Online research in philosophy

As a theory of reasoning, logic has—or ought to have—nothing to do with metaphysics. It ought to have nothing to do with questions concerning what there is, or whether there is anything at all. It is precisely because of its metaphysical commitments that Aristotelian syllogistics, for example, was eventually deemed inadequate as a canon of pure logical reasoning. The inference from an A-form statement such as (1) All humans are mortal to the corresponding I-form statement.

Comparing the three-form reasoning of new Hetu-vidya with Western logic, scholars have put forward four perspectives. Combining their strengths and shortcomings, and the examples of Hetu-vidya reasoning, we can conclude that the three-form reasoning should have four forms: (1) the affirmative expression of formal implication; (2) the modus ponens of hypothetical reasoning concerning sufficient conditions after universal instantiation; (3) the negative expression of a formal implication; and (4) the modus tollens of hypothetical reasoning concerning sufficient conditions after universal instantiation.

Yah boo sucks to the grammer wot we lernt in skool! Grammar (and the bad old traditional logic) says that quantifier phrases such as 'nobody', 'everyone', 'all women', 'some men' and 'a man' are in the same category as names such as 'Milly', 'Molly' and 'Mandy'. So, prior to their first corrective lessons, students are awfully muddled, the first and fundamental problem being the Woozle hunt for somebody called 'nobody'. Hoorah for modern logic and logic teachers! The story used to justify our current logics is entirely fictional. The claims about names and quantifier phrases in English are wildly false. Two of the heroes of modern logic, Russell and Hilbert, make the very mistakes which are falsely blamed on traditional logic. The villain, Meinong, turns out to have been working a different patch. Ideas ascribed to traditional grammar are modern inventions. Neither logicians nor grammarians can be trusted to tell the history of either grammar or logic.

Bertrand Russell, in the second of his 1914 Lowell lectures, Our Knowledge of the External World, asserted famously that ‘every philosophical problem, when it is subjected to the necessary analysis and purification, is found either to be not really philosophical at all, or else to be, in the sense in which we are using the word, logical’ (Russell 1993, p. 42). He went on to characterize that portion of logic that concerned the study of forms of propositions, or, as he called them, ‘logical forms’. This portion of logic he called ‘philosophical logic’. Russell asserted that ... some kind of knowledge of logical forms, though with most people it is not explicit, is involved in all understanding of discourse. It is the business of philosophical logic to extract this knowledge from its concrete integuments, and to render it explicit and pure. (p. 53) Perhaps no one still endorses quite this grand a view of the role of logic and the investigation of logical form in philosophy. But talk of logical form retains a central role in analytic philosophy. Given its widespread use in philosophy and linguistics, it is rather surprising that the concept of logical form has not received more attention by philosophers than it has. The concern of this paper is to say something about what talk of logical form comes to, in a tradition that stretches back to (and arguably beyond) Russell’s use of that expression. This will not be exactly Russell’s conception. For we do not endorse Russell’s view that propositions are the bearers of logical form, or that appeal to propositions adds anything to our understanding of what talk of logical form comes to. But we will be concerned to provide an account responsive to the interests expressed by Russell in the above quotations, though one clarified of extraneous elements, and expressed precisely. For this purpose, it is important to note that the concern expressed by Russell in the above passages, as the surrounding text makes clear, is a concern not just with logic conceived narrowly as the study of logical terms, but with propositional form more generally, which includes, e.g., such features as those that correspond to the number of argument places in a propositional function, and the categories of objects which propositional....

Abstract The paper presents an outline of a unified answer to five questions concerning logic: (1) Is logic in the mind or in the world? (2) Does logic need a foundation? What is the main obstacle to a foundation for logic? Can it be overcome? (3) How does logic work? What does logical form represent? Are logical constants referential? (4) Is there a criterion of logicality? (5) What is the relation between logic and mathematics?

The need to distinguish between logical and extra-logical varieties of inference, entailment, validity, and consistency has played a prominent role in meta-ethical debates between expressivists and descriptivists. But, to date, the importance that matters of logical form play in these distinctions has been overlooked. That’s a mistake given the foundational place that logical form plays in our understanding of the difference between the logical and the extra-logical. This essay argues that descriptivists are better positioned than their expressivist rivals to provide the needed account of logical form, and so better able to capture the needed distinctions. This finding is significant for several reasons: First, it provides a new argument against expressivism. Second, it reveals that descriptivists can make use of this new argument only if they are willing to take a controversial—but plausible—stand on claims about the nature and foundations of logic.

Introduction 1.1 GOALS This book is devoted to an in-depth investigation of some of the properties of Logical Form (LF). In particular, the primary aim of ...

In the works of Kant and his followers, the notion of form plays an important role in explaining the apriority, necessity and certainty of logic. Bernard Bolzano (1781–1848), an important early critic of Kant, found the Kantians' definitions of form imprecise and their explanations of the special status of logic deeply unsatisfying. Proposing his own conception of form, Bolzano developed radically different views on logic, truth in virtue of form, and other matters. This essay presents Bolzano's views in the light of his criticisms of the Kantian logicians.

These are not just tricks or puzzles, but are intimately connected with some of the liveliest and most basic philosophical disputes about logical form, ...