Combining Texts
Ideas for
'What is Logic?st1=Ian Hacking', 'Essays on Intellectual Powers 2: Senses' and 'On Second-Order Logic'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
13 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]
|
|
14249
|
Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
|
|
10830
|
Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos]
|
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
|
10829
|
A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
|
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 / G. Quantification / 2. Domain of Quantification
|
10832
|
'∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]
|
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]
|
5. Theory of Logic / K. Features of Logics / 4. Completeness
|
10834
|
Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
|
5. Theory of Logic / K. Features of Logics / 6. Compactness
|
13841
|
Why should compactness be definitive of logic? [Boolos, by Hacking]
|