centred around, but not wholly constituted by, intellectual contemplation. /// [Dominic Scott] In Nicomachean Ethics X 7-8, Aristotle distinguishes two kinds of eudaimonia, primary and secondary. The first corresponds to contemplation, the second to activity in accordance with moral virtue and practical reason. My task in this paper is to elucidate this distinction. Like Charles, I interpret it as one between paradigm and derivative cases; unlike him, I explain it in terms of similarity, not analogy. Furthermore, once the underlying nature of the distinction is understood, we can reconcile the claim that paradigm eudaimonia consists just in contemplation with a passage in the first book requiring eudaimonia to involve all intrinsic goods. (shrink)
Whereas arithmetical quantification is substitutional in the sense that a some-quantification is true only if some instance of it is true, it does not follow (and, in fact, is not true) that an account of the truth-conditions of the sentences of the language of arithmetic can be given by a substitutional semantics. A substitutional semantics fails in a most fundamental fashion: it fails to articulate the truth-conditions of the quantifications with which it is concerned. This is what is defended in (...) the paper. In particular, it is defended against remarks to the contrary in a well known paper on the subject. (shrink)
The fact that a group of axioms use the word 'true' does not guarantee that that group of axioms yields a theory of truth. For Davidson the derivability of certain biconditionals from the axioms is what guarantees this. We argue that the test does not work. In particular, we argue that if the object language has truth-value gaps, the result of applying Davidson''s definition of a theory of truth is that no correct theory of truth for the language is possible.
Let C1 and C2 be distinct moral codes formulated in English. Let C1 contain a norm N and C2 its negation. The paper construes the moral relativist as saying that if both codes are consistent, then, in the strongest sense of correctness applicable to moral norms, they are also both correct in the sense that they contain only correct moral norms. If we believe that the physical statements of English are true (false) in English, we will reject an analogous statement (...) made of physical theories. We will hold that the strongest sense of correctness applicable to physical statements is not system-relative. The moral relativist denies that there is any corresponding sense of correctness applicable to moral norms. That is, there is no notion of moral correctness that is not system-dependent. It is argued that, while the position may not be true, there is not a strictly logical basis for refuting it. (shrink)
Quine argues that if sentences that are set theoretically equivalent are interchangeable salva veritate, then all transparent operators are truth-functional. Criticisms of this argument fail to take into account the conditional character of the conclusion. Quine also argues that, for any person P with minimal logical acuity, if ‘belief’ has a sense in which it is a transparent operator, then, in that sense of the word, P believes everything if P believes anything. The suggestion is made that he intends that (...) result to show us that ‘believes’ has no transparent sense. Criticisms of this argument are either based on unwarranted assertions or on definitions of key terms that depart from Quine’s usage of those terms. (shrink)
It may be that all that matters for the modalities, possibility and necessity, is the object named by the proper name, not which proper name names it. An influential defender of this view is Saul Kripke. Kripke’s defense is criticized in the paper.
This title introduces students to non-classical logic, syllogistic, to quantificational and modal logic. The book includes exercises throughout and a glossary of terms and symbols. Taking students beyond classical mathematical logic, "Philosophical Logic" is a wide-ranging introduction to more advanced topics in the study of philosophical logic. Starting by contrasting familiar classical logic with constructivist or intuitionist logic, the book goes on to offer concise but easy-to-read introductions to such subjects as quantificational and syllogistic logic, modal logic and set theory. (...) Chapters of this title include: Sentential Logic; Quantificational Logic; Sentential Modal Logic; Quantification and Modality; Set Theory; Incompleteness; An Introduction to Term Logic; and, Modal Term Logic. In addition, the book includes a list of symbols and a glossary of terms for ease of reference and exercises throughout help students master the topics covered in the book. (shrink)
The paper purports to show, against Quine, that one can construct a language , which results from the extension of the theory of truth functions by introducing sentence letter quantification. Next a semantics is provided for this language. It is argued that the quantification is neither substitutional nor requires one to consider the sentence letters as taking entities as values.
