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This essay discusses Peirce’s appeal to logical machines as an argument against psychologism. It also contends that some of Peirce’s anti-psychologistic remarks on logic contain interesting premonitions arising from his perception of the asymmetry of proof complexity in monadic and relational logical calculi that were only given full formulation and explication in the early twentieth century through Church’s Theorem and Hilbert’s broad-ranging Entscheidungsproblem.

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The objective of the paper is to seek clarification on the relationship between epistemic relativism and scepticism. It is not infrequent to come across contemporary discussions of epistemic relativism that rely upon aspects of scepticism and, vice versa, discussions of scepticism drawing upon aspects of relativism. Our goal is to highlight the difference between them by illustrating that some arguments thought to be against relativism are actually against scepticism, that there are different ways of understanding the relationship between relativism and (...) scepticism, and that a commitment to either relativism or scepticism does not entail commitment to the other. The paper focuses upon the works of Peter Unger and Paul Boghossian to show how this terrain can be variously conceived and to illustrate that Boghossian's conception of the landscape is incorrect. (shrink)

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The classical paradox of the stone, namely, whether an omnipotent being can create a stone that the being itself cannot lift is traditionally circumvented by a response propounded by Thomas Aquinas, that even omnipotent beings cannot accomplish the logically impossible. However, in their paper “The New Paradox of the Stone,” Alfred R. Mele and M.P. Smith attempt to reinstate the paradox without falling foul of the Thomistic logical constraint. According to Mele and Smith, instead of interpreting the paradox as posing (...) a competition between a pair of omnipotent beings—represented by God at two different times—the paradox can be reformulated as posing a question about simultaneous competition between a pair of omnipotent beings. The purpose of this paper is, therefore, to probe the possibility of the simultaneous existence of two omnipotent beings in view of the theological arguments for the “unicity of the omnipotent.”. (shrink)

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This essay discusses Peirce’s appeal to logical machines as an argument against psychologism. It also contends that some of Peirce’s anti-psychologistic remarks on logic contain interesting premonitions arising from his perception of the asymmetry of proof complexity in monadic and relational logical calculi that were only given full formulation and explication in the early twentieth century through Church’s Theorem and Hilbert’s broad-ranging Entscheidungsproblem.

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The phrase ‘psychologism’ came into currency in the first half of the nineteen century to designate the philosophical movement advocated by the German thinkers Jakob Friedrich Fries and Friedrich Eduard Beneke in opposition to their contemporary dominant Hegelianism. They maintained that ‘the only instrument philosophical enquiry has at its disposal is self-observation and that there is no way to establish any truth other than by reducing it to the subjective elements of self-observation.’ Psychology is thus taken to be the first (...) philosophy and the basis of all other disciplines. All philosophical studies are accordingly indebted to the results of psychological inquiry for their theoretical data and ultimate justification. (shrink)

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The question, “Was Aristotle the first logicist?”, may appear anachronistic and elicit skepticism since the doctrine of logicism as a fully-fledged idea emerged only in the nineteenth century in the context of the debates surrounding the foundation of mathematics. Indeed, Bertrand Russell credits Gottlob Frege with being the first in “logicising” mathematics (Russell 1919, p. 7), where the thesis espouses that mathematical concepts and propositions are ultimately reducible to or derivable from a number of fundamental logical concepts and principles. However, (...) anachronistic appearances aside, in a fresh reexamination of some of the specific Aristotelian texts in Metaphysics and Prior Analytics, and especially focusing on Aristotle’s particular remarks on the status and significance of the principle of non-contradiction, one may textually argue for a nascent and burgeoning form of logicism in Aristotle, albeit within a much larger metaphysical context than mathematics. (shrink)

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In Fear of Knowledge, Paul Boghossian presents a series of arguments against epistemic relativism and constructivism, doctrines that he considers to have exerted an overly unjustified influence over the human and social sciences in the past two decades. In the presentation of his arguments, Boghossian charts out a terrain that closely identifies relativism with skepticism. Yet, the relationship between the two does not seem to be a simple matter of entailment or implication. The purpose of this paper is to clarify (...) the landscape surrounding relativism and skepticism and thereby to highlight their difference. The implications of such a clarification will include illustrating that some arguments thought to be against relativism are actually against skepticism, that there are very different ways of understanding the relationship between relativism and skepticism, and that a commitment to either relativism or skepticism does not entail commitment to the other. The overall objective is to show that Boghossian's conception of the terrain is incorrect and to offer an explanation for this pervasive misconception about the connection between relativism and skepticism. (shrink)

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