Ideas from 'Philosophy of Logic' by Willard Quine [1970], by Theme Structure

[found in 'Philosophy of Logic' by Quine,Willard [Prentice-Hall 1970,0-13-663625-x]].

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2. Reason / B. Laws of Thought / 3. Non-Contradiction
If you say that a contradiction is true, you change the meaning of 'not', and so change the subject
3. Truth / F. Semantic Truth / 2. Semantic Truth
Talk of 'truth' when sentences are mentioned; it reminds us that reality is the point of sentences
3. Truth / H. Deflationary Truth / 1. Redundant Truth
Truth is redundant for single sentences; we do better to simply speak the sentence
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
We can eliminate 'or' from our basic theory, by paraphrasing 'p or q' as 'not(not-p and not-q)'
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
My logical grammar has sentences by predication, then negation, conjunction, and existential quantification
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Maybe logical truth reflects reality, but in different ways in different languages
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Quine rejects second-order logic, saying that predicates refer to multiple objects [Hodes]
Quantifying over predicates is treating them as names of entities
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Excluded middle has three different definitions
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
Quantification theory can still be proved complete if we add identity
5. Theory of Logic / F. Referring in Logic / 1. Naming / f. Names eliminated
Names are not essential, because naming can be turned into predication
5. Theory of Logic / G. Quantification / 1. Quantification
Universal quantification is widespread, but it is definable in terms of existential quantification
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
You can't base quantification on substituting names for variables, if the irrationals cannot all be named
Some quantifications could be false substitutionally and true objectually, because of nameless objects
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Putting a predicate letter in a quantifier is to make it the name of an entity
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
A sentence is logically true if all sentences with that grammatical structure are true
8. Modes of Existence / B. Properties / 12. Denial of Properties
Predicates are not names; predicates are the other parties to predication
9. Objects / A. Existence of Objects / 1. Physical Objects
A physical object is the four-dimensional material content of a portion of space-time
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
Four-d objects helps predication of what no longer exists, and quantification over items from different times
10. Modality / B. Possibility / 8. Conditionals / b. Types of conditional
Some conditionals can be explained just by negation and conjunction: not(p and not-q)
19. Language / A. Nature of Meaning / 8. Synonymy
Single words are strongly synonymous if their interchange preserves truth
19. Language / D. Propositions / 6. Propositions Critique
It makes no sense to say that two sentences express the same proposition
There is no rule for separating the information from other features of sentences
We can abandon propositions, and just talk of sentences and equivalence
19. Language / F. Communication / 5. Pragmatics / a. Contextual meaning
A good way of explaining an expression is saying what conditions make its contexts true