Consider the general proposition that normally when people pain-behave they are in pain. Where a traditional philosopher like Mill tries to give an empirical proof of this proposition (the argument from analogy), Malcolm tries to give a transcendental proof. Malcolm’s argument is transcendental in that he tries to show that the very conditions under which we can have a concept provide for the application of the concept and the knowledge that the concept is truly as well as properly applied. The (...) natural basis for applying the concept of pain to someone else is pain-behavior like groaning and crying out. To know that a person pain-behaving is in pain is to rule out countervailing circumstances (smiles, exaggerated cries, winks, absence of plausible cause, and so on). The basic move by Malcolm is to make these special conditions a function merely of the concept of pain. (shrink)
In "Remarks on the Foundations of Mathematics" Wittgenstein discusses an argument that goes from Gödel’s incompleteness result to the conclusion that some truths of mathematics are unprovable. Wittgenstein takes issue with this argument. Wittgenstein’s remarks in this connection have received very negative reaction from some very prominent people, for example, Gödel and Dummett. The paper is a defense of what Wittgenstein has to say about the argument in question.
The force of sceptical inquiries into out knowledge of other people is a paradigm of the force that philosophical views can have. Sceptical views arise out of philosophical inquiries that are identical in all major respects with inquiries that we employ in ordinary cases. These inquiries employ perfectly mundane methods of making and assessing claims to know. This paper tries to show that these inquiries are conducted in cases that lack certain contextual ingredients found in ordinary cases. The paper concludes (...) that these ordinary methods of inquiry, when employed in these limited cases, put us in a position in which we actually cannot know. Thus our ability to know will be a function of the added contextual elements that are found in ordinary cases. A second conclusion is that we come literally to observe bodily behaviour in the course of the sceptical inquiry; while in ordinary cases we observe pain-behaviour. (shrink)
Determining whether the law of excluded middle requires bivalence depends upon whether we are talking about sentences or propositions. If we are talking about sentences, neither side has a decisive case. If we are talking of propositions, there is a strong argument on the side of those who say the excluded middle does require bivalence. I argue that all challenges to this argument can be met.
One of the things C. D Broad argued many years ago is that certain 'scientific' arguments against dualist interactionism come back in the end to a metaphysical bias in favor of materialism. Here the authors pursue this basic strategy against another 'scientific' argument against dualism itself. The argument is called 'the argument from continuity'. According to this argument the fact that organisms and species develop by insensible gradations renders dualism implausible. The authors try to demonstrate that this argument fails to (...) establish the implausibility of dualism. (shrink)
If a native of India asserts "Killing cattle is wrong" and a Nebraskan asserts "Killing cattle is not wrong", and both judgments agree with their respective moralities and both moralities are internally consistent, then the moral relativist says both judgments are fully correct. At this point relativism bifurcates. One branch which we call content relativism denies that the two people are contradicting each other. The idea is that the content of a moral judgment is a function of the overall moral (...) point of view from which it proceeds. The second branch which we call truth value relativism affirms that the two judgments are contradictory. Truth value relativism appears to be logically incoherent. How can contradictory judgments be fully correct? For though there will be a sense of correctness in which each judgment is correct — namely by that of being correct relative to the morality relative to which each was expressed — if contradictory, the judgments cannot both be true, and thus cannot both be correct in this most basic sense of correctness. We defend truth value relativism against this sort of charge of logical incoherence by showing it can be accommodated by the existing semantical metatheories of deontic logic. Having done this we go on to argue that truth value relativism is the best version of relativism. (shrink)
This paper reaches the conclusion that, while there are ordinary cases in which the pretending possibility is reasonable, these cases always contain some element that makes it reasonable. This will be the element we ask for when we ask why pretending possibility is raised. Knowledge that someone else is in pain is a matter of eliminating the proposed element or neutralizing its pain-negating aspect.
