Combining Texts
Ideas for
'Mahaprajnaparamitashastra', 'Logic for Philosophy' and 'Ecce Homo'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
20 ideas
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
13678
|
The most popular account of logical consequence is the semantic or model-theoretic one [Sider]
|
13682
|
Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider]
|
13680
|
Maybe logical consequence is a primitive notion [Sider]
|
13679
|
Maybe logical consequence is more a matter of provability than of truth-preservation [Sider]
|
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
13722
|
A 'theorem' is an axiom, or the last line of a legitimate proof [Sider]
|
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
13696
|
When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider]
|
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
13700
|
A 'total' function must always produce an output for a given domain [Sider]
|
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
13703
|
λ can treat 'is cold and hungry' as a single predicate [Sider]
|
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
13688
|
Good axioms should be indisputable logical truths [Sider]
|
13687
|
No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider]
|
5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
13691
|
Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider]
|
13690
|
Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider]
|
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
13685
|
Natural deduction helpfully allows reasoning with assumptions [Sider]
|
5. Theory of Logic / H. Proof Systems / 6. Sequent Calculi
13686
|
We can build proofs just from conclusions, rather than from plain formulae [Sider]
|
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
13697
|
Valuations in PC assign truth values to formulas relative to variable assignments [Sider]
|
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
13684
|
The semantical notion of a logical truth is validity, being true in all interpretations [Sider]
|
13704
|
It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider]
|
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
13724
|
In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider]
|
5. Theory of Logic / K. Features of Logics / 4. Completeness
13698
|
In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider]
|
5. Theory of Logic / K. Features of Logics / 6. Compactness
13699
|
Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider]
|