Combining Texts
Ideas for
'works', 'Logical Necessity' and 'On 'Generation and Corruption''
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
8 ideas
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
12195
|
Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt]
|
12199
|
There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt]
|
12201
|
We reject deductions by bad consequence, so logical consequence can't be deduction [Rumfitt]
|
5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
12194
|
Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' [Rumfitt]
|
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
12198
|
Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) [Rumfitt]
|
5. Theory of Logic / K. Features of Logics / 8. Enumerability
10082
|
There are infinite sets that are not enumerable [Cantor, by Smith,P]
|
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / b. Cantor's paradox
13483
|
Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it [Cantor, by Hart,WD]
|
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / e. Mirimanoff's paradox
8710
|
The powerset of all the cardinal numbers is required to be greater than itself [Cantor, by Friend]
|