For Rudolf Carnap the question ‘Do numbers exist?’ does not have just one sense. Asked from within mathematics, it has a trivial answer that could not possibly divide philosophers of mathematics. Asked from outside of mathematics, it lacks meaning. This paper discusses Carnap’s distinction and defends much of what he has to say.
This paper is a discussion of Frege's maxim that it is only in the context of a sentence that a word has a meaning. Quine reads the maxim as saying that the sentence is the fundamental unit of significance. Dummett rejects this as a truism. But it is not a truism since it stands in opposition to a conception of meaning held by John Locke and others. The maxim denies that a word has a sense independently of any sentence in (...) which it occurs. Dummett says this denial is inconsistent with the fact that people understand sentences they have never heard before. The maxim is defended against this attack. (shrink)
In Tractatus, Wittgenstein held that there are null sentences – prominently including logical truths and the truths of mathematics. He says that such sentences are without sense (sinnlos), that they say nothing; he also denies that they are nonsensical (unsinning). Surely it is what a sentence says which is true or false. So if a sentence says nothing, how can it be true or false? The paper discusses the issue.
Propositional identity is not expressed by a predicate. So its logic is not given by the ordinary first order axioms for identity. What are the logical axioms governing this concept, then? Some axioms in addition to those proposed by Arthur Prior are proposed.
This is a dialogue in which five characters are involved. Various issues in the philosophy of mathematics are discussed. Among those issues are these: numbers as abstract objects, our knowledge of numbers as abstract objects, a proof as showing a mathematical statement to be true as opposed to the statement being true in virtue of having a proof.
The goal of theodicy is to show how God could create our world with all its evil. This paper argues that the theodicist can achieve her goal only if she gives up one of these three propositions: (1) evil does not exist in heaven; (2) heaven is better than the present world; (3) heaven is a possible world. Second, it is argued that the theodicist can reject (3) without giving up her belief that heaven exists, so that (3) is her (...) best alternative. (shrink)
This paper seeks to explain why the argument from analogy seems strong to an analogist such as Mill and weak to the skeptic. The inference from observed behavior to the existence of feelings, sensations, etc., in other subjects is justified, but its justification depends on taking observed behavior and feelings, sensations, and so on, to be not merely correlated, but connected. It is claimed that this is what Mill had in mind.
A popular view is that the great discovery of Pythagoras was that there are irrational numbers, e.g., the positive square root of two. Against this it is argued that mathematics and geometry, together with their applications, do not show that there are irrational numbers or compel assent to that proposition.
The paper asks: are all tautologies true in a language with truth-value gaps? It answers that they are not. No tautology is false, of course, but not all are true. It also contends that not all contradictions are false in a language with truth-value gaps, though none are true.
Hilary Putnam suggests that the essence of the realist conception of mathematics is that the statements of mathematics are objective so that the true ones are objectively true. An argument for mathematical realism, thus conceived, is implicit in Putnam's writing. The first premise is that within currently accepted science there are objective truths. Next is the premise that some of these statements logically imply statements of pure mathematics. The conclusion drawn is that some statements of pure mathematics are objectively true. (...) A key principle assumed is that if one statement logically implies a second, then if the first is objectively true so is the second. A question about this principle is raised and answered. The problem with the argument is with the second premise. (shrink)
Suppose there is a domain of discourse of English, then everything of which any predicate is true is a member of that domain. If English has a domain of discourse, then, since ‘is a domain of discourse of English’ is itself a predicate of English and true of that domain, that domain is a member of itself. But nothing is a member of itself. Thus English has no domain of discourse. We defend this argument and go on to argue to (...) the same conclusion without relying on the supposition that English is a language which contains the predicate ‘is a domain of discourse of English’. (shrink)
Pavel Tichy presents an interpretation of Anselm’s Proslogion III argument. Tichy presents an interpretation of this argument and raises doubts about one of the premises. The authors contend that Tichy’s interpretation of Anselm is wrong. The argument Tichy comes to raise doubts about is not Anselm’s.
