This article traces the development of possible worlds semantics through the work of: Wittgenstein, 1913-1921; Feys, 1924; McKinsey, 1945; Carnap, 1945-1947; McKinsey, Tarski and Jónsson, 1947-1952; von Wright, 1951; Becker, 1952; Prior, 1953-1954; Montague, 1955; Meredith and Prior, 1956; Geach, 1960; Smiley, 1955-1957; Kanger, 1957; Hintikka, 1957; Guillaume, 1958; Binkley, 1958; Bayart, 1958-1959; Drake, 1959-1961; Kripke, 1958-1965.

The canonical version of possible worlds semantics for story prefixes is due to David Lewis. This paper reassesses Lewis's theory and draws attention to some novel problems for his account.

I explore the motivation and logical consequences of the idea that we have some (limited) ability to know contingent facts about the future, even in presence of the assumption that the future is objectively unsettled or indeterminate. I start by formally characterizing skepticism about the future. This analysis nudges the anti-skeptic towards the idea that if some propositions about the future are objectively indeterminate, then it may be indeterminate whether a suitably positioned agent knows them. -/- Philosophical Perspectives, Volume 35, (...) Issue 1, Page 50-69, December 2021. (shrink)

An investigation of Proclus' logic of the syllogistic and of negations in the Elements of Theology, On the Parmenides, and Platonic Theology. It is shown that Proclus employs interpretations over a linear semantic structure with operators for scalar negations (hypemegationlalpha-intensivum and privative negation). A natural deduction system for scalar negations and the classical syllogistic (as reconstructed by Corcoran and Smiley) is shown to be sound and complete for the non-Boolean linear structures. It is explained how Proclus' syllogistic presupposes converting the (...) tree of genera and species from Plato's diairesis into the Neoplatonic linear hierarchy of Being by use of scalar hyper and privative negations. (shrink)

A common and much-explored thought is Łukasiewicz's idea that the future is ‘indeterminate’—i.e., ‘gappy’ with respect to some claims—and that such indeterminacy bleeds back into the present in the form of gappy ‘future contingent’ claims. What is uncommon, and to my knowledge unexplored, is the dual idea of an overdeterminate future—one which is ‘glutty’ with respect to some claims. While the direct dual, with future gluts bleeding back into the present, is worth noting, my central aim is simply to sketch (...) and briefly explore an alternative glutty-future view, one that is conservative—indeed, entirely classical—with respect to the present. The structure of the paper runs as follows. §1 briefly sketches the target gap picture of an indeterminate future yielding gappy claims at the present. §2 presents the direct dual idea—a glut picture of an overdeterminate future yielding glutty claims at present. §3 sketches the central idea, a more interesting glut picture in which the future contains contradictory states but the present remains entirely classical. §4 contains a general defence of the idea, leaving it open as to whether the gappy-future view enjoys substantive virtues over the proposed glutty-future view of §3. (shrink)

A 1-ary sentential context is aggregative (according to a consequence relation) if the result of putting the conjunction of two formulas into the context is a consequence (by that relation) of the results of putting first the one formula and then the other into that context. All 1-ary contexts are aggregative according to the consequence relation of classical propositional logic (though not, for example, according to the consequence relation of intuitionistic propositional logic), and here we explore the extent of this (...) phenomenon, generalized to having arbitrary connectives playing the role of conjunction; among intermediate logics, LC, shows itself to occupy a crucial position in this regard, and to suggest a characterization, applicable to a broader range of consequence relations, in terms of a variant of the notion of idempotence we shall call componentiality. This is an analogue, for the consequence relations of propositional logic, of the notion of a conservative operation in universal algebra. (shrink)

The paper offers a historical survey of the emergence of logical formalization in twentieth-century analytically oriented philosophy of religion. This development is taken to have passed through three main ?stages?: a pioneering stage in the late nineteenth and early twentieth centuries (led by Frege and Russell), a stage of crisis in the 1920s and early 1930s (occasioned by Wittgenstein, logical positivists such as Carnap, and neo-Thomists such as Maritain), and a stage of rehabilitation in the 1930s, 1940s, and 1950s (led (...) by the Cracow Circle and Quine). (shrink)

Formal approaches that aim at representing human reasoning should be evaluated based on how humans actually reason. One way of doing so is to investigate whether psychological findings of human reasoning patterns are represented in the theoretical model. The computational logic approach discussed here is the so-called weak completion semantics which is based on the three-valued ᴌukasiewicz logic. We explain how this approach adequately models Byrne’s suppression task, a psychological study where the experimental results show that participants’ conclusions systematically deviate (...) from the classical logically correct answers. As weak completion semantics is a novel technique in the field of computational logic, it is important to examine how it corresponds to other already established non-monotonic approaches. For this purpose we investigate the relation of weak completion with respect to completion and three-valued stable model semantics. In particular, we show that well-founded semantics, a widely accepted approach in the field of non-monotonic reasoning, corresponds to weak completion semantics for a specific class of modified programs. (shrink)

A 4-valued framework is proposed to distinguish intuitionistically valid formulas within classical validities.

An inexact generalization like ‘ravens are black’ will be symbolized as a prepositional function with free variables thus: ‘Rx ⇒ Bx.’ The antecedent ‘Rx’ and consequent ‘Bx’ will themselves be called absolute formulas, while the result of writing the non-boolean connective ‘⇒’ between them is conditional. Absolute formulas are arbitrary first-order formulas and include the exact generalization ‘(x)(Rx → Bx)’ and sentences with individual constants like ‘Rc & Bc.’ On the other hand the non-boolean conditional ‘⇒’ can only occur as (...) the main connective in a formula. We shall also need to consider formulas with more than one free variable such as ‘xHy ⇒ xTy,’ which might express ‘if x is the husband of y then x is taller than y.’ Though it is inessential, it will simplify things to work in ‘n-languages’ with a finite number of individual constants c1,…, cn, which are interpreted as denoting the elements of the domains of the ‘n-models’ to be described below. (shrink)

According to Brouwer’s ‘theory of the exodus of consciousness’, our experience includes ‘egoicity’, a distinct kind of feeling. In this paper, we describe his phenomenology in order to explore and elaborate on the notion of egoic sensations. In the world of perception formed from sensations, some of them are, Brouwer claims, not completely separated or ‘estranged’ from the subject, which is to say they have a certain degree of egoicity. We claim this phenomenon can be explained in terms of the (...) primordial state of consciousness from where the ‘exodus’ starts. Having undertaken the analysis and interpretation of Brouwer’s descriptions and examples of egoic sensations, we provide a formal account of egoicity based on Brouwer’s definition of its relation to estrangement, desire and fear. We show that the four terms can be modeled by a classical and a graded logical hexagon, giving the corresponding axiomatizations. (shrink)