Combining Texts
Ideas for
'What is Logic?st1=Ian Hacking', 'Thinking About Mathematics' and 'Understanding the Infinite'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
10 ideas
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
|
13845
|
The various logics are abstractions made from terms like 'if...then' in English [Hacking]
|
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
|
13840
|
First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking]
|
|
13844
|
A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking]
|
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
|
13842
|
Second-order completeness seems to need intensional entities and possible worlds [Hacking]
|
|
15926
|
Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine]
|
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
|
8729
|
Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
|
|
15934
|
Mathematical proof by contradiction needs the law of excluded middle [Lavine]
|
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
|
13837
|
With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking]
|
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
|
13839
|
Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking]
|
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
|
13843
|
If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking]
|