It is argued that if there are truth-value gaps then the disquotational theory of truth is false. Secondly, it is argued that the same conclusion can be reached even without the assumption that there are truth-value gaps.
Nicholas Sturgeon has claimed that moral explanations constitute one area of disagreement between moral realists and noncognitivists. He claims that the correctness of such explanation is consistent with moral realism but not with noncognitivism. Does this difference characterize all other anti-realist views. This paper argues that it does not. Moral relativism is a distinct anti-realist view. And the correctness of moral explanation is consistent with moral relativism.
The idea underlying the Begriffsschrift account of identities was that the content of a sentence is a function of the things it is about. If so, then if an identity a=b is about the content of its contained terms and is true, then a=a and a=b have the same content. But they do not have the same content; so, Frege concluded, identities are not about the contents of their contained terms. The way Frege regarded the matter is that in an (...) identity the terms flanking the symbol for identity do not have their ordinary contents, but instead have themselves as their contents. In 'Uber Sinn und Bedeutung' Frege became convinced that if an identity a=b is about the signs a and b, then it expresses no proper knowledge. So, since it is evident that many such identities do express proper knowledge, Frege concluded that identities are not about their contained signs. So he became convinced that his Begriffsschrift account was incorrect. What was the error in the argument that led Frege to that account? It was thinking that the content of a sentence is a function of the contents of its constituent signs, that is, the things it is about. (shrink)
In this paper the authors recapitulate, justify, and defend against criticism the extension of the redundancy theory of truth to cover a wide range of uses of ‘true’ and ‘false’. In this they are guided by the work of A. N. Prior. They argue Prior was right about the scope and limits of the redundancy theory and that the line he drew between those uses of ‘true’ which are and are not susceptible to treatment via redundancy serves to distinguish two (...) important and mutually irreducible types of truth: redundancy truth and predicative truth. Only the latter serves for semantic theorizing. (shrink)
In this paper we give (1) a new interpretation to Nagel’s THE POSSIBILITY OF ALTRUISM and (2) use that interpretation to show that internalism and anti-realism are compatible, despite appearances to the contrary.
Two philosophical theories, mathematical Platonism and nominalism, are the background of six dialogues in this book. There are five characters in these dialogues: three are nominalists; the fourth is a Platonist; the main character is somewhat skeptical on most issues in the philosophy of mathematics, and is particularly skeptical regarding the two background theories.
Four views of arithmetical truth are distinguished: the classical view, the provability view, the extended provability view, the criterial view. The main problem with the first is the ontology it requires one to accept. Two anti-realist views are the two provability views. The first of these is judged to be preferable. However, it requires a non-trivial account of the provability of axioms. The criterial view is gotten from remarks Wittgenstein makes in Tractatus 6.2-6.22 . It is judged to be the (...) best of four views. It is also defended against objections. (shrink)
In this book a non-realist philosophy of mathematics is presented. Two ideas are essential to its conception. These ideas are (i) that pure mathematics--taken in isolation from the use of mathematical signs in empirical judgement--is an activity for which a formalist account is roughly correct, and (ii) that mathematical signs nonetheless have a sense, but only in and through belonging to a system of signs with empirical application. This conception is argued by the two authors and is critically discussed by (...) three philosophers of mathematics. (shrink)
This paper deals with the question of whether there is objectivist truth about set-theoretic matters. The dogmatist and skeptic agree that there is such truth. They disagree about whether this truth is knowable. In contrast, the relativist says there is no objective truth to be known. Two versions of relativism are distinguished in the paper. One of these versions is defended.
