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
8472

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
8476

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
8480

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
8474

Unlike elementary logic, set theory is not complete

4. Formal Logic / G. Formal Mereology / 1. Mereology
8465

Mereology has been exploited by some nominalists to achieve the effects of set theory

5. Theory of Logic / G. Quantification / 1. Quantification
8452

Traditionally, universal sentences had existential import, but were later treated as conditional claims

5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
8475

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
8454

The whole numbers are 'natural'; 'rational' numbers include fractions; the 'reals' include root2 etc.

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
8473

The logicists held that isamemberof is a logical constant, making set theory part of logic

7. Existence / E. Categories / 3. Proposed Categories
8458

Just individuals in Nominalism; add sets for Extensionalism; add properties, concepts etc for Intensionalism

14. Science / B. Scientific Theories / 1. Scientific Theory
8457

The Principle of Conservatism says we should violate the minimum number of background beliefs

19. Language / A. Nature of Meaning / 10. Denial of Meanings
8477

People presume meanings exist because they confuse meaning and reference

19. Language / C. Assigning Meanings / 3. Predicates
8471

Three ways for 'Socrates is human' to be true are nominalist, platonist, or Montague's way

19. Language / D. Propositions / 4. Mental Propositions
8484

If two people believe the same proposition, this implies the existence of propositions
