On translating logic

The paper comments on Dummett's Significance of Quine's Indeterminacy Thesis and discusses Quine's views on the translation of logical connectives. Some difficulties about the latter related to those raised by Morton (J. Phil. 70 (1973), 503–510) are considered. Quine seems here to be in a position considered by Dummett of not allowing a foreigner to be translated as conflicting with one's own firm theoretical commitment (in this case classical logic). But Dummett seems wrong in holding that entrenched theoretical statements must be stimulus analytic.A revised and expanded version of remarks at the Conference on Language, Intentionality, and Translation Theory, University of Connecticut, Storrs, March 2, 1973, commenting on Michael Dummett, The Significance of Quine's Indeterminacy Thesis. I am greatly indebted to the discussion at the Conference.     

La Evolucion de la filosofia de Wittgenstein

Summary The author claims that there is a basic difference between theTractatus and thePhilosophical Investigations; despite Bernstein's and O'Brien's claims to the contrary, there are, indeed, two Wittgensteins. Yet, to ascertain the difference between both we must look at Wittgenstein's conceptions of philosophy rather than at his views on logic and language. Wittgenstein's different, and even divergent, views on logic and language are grounded on his two views on philosophy and not the other way around. At the same time, Wittgenstein's views on philosophy are caused by his ways of conceiving the scope of philosophical activity in regard to language. Both in theTractatus and in thePhilosophical Investigations, Wittgenstein points out what is important in language for philosophy, but in each case he reaches very different conclusions. Now, when all is said, there remains one unifying factor in all of Wittgenstein's investigations: it is the question of the logic of language, which shifts positions from theTractatus to theInvestigations, so that what was earlier a hidden structure becomes later the grammar of its indefinitely complexe uses.     

To and from philosophy — Discussions with Gödel and Wittgenstein

I propose to sketch my views on several aspects of the philosophy of mathematics that I take to be especially relevant to philosophy as a whole. The relevance of my discussion would, I think, become more evident, if the reader keeps in mind the function of (the philosophy of) mathematics in philosophy in providing us with more transparent aspects of general issues. I shall consider: (1) three familiar examples; (2) logic and our conceptual frame; (3) communal agreement and objective certainty; (4) the transcommunal universality of mathematics; (5) the big jump to the potential infinite; (6) the reconciliation of local creation with the hypothesis of discovery; (7) Platonism as realism plus conceptualism; (8) foundational studies and mathematical practice; and (9) the decomposition of philosophical disagreements. The views of Gödel and Wittgenstein are emphasized in order to add specificity to the discussions.     

The logic and language of Nirvāna: A contemporary interpretation

In contrast to historically orientedapproaches, this paper tackles the concept ofNirvna from the perspective ofcontemporary philosophy of language. It focuseson four propositions: Nirvna exists;Nirvna does not exist; Nirvna existsand does not exist; Nirvna neither exists nordoes not exist. The Buddha's rejectionof these propositions is interpreted by meansof explicit and conditionaldefinitions of existence. Stalnaker's notion ofpragmatic presupposition providesan explanation why the propositions are withoutmeaning. After comparing theword ``Nirvna' with indexicals, propernames and theoretical terms, it is finallyasked what linguistic function the word has.     

Combining Possibilities and Negations

Combining non-classical (or sub-classical) logics is not easy, but it is very interesting. In this paper, we combine nonclassical logics of negation and possibility (in the presence of conjunction and disjunction), and then we combine the resulting systems with intuitionistic logic. We will find that Kracht's results on the undecidability of classical modal logics generalise to a non-classical setting. We will also see conditions under which intuitionistic logic can be combined with a non-intuitionistic negation without corrupting the intuitionistic fragment of the logic.     

Objectivity and the double standard for feminist epistemologies

The emphasis on the limitations of objectivity, in specific guises and networks, has been a continuing theme of contemporary analytic philosophy for the past few decades. The popular sport of baiting feminist philosophers — into pointing to what's left out of objective knowledge, or into describing what methods, exactly, they would offer to replace the powerful objective methods grounding scientific knowledge — embodies a blatant double standard which has the effect of constantly putting feminist epistemologists on the defensive, on the fringes, on the run.This strategy can only work if objectivity is transparent, simple, stable, and clear in its meaning. It most certainly is not. In fact, taking objectivity as a sort of beautiful primitive, self-evident in its value, and all-powerful in its revelatory power, requires careless philosophy, and the best workers in metaphysics, epistemology, and philosophy of science have made reworked definitions of objectivity absolutely central to their own projects. In fact, classic feminist concerns with exploring the impact of sex and gender on knowledge, understanding, and other relations between human beings and the rest of the world fall squarely within the sort of human and social settings thatare already considered central in most current analytic metaphysics, epistemology, and philosophy of science. I argue that the burden of proof is clearly on those who wish toreject the centrality and relevance of sex and gender to our most fundamental philosophical work on knowledge and reality.I am especially indebted to Helen Longino, Bojana Mladenovic, Ina Roy, Jonathan Sills, and David Smith for their time, discussion, and criticism of drafts of this paper.     

