Combining Texts

All the ideas for 'Intensional Logic', 'Frege' and 'Philosophy of Mathematics'

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12 ideas

2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
Aristotelian logic dealt with inferences about concepts, and there were also proposition inferences [Weiner]
4. Formal Logic / E. Nonclassical Logics / 8. Intensional Logic
If terms change their designations in different states, they are functions from states to objects [Fitting]
Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting]
4. Formal Logic / E. Nonclassical Logics / 9. Awareness Logic
Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting]
4. Formal Logic / E. Nonclassical Logics / 10. Justification Logics
Justication logics make explicit the reasons for mathematical truth in proofs [Fitting]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
Classical logic is deliberately extensional, in order to model mathematics [Fitting]
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
λ-abstraction disambiguates the scope of modal operators [Fitting]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
Definite descriptions pick out different objects in different possible worlds [Fitting]