Three theses are gleaned from Wittgenstein’s writing. First, extra-mathematical uses of mathematical expressions are not referential uses. Second, the senses of the expressions of pure mathematics are to be found in their uses outside of mathematics. Third, mathematical truth is fixed by mathematical proof. These theses are defended. The philosophy of mathematics defined by the three theses is compared with realism, nominalism, and formalism.
The paper’s purpose is to get clearer on what it is to express a proposition. A proposition is understood as anything that can be asserted, assumed, conjectured, stated, believed, and so on. It is not something that can be asked, ordered, requested, and so on. The paper tries to provide groundwork for a successful analysis by making distinctions and clarifying problems.
This paper is a critical exposition of Prior’s theory of truth as expressed by the following truth locutions: (1) ‘it is true that’ prefixed to sentences; (2) ‘true proposition’; (3) true belief’, ‘true assertion’, ‘true statement’, etc.; (4) ‘true sentence’.
A type theory constructed with reference to a particular language will associate with each monadic predicate P of that language a class of individuals C(P) of which it is categorically significant to predicate P (or which P spans, for short). The extension of P is a subset of C(P), which is a subset of the language’s universe of discourse. The set C(P) is a category discriminated by the language. The relation 'is spanned by the same predicates as' divides the language’s (...) universe of discourse into equivalence classes. These are the types discriminated by the language. This paper criticizes an attempt by Peter Strawson to explain terms peculiar to type theory in terms of other notions not peculiar to type theory. (shrink)
We here establish two theorems which refute a pair of what we believe to be plausible assumptions about differences between objectual and substitutional quantification. The assumptions (roughly stated) are as follows: (1) there is at least one set d and denumerable first order language L such that d is the domain set of no interpretation of L in which objectual and substitutional quantification coincide. (2) There exist interpreted, denumerable, first order languages K with indenumerable domains such that substitutional quantification deviates (...) from objectual quantification in K and this deviance remains for all name extensions I of K. We show these assumptions have actually been made, and then prove the refuting theorems. (shrink)
This is a dialogue in the philosophy of mathematics that focuses on these issues: Are the Peano axioms for arithmetic epistemologically irrelevant? What is the source of our knowledge of these axioms? What is the epistemological relationship between arithmetical laws and the particularities of number?
Mark Steiner criticizes some remarks Wittgenstein makes about Gödel. Steiner takes Wittgenstein to be disputing a mathematical result. The paper argues that Wittgenstein does no such thing. The contrast between the realist and the demonstrativist concerning mathematical truth is examined. Wittgenstein is held to side with neither camp. Rather, his point is that a realist argument is inconclusive.
Formal principals are isolated to reveal a structure embedded in a wide range of studies, each of which partitions a domain of individuals into types and categories. It is thought that any reasonable theory of types should include these principles.
We set out a doctrine about truth for the statements of mathematics—a doctrine which we think is a worthy competitor to realist views in the philosophy of mathematics—and argue that this doctrine, which we shall call 'mathematical relativism', withstands objections better than do other non-realist accounts.
An account of the logic of bivalent languages with truth-value gaps is given. This account is keyed to the use of tables introduced by S. C. Kleene. The account has two guiding ideas. First, that the bivalence property insures that the language satisfies classical logic. Second, that the general concepts of a valid sentence and an inconsistent sentence are, respectively, as sentences which are not false in any model and sentences which are not true in any model. What recommends this (...) approach is (1) its relative simplicity, and (2) the fact that it leaves the fundamental features of classical logic intact. (shrink)
Some of Austin's general statements about the doctrines of sense-datum philosophy are reviewed. It is concluded that Austin thought that in these doctrines "directly see" is given a new but inadequately explained and defined use. Were this so, the philosophical use of "directly see" would lack a definite sense and this would correspondingly affect the doctrines. They would lack definite truth-value. Against this, it is argued that the philosopher's use of "directly see" does not support Austin's general thesis that the (...) sense-datum doctrines lack truth-value. (shrink)
This is a dialogue in the philosophy of mathematics. The dialogue descends from the confident assertion that there are infinitely many numbers to an unresolved bewilderment about how we can know there are any numbers at all. At every turn the dialogue brings us only to realize more fully how little is clear to us in our thinking about mathematics.
