more from this thinker
|
more from this text
Single Idea 21612
[filed under theme 5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
]
Full Idea
Argument by Cases (or or-elimination) is the standard way of using disjunctive premises. If one can argue from A and some premises to C, and from B and some premises to C, one can argue from 'A or B' and the combined premises to C.
Gist of Idea
Or-elimination is 'Argument by Cases'; it shows how to derive C from 'A or B'
Source
Timothy Williamson (Vagueness [1994], 5.3)
Book Ref
Williamson,Timothy: 'Vagueness' [Routledge 1996], p.152
The
14 ideas
with the same theme
[proofs built from introduction and elimination rules]:
|
13832
|
Natural deduction shows the heart of reasoning (and sequent calculus is just a tool)
[Gentzen, by Hacking]
|
|
13753
|
Natural deduction takes proof from assumptions (with its rules) as basic, and axioms play no part
[Bostock]
|
|
13755
|
Excluded middle is an introduction rule for negation, and ex falso quodlibet will eliminate it
[Bostock]
|
|
13754
|
Natural deduction rules for → are the Deduction Theorem (→I) and Modus Ponens (→E)
[Bostock]
|
|
13758
|
In natural deduction we work from the premisses and the conclusion, hoping to meet in the middle
[Bostock]
|
|
18120
|
The Deduction Theorem is what licenses a system of natural deduction
[Bostock]
|
|
13823
|
In natural deduction, inferences are atomic steps involving just one logical constant
[Prawitz]
|
|
10602
|
A 'natural deduction system' has no axioms but many rules
[Smith,P]
|
|
21612
|
Or-elimination is 'Argument by Cases'; it shows how to derive C from 'A or B'
[Williamson]
|
|
13685
|
Natural deduction helpfully allows reasoning with assumptions
[Sider]
|
|
19298
|
Unlike axiom proofs, natural deduction proofs needn't focus on logical truths and theorems
[Hale]
|
|
18783
|
Many-valued logics lack a natural deduction system
[Mares]
|
|
15001
|
'Tonk' is supposed to follow the elimination and introduction rules, but it can't be so interpreted
[Sider]
|
|
18800
|
Introduction rules give deduction conditions, and Elimination says what can be deduced
[Rumfitt]
|