Ideas from 'Philosophy of Logic' by Hilary Putnam [1971], by Theme Structure

[found in 'Philosophy of Logic' by Putnam,Hilary [Routledge 1972,978-0-415-58125-7]].

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3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
For scientific purposes there is a precise concept of 'true-in-L', using set theory
4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
Modern notation frees us from Aristotle's restriction of only using two class-names in premises
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
The universal syllogism is now expressed as the transitivity of subclasses
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / a. Symbols of PC
'⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '(Px & Qx)'
4. Formal Logic / F. Set Theory ST / 3. Types of Set / a. Types of set
In type theory, 'x ∈ y' is well defined only if x and y are of the appropriate type
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
Before the late 19th century logic was trivialised by not dealing with relations
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
Asserting first-order validity implicitly involves second-order reference to classes
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
Unfashionably, I think logic has an empirical foundation
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
We can identify functions with certain sets - or identify sets with certain functions
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Having a valid form doesn't ensure truth, as it may be meaningless
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
Sets larger than the continuum should be studied in an 'if-then' spirit
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
Nominalism only makes sense if it is materialist
9. Objects / A. Existence of Objects / 2. Abstract Objects / b. Need for abstracta
Physics is full of non-physical entities, such as space-vectors
14. Science / A. Basis of Science / 4. Prediction
Most predictions are uninteresting, and are only sought in order to confirm a theory