Frege held that the result of applying a predicate to names lacks reference if any of the names lack reference. We defend the principle against a number of plausible objections. We put forth an account of consequence for a first-order language with identity in which the principle holds.
This book says Prior claims: (1) that a sentence never names; (2) what a sentence says cannot be otherwise signified; and (3) that a sentence says what it says whatever the type of its occurrence; (4) and that quantifications binding sentential variables are neither eliminable, substitutional, nor referential. The book develops and defends (1)-(3). It also defends (4) against the sorts of strictures on quantification of such philosophers as Quine and Davidson.
Peter Geach proposed a substitutional construal of quantification over thirty years ago. It is not standardly substitutional since it is not tied to those substitution instances currently available to us; rather, it is pegged to possible substitution instances. We argue that (i) quantification over the real numbers can be construed substitutionally following Geach's idea; (ii) a price to be paid, if it is that, is intuitionism; (iii) quantification, thus conceived, does not in itself relieve us of ontological commitment to real (...) numbers. (shrink)
A plausible line of thought runs as follows. If P is a semantically primitive predicate of a first order language L, then P requires its own clause in the definition of satisfaction integral to a definition of truth for L. Thus if L has infinitely many such P the satisfaction clause cannot be completed nor can a theory of truth for L. Robert Cummins takes issue with this line of argument. This paper takes issue with Cummins.
A doctrine that occurs intermittently in Quine’s work is that there is no extra-theoretic truth. This paper explores this doctrine, and argues that on its best interpretation it is inconsistent with three views Quine also accepts: bivalence, mathematical Platonism, and the disquotational account of truth.
Two different uses of ‘proposition’ are distinguished: the meaning of an eternal sentence is distinguished from that which can be asserted, believed, conjectured, and so on. It is argued that, in the second sense of ‘proposition’, it is not the case that every proposition can be expressed by an eternal sentence.
It is argued that Convention T and Basic Law V of Frege’s Grungesetze share three striking similarities. First, they are universal generalizations that are intuitively plausible because they have so many obvious instances. Second, both are false because they yield contradictions. Third, neither gives rise to a paradox.
Various authors of logic texts are cited who either suggest or explicitly state that the Gödel incompleteness result shows that some unprovable sentence of arithmetic is true. Against this, the paper argues that the matter is one of philosophical controversy, that it is not a mathematical or logical issue.
The significance of the semantical paradoxes for natural languages is examined. If Tarski’s reflections on the issue are correct, English is inconsistent. Paul Ziff responds to Tarskian reflections by arguing to the conclusion that no natural language is or can be inconsistent. The authors reject Ziff’s argument, but they defend something similar to its conclusion: no language, natural or otherwise, is or can be inconsistent in the way that Tarski holds languages capable of formulating the Epimenides are inconsistent.
Prior propounded a theory that, if correct, explains how it is possible for a statement about propositions to be true even if there are no propositions. The major feature of his theory is his treatment of sentence letters as bindable variables in non-referential positions. His theory, however, does not include a semantical account of the resulting quantification. The paper tries to fill that gap.
The following syllogism is considered: a string is not an expression unless it is tokenable; no one can utter, write, or in anyway token an infinite string; so no infinite string is an expression. The second premise is rejected. But the tokenability of an infinite sentence is not sufficient for it being an infinite expression. A further condition is that no finite sentence expresses that sentence’s truth-conditions. So it is an open question whether English contains infinite expressions.
The justification of the existence of the state should precede the justification of any particular organization of the state. The paper tries to give a clear argument facing anyone who sets out to do the first thing, which is to justify the existence of the state. The problem facing such a person is to identify which premise of the argument is false and explain why it is false.
