Much philosophy of logic is shaped, explicitly or implicitly, by the thought that logic is distinctively formal and abstracts from material content. The distinction between formal and material does not appear to coincide with the more familiar contrasts between a priori and empirical, necessary and contingent, analytic and synthetic—indeed, it is often invoked to explain these. Nor, it turns out, can it be explained by appeal to schematic inference patterns, syntactic rules, or grammar. What does it mean, then, to say that logic is distinctively formal?
Schlagwort: Logik
WTFormality.
Fast Past.
A period of time filled with exciting events will seem short in passing, but long in retrospect. However, a period of time in which little new happens (e.g. a protracted period of illness) will seem long in passing, but short in retrospect.
Michiel Van Lambalgen, Fritz Hamm - The Proper Treatment of Events
¬L²αβ II.
And then you realize it is even harder to say "I do not love you."
Because even less people know what this should mean.
42.
For example the field of real numbers forms a structure R whose elements are the real numbers, with signature consisting of the individual constant 0 to name the number zero, a 1-ary function symbol - for minus, and two 2-ary function symbols + and . for plus and times. At first sight we can't add a symbol to express 1/x, since all the named functions have to be defined on the whole domain of the structure, and there is no such real number as 1/0. But on second thoughts this is not a serious problem; any competent mathematician puts the condition ‘x is not zero’ before dividing by x, and so it never matters what the value of 1/0 is, and we can harmlessly take it to be 42. But most model theorists are uncomfortable with any kind of division by zero, so they stick with plus, times and minus.