Grazer Philosophische Studien

We address the impingement of Artificial Intelligence (AI) on logic, by examining the requirements posed on logic by knowledge representation and reasoning issues which A I has addressed. We then outline some of AI's contributions, via Logic Programming, to more dynamic forms of logic, in order to deal with knowledge in flux, namely: incomplete and contradictory information; hypotheses making through abduction; argumentation; diagnosis and debugging; updating; and learning. Along the way we delve into implications for the philosophy of knowledge.

Dummett's account of the semantic paradoxes in terms of his theory of indefinitely extensible concepts is compared with Bürge's account in terms of indexicality. Dummett's appeal to intuitionistic logic does not block the paradoxes but Bürge's attempt to avoid the Strengthened Liar is unconvincing. It is argued that in order to avoid the Strengthened Liar and other semantic paradoxes involving nonindexical expressions (constants), one must postulate that when we reflect on the paradoxes there are slight shifts in the meaning (not just reference) we ascribe to metalinguistic expressions (in particular 'say', and derivatively 'true' and 'false'). Consideration of metaphor and gradual linguistic change suggests that such semantic shifts are consistent with language-learning and communication. On this account there is no threat to classical logic, bivalence or the fundamental principles governing 'true' and 'false'.

Dummctt argues that classical quantification is illegitimate when the domain is given as the objects which fall under an indefinitely extensible concept, since in such cases the objects are not the required definite totality. The chief problem in understanding this complex argument is the crucial but unexplained phrase 'definite totality' and the associated claim that it follows from the intuitive notion of set that the objects over which a classical quantifier ranges form a set. 'Definite totality' is best understood as disguised plural talk like Cantor's 'consistent multiplicity', although this does not help in understanding how a totality could be anything other than definite. Moreover, contrary to his claims, Dummett's own notion of set is not intuitive and he does not demystify the set-theoretic paradoxes. In conclusion, it is argued that Dummett's context principle is responsible for the incoherent projection of the haziness of a conception of some objects onto reality.

The paper examines Dummett's argument for the indefinite extensibility of the concepts set, ordinal, real number, set of natural numbers, and natural number. In particular it investigates how the indefinite extensibility of the concept set affects our understanding of the notion of real number and whether the argument to the indefinite extensibility of the reals is cogent. It claims that Dummett is right to think of the universe of sets as an indefinitely extensible domain but questions the cogency of the further claim that this fact raises an issue as to what sets or real numbers there are.

Gödel and others held that impredicative specification is illegitimate in a constructivist framework but legitimate elsewhere. Michael Dummett argues to the contrary that impredicativity, though not necessarily illicit, needs justification regardless of whether one assumes the context is realist or constructivist. In this paper I defend the Gödelian position arguing that Dummett seeks a reduction of impredicativity to predicativity which is neither possible nor necessary. The argument is illustrated by considering first highly predicative versions of the equinumerosity axiom for cardinal number and Axiom V for sets, on the one hand, then classically consistent disjunctivised versions of Axiom V which are impredicative but can prove the well-foundedness of the semantics of weaker such systems, on the other.

In Michael Dummett's celebrated essay on Gödel's theorem he considers the threat posed by the theorem to the idea that meaning is use and argues that this threat can be annulled. In my essay I try to show that the threat is even less serious than Dummett makes it out to be. Dummett argues, in effect, that Gödel's theorem does not prevent us from "capturing" the truths of arithmetic; I argue that the idea that meaning is use does not require that we be able to "capture" these truths anyway. Towards the end of my essay I relate what I have been arguing first to Dummett's concept of indefinite extensibility and then to some of Wittgenstein's remarks on Gödel's theorem.

One of Michael Dummett's most striking contributions to the philosophy of mathematics is an argument to show that the correct logic to apply in mathematical reasoning is not classical but intuitionistic. In this article I wish to cast doubt on Dummett's conclusion by outlining an alternative, motivated by consideration of a well-known result of Kurt Gödel, to the standard view of the relationship between classical and intuitionistic arithmetic. I shall suggest that it is hard to find a perspective from which to arbitrate between the competing views.

