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Single Idea 9024
[filed under theme 5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
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Full Idea
The law of excluded middle, or 'tertium non datur', may be pictured variously as 1) Every closed sentence is true or false; or 2) Every closed sentence or its negation is true; or 3) Every closed sentence is true or not true.
Clarification
A 'closed sentence' has no free variables in it
Gist of Idea
Excluded middle has three different definitions
Source
Willard Quine (Philosophy of Logic [1970], Ch.6)
Book Ref
Quine,Willard: 'Philosophy of Logic' [Prentice-Hall 1970], p.83
A Reaction
Unlike many top philosophers, Quine thinks clearly about such things. 1) is the classical bivalent reading of excluded middle; 2) is the purely syntactic version; 3) leaves open how we interpret the 'not-true' option.
Related Ideas
Idea 8709
The law of excluded middle is syntactic; it just says A or not-A, not whether they are true or false [Friend]
Idea 17924
Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan]
The
25 ideas
from 'Philosophy of Logic'
10014
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Quine rejects second-order logic, saying that predicates refer to multiple objects
[Quine, by Hodes]
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9012
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Talk of 'truth' when sentences are mentioned; it reminds us that reality is the point of sentences
[Quine]
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9011
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Truth is redundant for single sentences; we do better to simply speak the sentence
[Quine]
|
9009
|
Single words are strongly synonymous if their interchange preserves truth
[Quine]
|
9007
|
It makes no sense to say that two sentences express the same proposition
[Quine]
|
9008
|
There is no rule for separating the information from other features of sentences
[Quine]
|
9010
|
We can abandon propositions, and just talk of sentences and equivalence
[Quine]
|
9017
|
Predicates are not names; predicates are the other parties to predication
[Quine]
|
9018
|
A physical object is the four-dimensional material content of a portion of space-time
[Quine]
|
9019
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Four-d objects helps predication of what no longer exists, and quantification over items from different times
[Quine]
|
9014
|
Some conditionals can be explained just by negation and conjunction: not(p and not-q)
[Quine]
|
9013
|
We can eliminate 'or' from our basic theory, by paraphrasing 'p or q' as 'not(not-p and not-q)'
[Quine]
|
9016
|
Names are not essential, because naming can be turned into predication
[Quine]
|
9015
|
Universal quantification is widespread, but it is definable in terms of existential quantification
[Quine]
|
9020
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My logical grammar has sentences by predication, then negation, conjunction, and existential quantification
[Quine]
|
9021
|
A good way of explaining an expression is saying what conditions make its contexts true
[Quine]
|
10828
|
Quantifying over predicates is treating them as names of entities
[Quine]
|
10012
|
Quantification theory can still be proved complete if we add identity
[Quine]
|
10705
|
Putting a predicate letter in a quantifier is to make it the name of an entity
[Quine]
|
9025
|
You can't base quantification on substituting names for variables, if the irrationals cannot all be named
[Quine]
|
9026
|
Some quantifications could be false substitutionally and true objectually, because of nameless objects
[Quine]
|
9024
|
Excluded middle has three different definitions
[Quine]
|
9023
|
If you say that a contradiction is true, you change the meaning of 'not', and so change the subject
[Quine]
|
9028
|
Maybe logical truth reflects reality, but in different ways in different languages
[Quine]
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9027
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A sentence is logically true if all sentences with that grammatical structure are true
[Quine]
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