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Wittgenstein: Epistemology Although Ludwig Wittgenstein is generally more known for his works on logic and on the nature of language, but throughout his philosophical journey he reflected extensively also on epistemic notions such as knowledge, belief, doubt, and certainty. This interest is more evident in his final notebook, published posthumously as On Certainty (1969, henceforth OC), where he offers a sustained and, at least apparently,
Epsilon Calculi Epsilon Calculi are extended forms of the predicate calculus that incorporate epsilon terms. Epsilon terms are individual terms of the form ‘εxFx’, being defined for all predicates in the language. The epsilon term ‘εxFx’ denotes a chosen F, if there are any F’s, and has an arbitrary reference otherwise. Epsilon calculi were originally developed to study certain forms of arithmetic, and set theory;
Mathematical Nominalism Mathematical nominalism can be described as the view that mathematical entities—entities such as numbers, sets, functions, and groups—do not exist. However, stating the view requires some care. Though the opposing view (that mathematical objects do exist) may seem like a somewhat exotic metaphysical claim, it is usually motivated by the thought that mathematical objects are required to exist in order for mathematical claims
Quantum Logic in Historical and Philosophical Perspective Quantum Logic (QL) was developed as an attempt to construct a propositional structure that would allow for describing the events of interest in Quantum Mechanics (QM). QL replaced the Boolean structure, which, although suitable for the discourse of classical physics, was inadequate for representing the atomic realm. The mathematical structure of the propositional language about classical systems is
Immanuel Kant: Logic For Immanuel Kant (1724–1804), formal logic is one of three paradigms for the methodology of science, along with mathematics and modern-age physics. Formal logic owes this role to its stability and relatively finished state, which Kant claims it has possessed since Aristotle. Kant’s key contribution lies in his focus on the formal and systematic character of logic as a “strongly proven” (apodictic) doctrine.
Artificial Intelligence Artificial intelligence (AI) would be the possession of intelligence, or the exercise of thought, by machines such as computers. Philosophically, the main AI question is “Can there be such?” or, as Alan Turing put it, “Can a machine think?” What makes this a philosophical and not just a scientific and technical question is the scientific recalcitrance of the concept of intelligence or thought