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  1. Philip Hugly & Charles Sayward (2006). Arithmetic and Ontology: A Non-Realist Philosophy of Arithmetic. rodopi.
    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 (...)
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  2. Philip Hugly & Charles Sayward (2006). Replies to Commentaries. Poznan Studies in the Philosophy of the Sciences and the Humanities 90 (1):369-386.
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  3. Philip Hugly & Charles Sayward (2002). There Is A Problem with Substitutional Quantification. Theoria 68 (1):4-12.
    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 (...)
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  4. Philip Hugly & Charles Sayward (2000). Frege on Identities. History and Philosophy of Logic 21 (3):195-205.
    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 (...)
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  5. Philip Hugly & Charles Sayward (1999). Did the Greeks Discover the Irrationals? Philosophy 74 (2):169-176.
    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.
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  6. Philip Hugly & Charles Sayward (1999). Null Sentences. Iyyun, The Jewish Philosophical Quarterly 48:23-36.
    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.
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  7. Philip Hugly & Charles Sayward (1998). A Fregean Principle. History and Philosophy of Logic 19 (3):125-135.
    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.
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  8. Philip Hugly & Charles Sayward (1998). Kripke on Necessity and Identity. Philosophical Papers 27 (3):151-159.
    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.
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  9. Philip Hugly & Charles Sayward (1996). Intentionality and Truth: An Essay on the Philosophy of Arthur Prior. kluwer.
    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.
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  10. Philip Hugly & Charles Sayward (1995). What’s So Special About Sentences? Communication and Cognition 28 (4):409-25.
    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 (...)
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  11. Philip Hugly & Charles Sayward (1994). Quantifying Over the Reals. Synthese 101 (1):53 - 64.
    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 (...)
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  12. Philip Hugly & Charles Sayward (1994). The Internal/External Question. Grazier Philosophishe Studien 47:31-41.
    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.
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  13. Philip Hugly & Charles Sayward (1993). Two Concepts of Truth. Philosophical Studies 70 (1):35 - 58.
    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 (...)
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  14. Philip Hugly & Charles Sayward (1993). The Disquotational Theory of Truth is False. Philosophia 22 (3-4):331-339.
    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.
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  15. Philip Hugly & Charles Sayward (1993). Theories of Truth and Truth-Value Gaps. Linguistics and Philosophy 16 (6):551 - 559.
    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.
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  16. Philip Hugly & Charles Sayward (1992). Classical Logic and Truth-Value Gaps. Philosophical Papers 21 (2):141-150.
    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 (...)
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  17. Philip Hugly & Charles Sayward (1992). Redundant Truth. Ratio 5 (1):24-37.
    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.
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  18. Kai Nielsen, Michael Pendlebury, Philip Percival, Mark Sainsbury, David Sapire, Charles Sayward, Philip Hugly, Mark Timmons & Terence Horgan (1992). MILLER, Seumas Joint Action. Philosophical Papers 1 (259):65.
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  19. Philip Hugly & Charles Sayward (1991). Prior and Lorenzen on Quantification. Grazer Philosophishe Studien 41:150-173.
    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 (...)
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  20. Philip Hugly & Charles Sayward (1990). Moral Relativism and Deontic Logic. Synthese 85 (1):139 - 152.
    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 (...)
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  21. Philip Hugly & Charles Sayward (1990). Offices and God. Sophia 29:29-34.
    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.
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  22. Philip Hugly & Charles Sayward (1990). Tractatus 6.2–6.22. Philosophical Investigations 13 (2):126-136.
    It is argued that Wittgenstein’s remarks 6.2-6.22 Tractatus fare well when one focuses on non-quantificational arithmetic, but they are problematic when one moves to quantificational arithmetic.
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  23. Philip Hugly & Charles Sayward (1990). Quine's Relativism. Ratio 3 (2):142-149.
    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.
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  24. Philip Hugly & Charles Saywood (1990). Offices and God. Sophia 29 (3):29-34.
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  25. Philip Hugly & Charles Sayward (1989). Are All Tautologies True? Logique Et Analyse 125 (125-126):3-14.
    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.
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  26. Philip Hugly & Charles Sayward (1989). Can There Be a Proof That an Unprovable Sentence of Arithmetic is True? Dialectica 43 (43):289-292.
