A Companion to Philosophical Logic
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This collection of newly comissioned essays by international contributors offers a representative overview of the most important developments in contemporary philosophical logic.
- Presents controversies in philosophical implications and applications of formal symbolic logic.
- Surveys major trends and offers original insights.
conclusion. As a result, he not only has an enumeration of all the valid forms of ‘argument in the figures,’ he also has shown that all of them can be ‘reduced’ to the basic four forms. He even shows that two of the basic forms can be derived from the other two using somewhat longer deductions. Following this treatment, he argues that every valid argument whatsoever can be ‘reduced’ to the valid forms of argument ‘in the figures.’ His defense of this is necessarily more complex, since it includes
man. Therefore: Sortes is mortal. 30 HISTORY OF LOGIC: MEDIEVAL This consequence remains valid under all (uniform) substitutions (salva congruitate) of other terms put in place of Sortes, mortal, and man. Formal consequence is opposed to material consequence, for instance the consequence Sortes is a man. Therefore: Sortes is mortal. holds only materially, since it does not hold ‘in all terms.’ Material consequence can be compared to (Carnap’s contemporary notion of) ‘meaning postulates.’
GQ system of quantification, then, this kind of claim can be represented along the following lines: ‘[All (x): Man (x)] Mortal (x).’ On this kind of model, quantifier expressions are said to be binary or restricted, requiring a common noun to act in tandem with a quantifier to bind a variable. Unlike predicate logic, GQ is a second-order logical system: roughly, this means that the objects quantifiers are taken to range over are sets (of objects), rather than their constituents (i.e. the objects
happy.’ Then we can formulate a sentence like ‘Most girls are happy’ as: [Most (x): Girls (x)] Happy(x)’, which yields precisely the interpretation we were after – it tells us that, given the set of girls, the majority of this set are happy. However, to adopt this kind of proposal is precisely to reject the Fregean form of quantification for sentences involving ‘most,’ in favor of something like the GQ proposal which treats quantifiers as binary expressions (i.e. as requiring both a quantifier
or expresses a false proposition, and that would require a principle for disjunction.) The Grelling Liar (GL) involves the predicate ‘heterological’ defined as “a predicate which expresses [as a term in some systematic usage – expression cannot be analyzed here] a property of which it is not itself an instance.” This self-reference seems to threaten both the saying that ‘heterological’ is heterological and the saying that it is not. The answer is that there is no such property as that of being a