Combining Philosophers

All the ideas for Anselm, George Boole and Ori Simchen

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18 ideas

3. Truth / A. Truth Problems / 1. Truth
Anselm of Canterbury identified truth with God [Anselm, by Engel]
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
Boole applied normal algebra to logic, aiming at an algebra of thought [Boole, by Devlin]
Boole's notation can represent syllogisms and propositional arguments, but not both at once [Boole, by Weiner]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
The Barcan Formulas express how to combine modal operators with classical quantifiers [Simchen]
The Barcan Formulas are orthodox, but clash with the attractive Actualist view [Simchen]
BF implies that if W possibly had a child, then something is possibly W's child [Simchen]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
Boole made logic more mathematical, with algebra, quantifiers and probability [Boole, by Friend]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
Boole's method was axiomatic, achieving economy, plus multiple interpretations [Boole, by Potter]
10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism
Serious Actualism says there are no facts at all about something which doesn't exist [Simchen]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
An existing thing is even greater if its non-existence is inconceivable [Anselm]
Conceiving a greater being than God leads to absurdity [Anselm]
Even the fool can hold 'a being than which none greater exists' in his understanding [Anselm]
If that than which a greater cannot be thought actually exists, that is greater than the mere idea [Anselm]
A perfection must be independent and unlimited, and the necessary existence of Anselm's second proof gives this [Malcolm on Anselm]
The word 'God' can be denied, but understanding shows God must exist [Anselm]
Guanilo says a supremely fertile island must exist, just because we can conceive it [Anselm]
Nonexistence is impossible for the greatest thinkable thing, which has no beginning or end [Anselm]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
Anselm's first proof fails because existence isn't a real predicate, so it can't be a perfection [Malcolm on Anselm]