This paper gives a semantical account for the (i)ordinary propositional calculus, enriched with quantifiers binding variables standing for sentences, and with an identity-function with sentences as arguments; (ii)the ordinary theory of quantification applied to the special quantifiers; and (iii)ordinary laws of identity applied to the special function. The account includes some thoughts of Roman Suszko as well as some thoughts of Wittgenstein's Tractatus.
The fundamental thought of moral relativism is set out as follows: moral criteria, derived from overall moral points of view, are used to derive particular moral judgments. Thus such a judgment might be correct relative to one overall moral point of view and incorrect relative to another. The evaluation of an overall moral point of view does not involve the application of moral criteria. Rather, the evaluation of a morality takes us outside the province of morality. The result of sharpening (...) this view is a doctrine called system relativism. System relativism is contrasted with other conceptions of moral relativism that have recently been propounded. It is argued that system relativism is the most defensible version. (shrink)
A common assumption among philosophers is that every language has at most denumerably many expressions. This assumption plays a prominent role in many philosophical arguments. Recently formal systems with indenumerably many elements have been developed. These systems are similar to the more familiar denumerable first-order languages. This similarity makes it appear that the assumption is false. We argue that the assumption is true.
The principal question asked in this paper is: in the case of attributive usage, is the definite description to be analyzed as Russell said or is it to be treated as a referring expression, functioning semantically as a proper name? It answers by defending the former alternative.
Russell held that the theory of natural numbers could be derived from three primitive concepts: number, successor and zero. This leaves out multiplication and addition. Russell introduces these concepts by recursive definition. It is argued that this does not render addition or multiplication any less primitive than the other three. To this it might be replied that any recursive definition can be transformed into a complete or explicit definition with the help of a little set theory. But that is a (...) point about set theory, not number theory. (shrink)
Doubts are raised about the claim that on mastering a finite vocabulary and a finitely stated set of rules we are prepared to understand a potential infinitude of sentences. One doubt is about understanding a potential infinitude of sentences. A second doubt is about the assumption that understanding a sentence must be a matter of figuring out its meaning from an antecedent knowledge of the meaning of its words and applying rules.
The paper argues that the liar paradox teaches us these lessons about English. First, the paradox-yielding sentence is a sentence of English that is neither true nor false in English. Second, there is no English name for any such thing as a set of all and only true sentences of English. Third, ‘is true in English’ does not satisfy the axiom of comprehension.
Here we give a semantical account of propositional quantification that is intended to formally represent Russell’s view that one cannot express a proposition about "all" propositions. According to the account the authors give, Russell’s view bears an interesting relation to the view that there are no sets which are members of themselves.
The standard response is illustrated by E, J. Lemmon's claim that if all objects in a given universe had names and there were only finitely many of them, then we could always replace a universal proposition about that universe by a complex proposition. It is because these two requirements are not always met that we need universal quantification. This paper is partly in agreement with Lemmon and partly in disagreement. From the point of view of syntax and semantics we can (...) replace a universal proposition about any universe (finite or infinite, countable or uncountable) by a complex proposition (= sentence built up from atomic sentences and the connectives). But from the point of view of communication such a replacement is not possible if the universe is infinite. (shrink)
A strong and weak version of the redundancy theory of truth are distinguished. An argument put forth by Michael Dummett concludes that the weak version is vitiated by truth-value gaps. The weak version is defended against this argument. The strong version, however, is vitiated by truth-value gaps.
On the basis of observations J. J. C. Smart once made concerning the absurdity of sentences like 'The seat of the bed is hard', a plausible case can be made that there is little point to developing a theory of types, particularly one of the sort envisaged by Fred Sommers. The authors defend such theories against this objection by a partial elucidation of the distinctions between the concepts of spanning and predicability and between category mistakenness and absurdity in general. The (...) argument suggests that further clarification of the concepts of spanning and category mistakenness should be sought in reflection upon the more familiar concepts of a sort of thing and a predicate category. (shrink)
There are plausible objections to substitutional construals of generalization. But these objections do not apply to a substitutional construal of generalization proposed by Peter Geach several years ago. This paper examines Geach’s conception.
