Combining Texts

Ideas for 'Intensional Logic', 'People and Their Bodies' and 'Parts'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

4 ideas

5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
11026 Classical logic is deliberately extensional, in order to model mathematics [Fitting]
     Full Idea: Mathematics is typically extensional throughout (we write 3+2=2+3 despite the two terms having different meanings). ..Classical first-order logic is extensional by design since it primarily evolved to model the reasoning of mathematics.
     From: Melvin Fitting (Intensional Logic [2007], §1)
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
12876 Philosophy is stuck on the Fregean view that an individual is anything with a proper name [Simons]
     Full Idea: Modern philosophy is still under the spell of Frege's view that an individual is anything that has a proper name. (Note: But not only are empty names now recognised, but some are aware of the existence of plural reference).
     From: Peter Simons (Parts [1987], 8.1)
     A reaction: Presumably every electron in the universe is an individual, and every (finite) number which has never been named has a pretty clear identity. Presumably Pegasus, John Doe, and 'the person in the kitchen' have to be accommodated.
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
11028 λ-abstraction disambiguates the scope of modal operators [Fitting]
     Full Idea: λ-abstraction can be used to abstract and disambiguate a predicate. De re is [λx◊P(x)](f) - f has the possible-P property - and de dicto is ◊[λxP(x)](f) - possibly f has the P-property. Also applies to □.
     From: Melvin Fitting (Intensional Logic [2007], §3.3)
     A reaction: Compare the Barcan formula. Originated with Church in the 1930s, and Carnap 1947, but revived by Stalnaker and Thomason 1968. Because it refers to the predicate, it has a role in intensional versions of logic, especially modal logic.
5. Theory of Logic / G. Quantification / 6. Plural Quantification
12845 Some natural languages don't distinguish between singular and plural [Simons]
     Full Idea: The syntactic distinction between singular and plural is not a universal feature of natural languages. Chinese manages nicely without it, and Sanskrit makes a tripartite distinction between singular, dual, and plural (more than two).
     From: Peter Simons (Parts [1987], 4.3)
     A reaction: Simons is mounting an attack on the way in which modern philosophy and logic has been mesmerised by singular terms and individuated objects. Most people seem now to agree with Simons. There is stuff, as well as plurals.