Combining Philosophers

All the ideas for Lynch,MP/Glasgow,JM, Gerhard Gentzen and Dean W. Zimmerman

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15 ideas

5. Theory of Logic / A. Overview of Logic / 2. History of Logic
Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna]
The logical connectives are 'defined' by their introduction rules [Gentzen]
Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
Natural deduction shows the heart of reasoning (and sequent calculus is just a tool) [Gentzen, by Hacking]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave]
7. Existence / C. Structure of Existence / 3. Levels of Reality
A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow]
7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow]
7. Existence / D. Theories of Reality / 6. Physicalism
Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow]
The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow]
8. Modes of Existence / D. Universals / 3. Instantiated Universals
An immanent universal is wholly present in more than one place [Zimmerman,DW]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
If only two indiscernible electrons exist, future differences must still be possible [Zimmerman,DW]
Discernible differences at different times may just be in counterparts [Zimmerman,DW]
27. Natural Reality / D. Time / 1. Nature of Time / g. Growing block
Neither 'moving spotlight' nor 'growing block' views explain why we care what is present or past [Zimmerman,DW]
27. Natural Reality / D. Time / 2. Passage of Time / e. Tensed (A) series
A-theorists, unlike B-theorists, believe some sort of objective distinction between past, present and future [Zimmerman,DW]