Search

We show that provability in the implicational fragment of relevance logic is complete for doubly exponential time, using reductions to and from coverability in branching vector addition systems. [ABSTRACT FROM PUBLISHER]

In the Tractatus, Wittgenstein advocates two major notational innovations in logic. First, identity is to be expressed by identity of the sign only, not by a sign for identity. Secondly, only one logical operator, called “N” by Wittgenstein, should be employed in the construction of compound formulas. We show that, despite claims to the contrary in the literature, both of these proposals can be realized, severally and jointly, in expressively complete systems of first-order logic. Building on early work of Hintikka’s, we identify three ways in which the first notational convention can be implemented, show that two of these are compatible with the text of the Tractatus, and argue on systematic and historical grounds, adducing posthumous work of Ramsey’s, for one of these as Wittgenstein’s envisaged method. With respect to the second Tractarian proposal, we discuss how Wittgenstein distinguished between general and non-general propositions and argue that, claims to the contrary notwithstanding, an expressively adequate N-operator notation is implicit in the Tractatus when taken in its intellectual environment. We finally introduce a variety of sound and complete tableau calculi for first-order logics formulated in a Wittgensteinian notation. The first of these is based on the contemporary notion of logical truth as truth in all structures. The others take into account the Tractarian notion of logical truth as truth in all structures over one fixed universe of objects. Here the appropriate tableau rules depend on whether this universe is infinite or finite in size, and in the latter case on its exact finite cardinality.As it is obviously easy to express how propositions can be constructed by means of this operation and how propositions are not to be constructed by means of it, this must be capable of exact expression.5.503 [ABSTRACT FROM PUBLISHER]

The article focuses on the knowledge of counterfactuals of social epistemology. It states that its objective is to outline a picture of the average knowledge of counterfactuals and utilize it to bring up a problem for the conventional philosophical duality among a priori and a posteriori knowledge. It notes that the capability to judge counterfactuals registers all the cognitive capabilities to assess sentences.

Examines the logical relation between the Is and the Ought that was weaker than entailment, and indeed neither deductive nor inductive. Prominent post-1950s examples of claims that Is-like statements can support Ought-like statements; Argument that the support that some primarily descriptive statements give to normative conclusions looks like logical support; Reasons why some forms of support have an affinity to logical relations.

Discusses the book "Aquinas on Being," by Anthony Kenny and logicism. Observations regarding the book; Metaphysical doctrine of Thomas Aquinas; Views of both Aquinas and Kenny on logicism.

Argues that equivocation described as a fallacy is not a logical concept but an epistemic one. Claim that the arguments of one who equivocates is not logically flawed but is unpersuasive; Assertion that only arguments which are unpersuasive in a certain way involve equivocations.

Logic ought to guide our thinking. It is better, more rational, more intelligent to think logically than to think illogically. Illogical thought leads to bad judgment and error. In any case, if logic had no role to play as a guide to thought, why should we bother with it?The somewhat naïve opinions of the previous paragraph are subject to attack from many sides. It may be objected that an activity does not count as thinking at all unless it is at least minimally logical, so logic is constitutive of thought rather than a guide to it. Or it may be objected that whereas logic describes a system of timeless relations between propositions, thinking is a dynamic process involving revisions, and so could not use a merely static guide. Or again the objection may be that there is no such thing as logic, only a whole variety of different logics, not all of which could possibly be good guides. [ABSTRACT FROM PUBLISHER]

0 Consider ‘I’ as used by a given speaker and some ordinary proper name of that speaker: are these two coreferential singular terms which differ in Fregean sense? If they could be shown to be so, we might be able to explain the logical and epistemological peculiarities of ‘I’ by appeal to its special sense and yet feel no temptation to think of its reference as anything more exotic than a human being. [ABSTRACT FROM PUBLISHER]

If you are told or otherwise believe an either—or proposition, the question may easily arise what makes it true. ‘The potato crop in Ruritania was halved by blight in 1928’ — ‘Well then, either the expected, planned-for crop was in excess of the people's needs, or there was a shortage of potatoes that year, or a lot were imported …’. That seems a fair deduction, and we may ask which was true. If only one was, then we'd say it made the disjunction true. If all were, then all of them did. [ABSTRACT FROM PUBLISHER]

The front cover of the journal is presented along with the issue's editors and information on membership and subscriptions and table of contents.