Ideas of Alex Orenstein, by Theme

[American, fl. 2002, Professor at the City University of New York.]

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4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
Sentential logic is consistent (no contradictions) and complete (entirely provable)
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
Axiomatization simply picks from among the true sentences a few to play a special role
4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
S4: 'poss that poss that p' implies 'poss that p'; S5: 'poss that nec that p' implies 'nec that p'
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Unlike elementary logic, set theory is not complete
4. Formal Logic / G. Formal Mereology / 1. Mereology
Mereology has been exploited by some nominalists to achieve the effects of set theory
5. Theory of Logic / G. Quantification / 1. Quantification
Traditionally, universal sentences had existential import, but were later treated as conditional claims
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
The substitution view of quantification says a sentence is true when there is a substitution instance
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
The whole numbers are 'natural'; 'rational' numbers include fractions; the 'reals' include root-2 etc.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
The logicists held that is-a-member-of is a logical constant, making set theory part of logic
7. Existence / E. Categories / 3. Proposed Categories
Just individuals in Nominalism; add sets for Extensionalism; add properties, concepts etc for Intensionalism
14. Science / B. Scientific Theories / 1. Scientific Theory
The Principle of Conservatism says we should violate the minimum number of background beliefs
19. Language / A. Nature of Meaning / 10. Denial of Meanings
People presume meanings exist because they confuse meaning and reference
19. Language / C. Assigning Meanings / 3. Predicates
Three ways for 'Socrates is human' to be true are nominalist, platonist, or Montague's way
19. Language / D. Propositions / 4. Mental Propositions
If two people believe the same proposition, this implies the existence of propositions