Two kinds of functionalism are distinguished: intensional and extensional. The former is argued to be superior to the latter. The former is also defended against two objections independently put forth by Ned Block and John Searle.
The purpose of this paper is to uncover and correct several confusions about expressions, tokens and the relations between them that crop up in even highly sophisticated writing about language and logic.
A case against Prior’s theory of propositions goes thus: (1) everyday propositional generalizations are not substitutional; (2) Priorean quantifications are not objectual; (3) quantifications are substitutional if not objectual; (4) thus, Priorean quantifications are substitutional; (5) thus that Priorean quantifications are not ontologically committed to propositions provides no basis for a similar claim about our everyday propositional generalizations. Prior agrees with (1) and (2). He rejects (3), but fails to support that rejection with an account of quantification on which there (...) could be quantifications that are neither substitutional nor objectual. The paper draws from the work of Lorenzen an alternative conception of quantification in terms of which that needed account can be given. (shrink)
Let A, B, C stand for sentences expressing propositions; let A be a component of C; let C A/B be just like C except for replacing some occurrence of A in C by an occurrence of B; let = be a binary connective for propositional identity read as ‘the proposition that __ is the very same proposition as …’. Then authors defend adding ‘from C = C A/B infer A = B’ to Prior’s rules for propositional identity, appearing in OBJECTS (...) OF THOUGHT. (shrink)
This paper pushes to the claim that the following is Descartes’s fundamental thesis: something has self-presenting states and self-presenting states only. Were he to have established this he would have revamped our worldview in essentially the manner he wished to revamp it. From this proposition one can get an argument for the substance view of the mind in Descartes’s writings.
Two cases are distinguished. In one case two predicates belong to distinct languages. A straight-forward argument is presented that the predicates might be synonymous without being coextensive. In the second case the predicates belong to the same language. Here the issue is more involved, but the same conclusion is reached.
In this paper the authors argue that if Tarski’s definition of truth for the calculus of classes is correct, then set theories which assert the existence of proper classes (classes which are not the member of anything) are incorrect.
The morality of an economic system characterized as an Adam Smith type system is compared with one characterized by central planning. A prima facie case is made that, while the latter has attributes that satisfy a necessary condition for having moral attributes, the former does not and, as a result, has no moral attributes. But then a deeper look at the situation reveals that the directed systems really do not satisfy the necessary condition either. Both the directed and undirected systems (...) end up in the same boat. Neither have any moral attributes. (shrink)
In his book 'Wittgenstein on the foundations of Mathematics', Crispin Wright notes that remarkably little has been done to provide an unpictorial, substantial account of what mathematical platoninism comes to. Wright proposes to investigate whether there is not some more substantial doctrine than the familiar images underpinning the platonist view. He begins with the suggestion that the essential element in the platonist claim is that mathematical truth is objective. Although he does not demarcate them as such, Wright proposes several different (...) tests for objectivity. The paper finds problems with each of these tests. (shrink)
Quine’s way of dealing with the semantical paradoxes (Ways of Paradox, pp. 9-10) is criticized. The criticism is based on three premises: (1) no learnable language has infinitely many semantical primitives; (2) any language of which Quine’s theory is true has infinitely many semantical primitives; (3) English is a learnable language. The conclusion drawn is that Quine’s theory is not true of English.
The paper argues that two apparently attractive conceptions of an eternal sentence are defective. An alternative conception is presented which the authors think allows greater insight into the nature of semantic concepts.
It is argued that English is finite. By this is meant that it contains only finitely many expressions. The conclusion is reached by arguing: (1) only finitely many expressions of English are tokenable; (2) if E is an expression of English, then E is tokenable.