Incompatible empirically equivalent theories: A structural explication

The thesis of the empirical underdetermination of theories (U-thesis) maintains that there are incompatible theories which are empirically equivalent. Whether this is an interesting thesis depends on how the term incompatible is understood. In this paper a structural explication is proposed. More precisely, the U-thesis is studied in the framework of the model theoretic or emantic approach according to which theories are not to be taken as linguistic entities, but rather as families of mathematical structures. Theories of similarity structures are studied as a paradigmatic case. The structural approach further reveals that the U-thesis is related to problems of uniqueness in the representational theory of measurement, questions of geometric conventionalism, and problems of structural underdetermination in mathematics.I'd like to thank three anonymous referees for valuable comments on earlier versions of this paper and Thomas E. Uebel for linguistic advice.     

Negation as Cancellation, and Connexive Logic

Of the various accounts of negation that have been offered by logicians in the history of Western logic, that of negation as cancellation is a very distinctive one, quite different from the explosive accounts of modern "classical" and intuitionist logics, and from the accounts offered in standard relevant and paraconsistent logics. Despite its ancient origin, however, a precise understanding of the notion is still wanting. The first half of this paper offers one. Both conceptually and historically, the account of negation as cancellation is intimately connected with connexivist principles such as ¬( ¬). Despite this, standard connexivist logics incorporate quite different accounts of negation. The second half of the paper shows how the cancellation account of negation of the first part gives rise to a semantics for a simple connexivist logic.     

Dummett's intuitionism is not strict finitism

Michael Dummett's anti-realism is founded on the semantics of natural language which, he argues, can only be satisfactorily given in mathematics by intuitionism. It has been objected that an analog of Dummett's argument will collapse intuitionism into strict finitism. My purpose in this paper is to refute this objection, which I argue Dummett does not successfully do. I link the coherence of strict finitism to a view of confirmation — that our actual practical abilities cannot confirm we know what would happen if we could compute impracticably vast problems. But to state his case, the strict finitists have to suppose that we grasp the truth conditions of sentences we can't actually decide. This comprehension must be practically demonstrable, or the analogy with Dummett's argument fails. So, our actual abilities must be capable of confirming that we know what would be the case if actually undecidable sentences were true, contradicting the view of confirmation. I end by considering objections.I especially want to thank Alex George and Philip Kitcher for their help on this paper. I'd also like to thank the members of the Propositional Attitudes Task Force, Jane Braaten, Jay Garfield, Lee Bowie, Murray Kitely and Tom Tymoczko. My thanks also to Peter Godfrey-Smith and the anonymous reviewers of Synthese, one of whom was particularly helpful.     

Five Observations Concerning the Intended Meaning of the Intuitionistic Logical Constants

This paper contains five observations concerning the intended meaning of the intuitionistic logical constants: (1) if the explanations of this meaning are to be based on a non-decidable concept, that concept should not be that of `proof"; (2) Kreisel"s explanations using extra clauses can be significantly simplified; (3) the impredicativity of the definition of can be easily and safely ameliorated; (4) the definition of in terms of `proofs from premises" results in a loss of the inductive character of the definitions of and and (5) the same occurs with the definition of in terms of `proofs with free variables".     

Number: From the Nyāya to Frege-Russell

The aim of this paper is to present the Nyya concept of number in the light of contemporary philosophy and to show that the Frege-Russell concept of number does not contradict the Nyya concept of number but rather supplements it.     

Re-Interpretation in Historiography: John Dewey and the Neo-Humanist Tradition

Did John Deweys new philosophy of education really try to dissolve the whole block of tradition or is his debt namely to educational core-concepts of neo-humanism deeper than he was prepared to acknowledge? After some general remarks on the process of reception as productive re-adaptation and its implication for historiography I will deal with Deweys own contexts that shape the interpretative grid through which he receives the tradition. Two case studies attempt to illustrate both continuity and discontinuity with a specific part of this tradition, namely two critical perspectives within German neo-humanism: Georg Wilhelm Friedrich Hegel and Johann Friedrich Herbart.     