Although Brouwer is well known for his Intuitionistic philosophy of mathematics, a constructivist philosophy which calls for restricted use of certain logical principles, there is much less awareness of the well-developed metaphysical basis which underlies those restrictions. In the first half of this paper I outline a basic interpretation of Brouwer's metaphysics, and then in the second half consider the compatibility of that metaphysics with Dummett's argument for a principled non-metaphysical approach to intuitionism. I conclude that once the variously misleading accretions of the central concepts - metaphysics and logic - are set aside, Dummett and Brouwer's accounts can be seen to be at the very least compatible, if not complementar

In "Truth" Michael Dummett presents a case for intuitionist logic as the logic of ordinary discourse. The case depends on a supposed need to make two intuitions mesh: first, that it is senseless to suppose, of any statement, that it is neither true nor false; second, that there is no guarantee, for every statement, that either there is something in the world to make it true, or there is something to make it false. This paper argues, developing a notion of natural isostheneia, that Dummett's first intuition is wrong as he reads it, and that, consequently, his case for intuitionist logic collapses.

On a classical conception, knowing the sense of a proposition is knowing its truth-condition, rather than simply knowing how to verify the proposition, or how to find its implications (whether deductive implications or implications for action). But knowing the truth-condition of a proposition is not unrelated to your use of particular methods for verifying the proposition, or finding its implications. Rather, your knowledge of the truth-condition of the proposition has to justify the use of particular methods for verifying it, or finding its implications. And your knowledge of the truth-condition of the proposition has to be what causes your use of particular methods for verifying it or finding its implications. So on a classical picture, we do not appeal to knowledge of sense only in explaining the informativeness of identities. We have to think of knowledge of sense as what causes, and justifies, your use of particular ways of verifying or finding the implications of a proposition. I argue that in the case of a perceptual demonstrative, like 'that star' or 'that mountain', it is conscious attention to the object that causes, and justifies, your use of particular ways of verifying or finding the implications of propositions involving the demonstrative. So conscious attention to the object is what constitutes your grasp of the sense of the demonstrative. This runs counter to the philosophical tradition since Locke, which takes it that the role of experience in understanding has to do solely with the verification of propositions. I argue that once we think of conscious attention as a pre-intentional acquaintance with the object itself, we can see how it is possible to think of understanding as consisting in knowledge of classical truth-conditions.

First, we argue that Dummett, in his accusing Husserl of psychologism, does not pay sufficient attention to the phenomenological framework of Husserl's philosophy. This framework must be taken into account for understanding why Husserl is not a psychologist in the theory of meaning. Second, it is shown that the thoughts required by Evans' theory of understanding indexical utterances are not to be identified with mental events as understood by psychologism. We then emphasize what Husserl's and Evans' explanation of the mind share, and finally argue that Dummett's anti-psychologism is based on a psychologistic view of consciousness which is not questioned by Dummett.

The „Paradox of the Concept Horse" arises on the assumption of the Reference Principle: that co-referential expressions should be cross-substitutable salva veritate in extensional contexts and salva congruitate in all. Accordingly no singular term can co-refer with an unsaturated expression. The paper outlines a number of desiderata for a satisfactory response to the problem and argues that recent treatments by Dummett and Wiggins fall short by their lights. It is then pointed out that a more consistent perception of the requirements of the Reference Principle leads not to the Paradox but to the result that Frege had no business extending the notion of Bedeutung to unsaturated expressions in the first place. Rather the relation between, e.g., predicates and the entities that comprise the range of higher-order logical variables must be logically unlike that between singular terms and their referents; the way is therefore opened for singular terms to refer to entities of the former kind after all. The Concept Horse is a concept (and a Fregean object too.)

