### Ideas from 'Philosophy of Logic' by Hilary Putnam , 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
 18951 For scientific purposes there is a precise concept of 'true-in-L', 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 class-names 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. First-Order Logic
 18956 Asserting first-order validity implicitly involves second-order 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 'if-then' 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 non-physical entities, such as space-vectors
###### 14. Science / A. Basis of Science / 4. Prediction
 18960 Most predictions are uninteresting, and are only sought in order to confirm a theory