Branching space-time

Branching space-time is a simple blend of relativity and indeterminism. Postulates and definitions rigorously describe the causal order relation between possible point events. The key postulate is a version of everything has a causal origin; key defined terms include history and choice point. Some elementary but helpful facts are proved. Application is made to the status of causal contemporaries of indeterministic events, to how splitting of histories happens, to indeterminism without choice, and to Einstein-Podolsky-Rosen distant correlations.     

MacIntyre and the Idea of an Educated Public

Some years ago, 1985, Alasdair MacIntyre wrote a paper onThe Idea of an Educated Public in which he argued that the only route open for educators for the future, in order to emerge out of the current moral crisis created by the emotivist modernist culture is to bring back the idea of an educated public from the Scottish Enlightenment and to regard education as education into such a public. The notion of an educated public, in effect, reappears also in all his later books on moral philosophy, particular his latest,Three Rival Theories of Moral Enquiry, where he takes up his original proposal that educated publics should grow around universities and canvasses the new idea that under contemporary conditions what we may need is not one universal university but three kinds contextualized within the three rival kinds of cultural and moral programmes he identifies, and, correspondingly, three kinds of educated public. This paper tries to trace the evolution of MacIntyre's idea of an educated public throughout his work, (1) arguing that there is one particular perspective on the idea which he strangely omits, that represented by Dewey/Habermas, and (2) critiquing his final solution on the basis of its possibility and political desirability.     

Dowód aksjomatyzowalności pewnychn-wartościowych rachunków zdań

Praca ta zostaa wykonana pod kierunkiem prof. drJerzego Supeckiego. Jej szczególny przypadek dotyczcyn-wartociowego rachunku zda o jednej wartoci wyrónionej by referowany w Warszawie na zjedzie Grupy Logiki Instytutu Filozofii i Socjologii PAN. Streszczenie tego referatu [5] zostao wydrukowane w Sprawozdaniach Wydziau Nauk Spoecznych PAN.Allatum est die 19 Aprilis 1963     

The probabilistic import of illatives

It is not only overtly probabilistic illatives like makes it certain that but also apparently non-probabilistic ones like therefore that have probabilistic import. Illatives like therefore convey the meaning that the premise confers on the conclusion a probability not only greater than 0 but also greater than 1/2. But because they do not say whether that probability is equal to or less than 1, these illatives are appropriately called neutral.     

Anti-realist truth and concepts of superassertibility

Crispin Wright offers superassertibility as an anti-realist explication of truth. A statement is superassertible, roughly, if there is a state of information available which warrants it and it is warranted by all achievable enlargements of that state of information. However, it is argued, Wright fails to take account of the fact that many of our test procedures are not sure fire, even when applied under ideal conditions. An alternative conception of superassertibility is constructed to take this feature into account. However, it is then argued that when this revised concept of superassertibility is taken as the truth predicate of probability statements, statements whose test procedures are paradigmatically not sure fire, then any anti-realist theory of the sense of such probability statements cannot be compositional, in Dummett's sense of compositional.     

O liczbach kardynalnych

Tre: Wstp. I. Niektóre pojcia i prawa teorii klas stosunków. II. O klasach abstrakcji. III. O równoskadnikowoci. IV. O kardynalnych liczbach skadników. V. O. stosowanej teorii równoskadnikowoci. VI. O relacji równej liczby elementów. VII. Stosunek obu poj liczb kardynalnych. Zakoczenie.Allatum est die 30 Augusti 1961     

Complete Infinitary Type Logics

For each regular cardinal , we set up three systems of infinitary type logic, in which the length of the types and the length of the typed syntactical constructs are < . For a fixed , these three versions are, in the order of increasing strength: the local system ₍₎, the global system g₍₎ (the difference concerns the conditions on eigenvariables) and the -system ₍₎ (which has anti-selection terms or Hilbertian -terms, and no conditions on eigenvariables). A full cut elimination theorem is proved for the local systems, and about the -systems we prove that they admit cut-free proofs for sequents in the -free language common to the local and global systems. These two results follow from semantic completeness proofs. Thus every sequent provable in a global system has a cut-free proof in the corresponding -systems. It is, however, an open question whether the global systems in themselves admit cut elimination.