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All the ideas for 'Boole calculus and the Concept script', 'works' and 'Nominalism and Substitutional Quantifiers'

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19 ideas

5. Theory of Logic / A. Overview of Logic / 2. History of Logic
11022 Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10794 The nominalist is tied by standard semantics to first-order, denying higher-order abstracta [Marcus (Barcan)]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
11065 The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna]
11023 The logical connectives are 'defined' by their introduction rules [Gentzen]
11213 Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
10786 Anything which refers tends to be called a 'name', even if it isn't a noun [Marcus (Barcan)]
10788 Nominalists see proper names as a main vehicle of reference [Marcus (Barcan)]
5. Theory of Logic / G. Quantification / 1. Quantification
10799 Nominalists should quantify existentially at first-order, and substitutionally when higher [Marcus (Barcan)]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10791 Substitutional semantics has no domain of objects, but place-markers for substitutions [Marcus (Barcan)]
10790 Quantifiers are needed to refer to infinitely many objects [Marcus (Barcan)]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
10785 Maybe a substitutional semantics for quantification lends itself to nominalism [Marcus (Barcan)]
10795 Substitutional language has no ontology, and is just a way of speaking [Marcus (Barcan)]
10798 A true universal sentence might be substitutionally refuted, by an unnamed denumerable object [Marcus (Barcan)]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10067 Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave]
7. Existence / A. Nature of Existence / 3. Being / i. Deflating being
10787 Is being just referent of the verb 'to be'? [Marcus (Barcan)]
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
10789 Nominalists say predication is relations between individuals, or deny that it refers [Marcus (Barcan)]
9. Objects / A. Existence of Objects / 3. Objects in Thought
10796 If objects are thoughts, aren't we back to psychologism? [Marcus (Barcan)]
9. Objects / F. Identity among Objects / 2. Defining Identity
10797 Substitutivity won't fix identity, because expressions may be substitutable, but not refer at all [Marcus (Barcan)]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
18265 We don't judge by combining subject and concept; we get a concept by splitting up a judgement [Frege]