Online research in philosophy

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions.

I analyze here biological regression equations known in the literature as allometries and scaling laws. My focus is on the alleged lawlike status of these equations. In particular I argue against recent views that regard allometries and scaling laws as representing universal, non-continent, and/or strict biological laws. Although allometries and scaling laws appear to be generalizations applying to many taxa, they are neither universal nor exceptionless. In fact there appear to be exceptions to all of them. Nor are the constants in allometries and scaling laws truly constant, stable, or universal in character, but vary in value across different taxa and background conditions. Moreover, these equations represent evolutionary, strongly contingent generalizations, which threatens their lawlike status. Lastly, allometries and scaling laws do not offer stable probabilities to which they hold in different backgrounds. I further suggest that many allometries and scaling laws function to elucidate explananda rather than explanantia or covering laws.

Consider the following argument: All men are mortal; Socrates is a man; therefore, Socrates is mortal. Intuitively, what makes this a valid argument has nothing to do with Socrates, men, or mortality. Rather, each sentence in the argument exhibits a certain logical form, which, together with the forms of the other two, constitute a pattern that, of itself, guarantees the truth of the conclusion given the truth of the premises. More generally, then, the logical form of a sentence of natural language is what determines both its logical properties and its logical relations to other sentences. The logical form of a sentence of natural language is typically represented in a theory of logical form by a well-formed formula in a ‘logically pure’ language whose only meaningful symbols are expressions with fixed, distinctly logical meanings (e.g., quantifiers). Thus, the logical forms of the sentences in the above argument would be represented in a theory based on pure predicate logic by the formulas ‘∀x(Fx ⊃ Gx)’, ‘Fy’, and ‘Gy’, respectively, where ‘F’, ‘G’, and ‘y’ are all free variables. The argument’s intuitive validity is then explained in virtue of the fact that the logical forms of the premises formally entail the logical form of the conclusion. The primary goal of a theory of logical form is to explain as broad a range of such intuitive logical phenomena as possible in terms of the logical forms that it assigns to sentences of natural language.

This paper analyzes the logical form of valuing. I argue that valuing a concept or property is a universal statement qua logical form, that valuing an object is an existential statement qua logical form, and, furthermore, that a correct analysis of the logical form of valuing contains doxastic operators. I show that these ingredients give rise to an interesting interplay between uniform and ununiform quantification, on the one hand, and de dicto and de re beliefs, on the other. I apply this analysis to the value of political freedom. The received view is that the value of freedom lies in the value of the specific things one is free to do. But Ian Carter has recently shown that freedom has irreducible, "non-specific" value, too. I show that underlying the debate between the proponents of the received view and their critics is a disagreement about logical form: ununiform de dicto beliefs about freedom as a concept, for the received view, and uniform half-de dicto-half-de re beliefs about freedom as an object, for its critics.

The purpose of this paper is to make a simple observation regarding the Johnson-Carnap continuum of inductive methods (see Johnson 1932, carnap 1952). From the outset, a common criticism of this continuum was its failure to permit the confirmation of universal generalizations: that is, if an event has unfailingly occurred in the past, the failure of the continuum to give some weight to the possibility that the event will continue to occur without fail in the future. The Johnson-Carnap continuum is the mathematical consequence of an axiom termed Johnson's sufficientness postulate, the thesis of this paper is that, properly viewed, the failure of the Johnson-Carnap continuum to confirm universal generalizations is not a deep fact, but rather an immediate consequence of the sufficientness postulate; and that if this postulate is modified in the minimal manner necessary to eliminate such an entailment, then the result is a new continuum that differs from the old one in precisely one respect: it enjoys the desideratum of confirming universal generalizations.

Over the years, I’ve been asked many times what “logical form” is, as applied to natural language. This is a natural enough question to address to me; after all, I’ve written a book titled Logical Form, and I’ve been asked to write any number of papers on the topic. This question, it seems to me, is certainly a “big” question, and big questions deserve big answers. I must admit, however, to being somewhat baffled as to how to do this satisfactorily, since big answers to big questions unfortunately tend to the trivial. With a nod to Wittgenstein, logical form has always seemed to me to be something that you know it when you see it; it is clear enough when it pops up, but one is hard pressed to say just what it is, to define it. This is so even though the meanings of the words “logical” and “form” seem straightforward enough; what I find puzzling is how the first word is supposed to modify the second. What is it that makes a form logical, as opposed to something else that is not logical? This, it seems to me, is a very hard question to answer indeed, for if we cannot contrast logical form with some other type of form, then every form (or no form) is a logical form, and we have arrived at the triviality previously mentioned.

Former discussions of biological generalizations have focused on the question of whether there are universal laws of biology. These discussions typically analyzed generalizations out of their investigative and explanatory contexts and concluded that whatever biological generalizations are, they are not universal laws. The aim of this paper is to explain what biological generalizations are by shifting attention towards the contexts in which they are drawn. I argue that within the context of any particular biological explanation or investigation, biologists employ two types of generations. One type identifies causal regularities exhibited by particular kinds of biological entities. The other type identifies how these entities are distributed in the biological world.

Although our theories are not precisely true, scientific realists contend that we should admit their objects into our ontology. One justification--offered by Sellars and Putnam--is that current theories belong to series that converge to ideally adequate theories. I consider the way the commitment to convergence reflects on the interpretation of lawlike claims. I argue that the distinction between lawlike and accidental generalizations depends on our cognitive interests and reflects our commitment to the direction of scientific progress. If the sciences disagree about the lawlikeness of some generalization(s), as an argument of Davidson's suggests, it follows from the interest relatively of lawlikeness that the laws of a science do not determine the essences of their objects. I conclude that this form of scientific realism provides no metaphysical support for essentialism.

The thesis of this paper is that extensional language alone provides an essentially inadequate foundation for the logical formalization of any lawlike statement. The arguments presented are intended to demonstrate that lawlike sentences are logically general dispositional statements requiring an essentially intensional reduction sentence formulation. By introducing a non-extensional logical operator, the 'fork', the difference between universal and statistical laws emerges in a distinction between dispositional predicates of universal strength as opposed to those of merely statistical strength. While the logical form of universal and statistical laws appears to be fundamentally dissimilar on the standard account, from this point of view their syntactical structure is basically the same.

On this conception, the semantic types of its primitive terms and their mode of combination determine the logical form of a sentence as it relates to determining under what conditions it is true. We develop this idea in the framework of truth-theoretic semantics. We argue that the semantic form of a declarative sentence in a language L is revealed by a (canonical) proof of its T-sentence in an interpretive truth theory for L. We give a precise characterization of sameness of logical form between any two declarative sentences in any two languages in terms of the notion of corresponding proofs in interpretive truth theories for the languages. We illustrate the utility of this approach with a number of examples. We then extend the characterization to non-declaratives in a generalization of truth-theoretic semantics that appeals to fulfillment conditions, of which truth conditions are one variety. On this approach, logical forms are not reified, and the notion of sameness of logical form is treated as conceptually basic. We discuss the relation of this conception of logical form to the project of identifying logical constants, reviewing two approaches, one of which takes topic neutrality as central, the other recursion. We argue that the project of identifying logical constants for the purposes of classifying together valid arguments is largely independent of that of identifying logical form of sentences, and urge an ecumenical approach to extending talk of logical constants beyond where it is currently well grounded.