A note on mathematical pluralism and logical pluralism

Mathematical pluralism notes that there are many different kinds of pure mathematical structures—notably those based on different logics—and that, qua pieces of pure mathematics, they are all equally good. Logical pluralism is the view that there are different logics (consequence relations), which are, in an appropriate sense, equally good. Some, such as Shapiro (Varieties of logic, Oxford University Press, Oxford, 2014), have argued that mathematical pluralism entails logical pluralism. In this brief note I argue that this does not follow. There is a crucial distinction to be drawn between the preservation of truth (simpliciter) and the preservation of truth-in-a-structure; and once this distinction is drawn, this suffices to block the argument. The paper starts by clarifying the relevant notions of mathematical and logical pluralism. It then explains why the argument from the first to the second does not follow. A final section considers a few objections.

     

Grammatical analysis and logical analysis in France

It is well known that, in France, this important movement, which originated in Port-Royal, did not remain exactly on the same basis during its development. In this paper we attempt to show how a new concept (the logical analysis of sentence from phrase) was proposed by Du Marsais (see grammatical articles of the Encyclopédie), Beauzée (1767) and, finally, Letellier (1805, 1811).     

The philosophy of logical wholism

The present paper is one installment in a lengthy task, the replacement of atomistic interpretations of Wittgenstein's Tractatus by a wholistic interpretation on which the world-in-logical-space is not constructed out of objects but objects are abstracted from out of that space. Here, general arguments against atomism are directed toward a specific target, the four aspects of the atomistic reading of Tractatus given in the Hintikkas' Investigating Wittgenstein (Hintikka & Hintikka 1986). The aspects in question are called the semantical, metaphysical, epistemological and formal.What follows a précis of the Hintikkas' rendering of Wittgenstein's perspective is a characterization of the wholistic interpretation, comparing Wittgenstein's world and the transcendental conditions it sets upon possible notation to a blank page and the conditions it sets upon what is about to be written there. There will not be occasion to bring arguments against each plank in the atomist's platform or in support of each facet of wholism. But there is an extended treatment of the first two aspects — the semantical and metaphysical — which takes off from Wittgenstein's determination that, in his hands, logic must take care of itself.The second half of the paper contains a negative assessment of the support the atomistic reading can glean from the texts of Tractatus and Notebooks. From a detailed look into a range of relevant textual and translational issues, we find little there to encourage that interpretation and much to discourage it.The paper closes on a preliminary consideration of one segment of the formal aspect of the Hintikkas' atomism, the idea that the analysis of Tractatus is the analysis of Russell or is, at worst, a near relative. Examination shows that Wittgenstein would have little reason to model his analysis on that of Russell. The fundamentally wholistic vision expressed in Tractatus requires a distinctively non-Russellian, decompositional version of analysis.Words are like a film on deep water Ludwig Wittgenstein Notebooks 1914–1916 A highly condensed version of the ideas here presented will appear in the article Hintikka's Tractatus in Proceedings of the XIVth International Wittgenstein Symposium, Wittgenstein Centenary Celebration, 1991.     

The logical study of science

The relation between logic and philosophy of science, often taken for granted, is in fact problematic. Although current fashionable criticisms of the usefulness of logic are usually mistaken, there are indeed difficulties which should be taken seriously — having to do, amongst other things, with different scientific mentalities in the two disciplines (section 1). Nevertheless, logic is, or should be, a vital part of the theory of science. To make this clear, the bulk of this paper is devoted to the key notion of a scientific theory in a logical perspective. First, various formal explications of this notion are reviewed (section 2), then their further logical theory is discussed (section 3). In the absence of grand inspiring programs like those of Klein in mathematics or Hilbert in metamathematics, this preparatory ground-work is the best one can do here. The paper ends on a philosophical note, discussing applicability and merits of the formal approach to the study of science (section 4).I would like to thank David Pearce and Veikko Rantala for their helpful comments.     

Dialogue on the hypothetical character of logical analysis

Reconstructing Popper's research programme for the Human Sciences, Noretta Koertge (Inquiry, Vol. 18 [1975]) has given a deductive‐nomological account of explanations of actions by means of a Rationality Principle. It is argued here that such a Rationality Principle is fundamentally redundant. Neither is it logically necessary in order to deduce a cognitive action‐explanandum, nor can it be given a semantic non‐empty interpretation, at least not within Koertge's own syllogism. Any attempt to save the Rationality Principle as unfalsifiablc but nevertheless indispensable for action explanations is rejected in the light of possible alternative action explanations by empirical and therefore in principle falsifiable psychological laws.     

The logical form of categorical sentences

In this paper, I propose an account of self-knowledge for desires. According to this account, we form beliefs about our own desires on the basis of our grounds for those desires. First, I distinguish several types of desires and their corresponding grounds. Next, I make the case that we usually believe that we have a certain desire on the basis of our grounds for it. Then, I argue that a belief formed thus is epistemically privileged. Finally, I compare this account to two other similar accounts of self-knowledge.