Bei normalen Täuschungen verträgt sich die Erwartung des Täuschers auf Erfolg nicht mit der Erwartung, daß der Täuschungsversuch auf Seiten des Täuschungsadressaten als solcher erkannt werden wird. Ist Täuschung überhaupt mit Offenheit (erwartetem bzw. gar intendiertem Erkanntwerden) verträglich? Bei nicht-normalen Täuschungen: Ja. Nicht-normale Täuschungen sind solche, bei denen der Täuscher nur dann mit einem Täuschungserfolg rechnen zu können glaubt, wenn ihm seine Täuschungs-Adressatin außer seiner Täuschungsabsicht auch noch einen Irrtum unterstellt. Wie sieht die Logik solcher Täuschungsversuche aus? Und was sind deren (psychologische) Grenzen?

William James's Konzeption der Wahrheit enthält sowohl realistische als auch antirealistische Elemente. Sie ist im wesentlichen das Resultat der Anwendung seiner pragmatischen Regel, des Kerns seiner Ansichten über Bedeutung, auf den Wahrheitsbegriff James' vorrangiges Ziel ist es, die Theorie der Wahrheit und die Theorie der Erkenntnis in einen engeren Zusammenhang zu bringen, als dies im Rahmen der klassischen Korrespondenztheorie geschehen ist. Dabei gelangt er zu der bahnbrechenden epistemologischen Einsicht, daß es möglich ist, den Fallibilismus mit einer antiskeptischen Grundeinstellung zu verbinden. In seiner berechtigten Kritik am traditionellen Mythos der Gewißheit schießt James jedoch über das Ziel hinaus: Er verwandelt Wahrheit selbst in einen epistemischen Begriff und nimmt ihre damit zwangsläufig einhergehende Relativierung in Kauf Dabei übersieht er, daß es durchaus möglich ist, den Fallibilismus mit einer absoluten Konzeption der Wahrheit zu verbinden.

David Pears's contention that the Tractatus is to be understood as advancing a form of metaphysical realism is defended against McGuinness's view that Tractatus 1-2.063 is to be treated just as introducing a metaphysical myth that may be employed to bring into prominence salient features of propositions. Starting with a discussion of the involved difficulties, e.g., determining (1) whether Wittgenstein does in fact provide an argument for the existence of simple objects (2) what this object is and (3) what role the existence of simple objects plays within the Picture Theory of the Proposition, Wittgenstein's argument for the existence of simple objects is reconstructed, augmenting Pears's existing account by providing further details of why Wittgenstein held that determinacy of sense requiresthe existence of simple objects.

Feigl approaches philosophy of mind in the monist perspective of Logical Empiricism but he does not treat the mind-body problem in an eliminative manner. Although he modified his positions and wavered between strict reductionism and explicit non-reductionism, he never abandoned his conviction that the mind-body problem is not a pseudoproblem. Especially in his 'double-knowledge-view' he concedes private mental states that physical theory cannot account for and develops an identity theory that integrates two epistemic features - the way of immediate experience and the indirect way of knowledge-by-description. Feigl's complex treatment of the mind-body problem retains its systematical importance even in the light of later developments in philosophy of mind.

Analyses, in the simplest form assertions that aim to capture an intimate link between two concepts, are viewed since Russell's theory of definite descriptions as analyzing descriptions. Analysis therefore has to obey the laws governing definitions including some form of a Substitutivity Principle (SP). Once (SP) is accepted the road to the paradox of analysis is open. Popular reactions to the paradox involve the fundamental assumption (SV) that sentences differing only in containing an analysandum resp. an analysans express the same proposition, because analysandum and analysans are the same entity. Following suggestions of Gupta and Belnap it is argued that (SV) should be rejected.

Normative nonrealism denies, first, that some things are good or bad independently of facts about the attitudes of moral agents and, second, that attitude-independent moral facts determine what is rational. This implies that facts about what is rational are logically prior to what is moral. Nonrealism commonly assumes (a) that moral realism is false or unjustifiable, (b) that there is a conceptual connection between morality and rationality and (c) that the particular theory of rationality is the correct account of rationality. Facing the threat of relativism when abandoning (c) it is argued that (c) is at least dubious. Semantic considerations concerning the meaning of "rationality" are sketched and the full-information approach of decision making, intemalism and extemalism are discussed in the light of "Why care?"-questions with the resuh that these questions do serious damage to nonrealist approaches to rationality and reason-based morality.