Ideas from 'Philosophy of Logic' by Hilary Putnam [1971], by Theme Structure
[found in 'Philosophy of Logic' by Putnam,Hilary [Routledge 1972,9780415581257]].
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3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
18951

For scientific purposes there is a precise concept of 'trueinL', using set theory

4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
18953

Modern notation frees us from Aristotle's restriction of only using two classnames in premises

4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
18949

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
18952

'⊃' ('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
18958

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
18954

Before the late 19th century logic was trivialised by not dealing with relations

5. Theory of Logic / A. Overview of Logic / 5. FirstOrder Logic
18956

Asserting firstorder validity implicitly involves secondorder reference to classes

5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
18962

Unfashionably, I think logic has an empirical foundation

5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
18961

We can identify functions with certain sets  or identify sets with certain functions

5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
18955

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
18959

Sets larger than the continuum should be studied in an 'ifthen' spirit

8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
18957

Nominalism only makes sense if it is materialist

9. Objects / A. Existence of Objects / 2. Abstract Objects / b. Need for abstracta
18950

Physics is full of nonphysical entities, such as spacevectors

14. Science / A. Basis of Science / 4. Prediction
18960

Most predictions are uninteresting, and are only sought in order to confirm a theory