    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.
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  27. Philip Hugly & Charles Sayward (1989). Can There Be A Proof That Some Unprovable Arithmetic Sentence Is True? Dialectica 43 (3):289-292.
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  28. Philip Hugly & Charles Sayward (1989). Mathematical Relativism. History and Philosophy of Logic 10:53-65.
    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.
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  29. Philip Hugly (1987). Crowell on Nietzsche on Truth. International Studies in Philosophy 19 (2):19-28.
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  30. Philip Hugly & Charles Sayward (1987). Domains of Discourse. Logique Et Analyse 117:173-176.
    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 (...)
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  31. Philip Hugly & Charles Sayward (1987). Relativism and Ontology. Philosophical Quarterly 37 (148):278-290.
    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.
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  32. Philip Hugly & Charles Sayward (1987). Why Substitutional Quantification Does Not Express Existence. Theory and Decision 50:67-75.
    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.
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  33. Philip Hugly & Charles Sayward (1987). Do We Need Models? Notre Dame Journal of Formal Logic 28 (3):414-422.
    The aim of this paper is to provide a nondenotational semantics for first-order languages which will match one for one each distribution of truth-values available in terms of a denotational semantics.
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  34. Philip Hugly & Charles Sayward (1986). What is an Infinite Expression? Philosophia 16 (1):45-60.
    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.
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  35. Philip Hugly & Charles Sayward (1985). Is Moral Relativism Consistent? Analysis 45 (1):40-44.
    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 (...)
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  36. Philip Hugly & Charles Sayward (1984). Do We Need Quantification? Notre Dame Journal of Formal Logic 25 (4):289-302.
    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 (...)
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  37. Philip Hugly & Charles Sayward (1983). Can a Language Have Indenumerably Many Expressions? History and Philosophy of Logic 4 (1-2):73-82.
    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.
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  38. Philip Hugly & Charles Sayward (1982). Indenumerability and Substitutional Quantification. Notre Dame Journal of Formal Logic 23 (4):358-366.
    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 (...)
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  39. Philip Hugly & Charles Sayward (1981). Bound Variables and Schematic Letters. Logique Et Analyse 95:425-429.
    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.
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  40. Philip Hugly & Charles Sayward (1981). Expressions and Tokens. Analysis 41 (4):181-187.
    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.
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  41. Philip Hugly & Charles Sayward (1981). Completeness Theorems for Two Propositional Logics in Which Identity Diverges From Mutual Entailment. Notre Dame Journal of Formal Logic 22 (3):269-282.
    Anderson and Belnap devise a model theory for entailment on which propositional identity equals proposional coentailment. This feature can be reasonably questioned. The authors devise two extensions of Anderson and Belnap’s model theory. Both systems preserve Anderson and Belnap’s results for entailment, but distinguish coentailment from identity.
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  42. Philip Hugly (1980). Reflections on an Extensionality Theorem. Notre Dame Journal of Formal Logic 21 (1):45-50.
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  43. Philip Hugly & Charles Sayward (1980). Is English Inconsistent? Erkenntnis 15 (3):343 - 347.
    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.
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  44. Philip Hugly & Charles Sayward (1980). Tarski and Proper Classes. Analysis 40 (4):6-11.
    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.
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  45. Philip Hugly & Charles Sayward (1979). A Problem About Conversational Implicature. Linguistics and Philosophy 3 (1):19 - 25.
    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 (...)
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  46. Philip Hugly & Charles Sayward (1979). More on Propositional Identity. Analysis 39 (3):129-132.
    We give a semantical account of propositional identity which is stronger than mutual entailment. That is, according to our account: (1) if A = B is true in a model, so are A 'validates' B and B 'validates' A. (2) There exist models m such that A 'validates' B and B 'validates' A are true in m but A = B is not true in m. According to our account the following rule is sound: (3) from (.. A..) = (.. (...)
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  47. Philip Hugly & Charles Sayward (1979). Paradox and Semantical Correctness. Analysis 39 (4):166-169.
    In a series of papers R. L. Martin propounds a theory for dealing with the semantical paradoxes. This paper is a criticism of that theory.
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  48. Philip Hugly & Charles Sayward (1979). The Lessons of the Liar. Theory and Decision 11 (1):55-70.
    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.
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