Classical Logic and the Strict Tolerant Hierarchy

Journal of Philosophical Logic - In their recent article “A Hierarchy of Classical and Paraconsistent Logics”, Eduardo Barrio, Federico Pailos and Damien Szmuc (BPS hereafter) present...     

A Family of Strict/Tolerant Logics

Journal of Philosophical Logic - Strict/tolerant logic, ST, evaluates the premises and the consequences of its consequence relation differently, with the premises held to stricter standards while...     

Strict finitism

Conclusion Dummett's objections to the coherence of the strict finitist philosophy of mathematics are thus, at the present time at least, ill-taken. We have so far no definitive treatment of Sorites paradoxes; so no conclusive ground for dismissing Dummett's response — the response of simply writing off a large class of familiar, confidently handled expressions as semantically incoherent. I believe that cannot be the right response, if only because it threatens to open an unacceptable gulf between the insight into his own understanding available to a philosophically reflective speaker and the conclusions available to one confined to observing the former's linguistic practice; for an observer of our linguistic practice could never justifiably arrive at the conclusion that red, child, etc., are governed by inconsistent rules. But the Sorites is not the subject of this paper. The points I hope to have made plausible are: that a generalized intuitionist position cannot be so much as formulated and that even a most local intuitionism, argued for the special case of arithmetic, is hard pressed effectively to stabilize and defend itself; that strict finitism remains the natural outcome of the anti-realism which Dummett has propounded by way of support for the intuitionist philosophy of mathematics; that it is powerfully buttressed by the ideas of the latter Wittgenstein on rule-following; and that there is no extant compelling reason to suppose that its involvement with predicates of surveyability calls its coherence into question. The correct philosophical assessment of strict finitism, and its proper mathematical exegesis, remain absolutely open, almost virgin issues. This is not a situation which philosophers of mathematics should tolerate very much longer.The term was introduced by Kreisel in [6] to denote what he took to be an aspect of Wittgenstein's later philosophy of mathematics; and taken over by Kielkopf (Strict Finitism, Mouton 1970) — misunderstanding, as it seems to me, both Kreisel and Wittgenstein — as a label for Wittgenstein's later philosophy of maths. in its entirety. It is not a happy label for the ideas I am concerned with, since it is only from non-strict finitist points of view that the strict finitist can be straightforwardly seen as stressing the finitude of human capacities, countenancing only finite sets, etc. (See subsections 5 and 6 below). But we need a labeel; and Dummett in [3] has already followed Kreisel's lead. Anyway, a rose by any other name,...     

Priorean Strict Implication, Q and Related Systems

We introduce a system PSI for a strict implication operator called Priorean strict implication. The semantics for PSI is based on partial Kripke models without accessibility relations. PSI is proved sound and complete with respect to that semantics, and Prior's system Q and related systems are shown to be fragments of PSI or of a mild extension of it.     

Free and Cheap Riding in Strict, Conservative Churches

Iannaccone (1994) uses rational choice theory to argue that strict rules (e.g., no smoking or drinking) raise average commitment levels in conservative churches because strictness discourages free riding. Tests of this assertion have been hampered, in part, by uncertainties concerning how free riding should be measured. We introduce a new, indirect measure of free (and cheap) riding, the level of positive skewness of a congregation's money contributions—that is, the extent to which a few members give much more than the mean amount while the majority gives much less. Using a study of giving in five denominations, we find that strict, conservative congregations have both higher mean giving and less skewness in the pattern of their giving. The higher mean-contribution levels at strict, conservative congregations are not simply due to each member giving more or a few members giving a lot more. Instead, as Iannaccone's model predicts, some combination of strict rules and/or conservative theology appears to systematically limit the proportion of free- and cheap-riding members giving far less than the mean and thus increase the proportion giving at or above the mean.     

Strict coherence,sigma coherence and the metaphysics of quantity

I would like to thanks Louis Narens for comments on an earlier version of this paper.     

Tolerant enactivist cognitive science

Enactivist (Embodied, Embedded, etc.) approaches in cognitive science and philosophy of mind are sometimes, though not always, conjoined with an anti-representational commitment. A weaker anti-representational claim is that ascribing representational content to internal/sub-personal processes is not compulsory when giving psychological explanations. A stronger anti-representational claim is that the very idea of ascribing representational content to internal, sub-personal processes is a theoretical confusion. This paper criticises some of the arguments made by Hutto and Myin (2013, 2017) for the stronger anti-representational claim and suggests that the default Enactivist view should be the weaker non-representational position.     

Strict Identity with No Overlap

Is standard, Kripke-style semantics for quantified modal logic compatible with the view that no individual may belong to more than one possible world? One is naturally inclined to answer in the negative, arguing that the view requires a Lewis-style, counterpart-theoretic semantics instead. Strictly speaking, however, this natural answer is wrong-headed. This note explains why.     

Experimental,Cross-Cultural,and Classical Indian Epistemology

Journal of Indian Council of Philosophical Research - This paper connects recent findings from experimental epistemology to several major themes in classical Indian epistemology. First, current...     

Classical conditioning,awareness, and brain systems

Memory is composed of several different abilities that are supported by different brain systems. The distinction between declarative (conscious) and nondeclarative (non-conscious) memory has proved useful in understanding the nature of eyeblink classical conditioning – the best understood example of classical conditioning in vertebrates. In delay conditioning, the standard procedure, conditioning depends on the cerebellum and brainstem and is intact in amnesia. Trace conditioning, a variant of the standard procedure, depends additionally on the hippocampus and neocortex and is impaired in amnesia. Recent studies have sharpened the contrast between delay and trace conditioning by exploring the importance of awareness. We discuss these new findings in relation to the brain systems supporting eyeblink conditioning and suggest why awareness is important for trace conditioning but not for delay conditioning.     

Strict Finitism and the Happy Sorites

Call an argument a ‘happy sorites’ if it is a sorites argument with true premises and a false conclusion. It is a striking fact that although most philosophers working on the sorites paradox find it at prima facie highly compelling that the premises of the sorites paradox are true and its conclusion false, few (if any) of the standard theories on the issue ultimately allow for happy sorites arguments. There is one philosophical view, however, that appears to allow for at least some happy sorites arguments: strict finitism in the philosophy of mathematics. My aim in this paper is to explore to what extent this appearance is accurate. As we shall see, this question is far from trivial. In particular, I will discuss two arguments that threaten to show that strict finitism cannot consistently accept happy sorites arguments, but I will argue that (given reasonable assumptions on strict finitistic logic) these arguments can ultimately be avoided, and the view can indeed allow for happy sorites arguments.