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All the ideas for 'Intensional Logic', 'works' and 'Sources of Knowledge of Mathematics'

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15 ideas

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]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Descartes showed a one-one order-preserving match between points on a line and the real numbers [Descartes, by Hart,WD]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Late in life Frege abandoned logicism, and saw the source of arithmetic as geometrical [Frege, by Chihara]
9. Objects / B. Unity of Objects / 2. Substance / e. Substance critique
Descartes thinks distinguishing substances from aggregates is pointless [Descartes, by Pasnau]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
Definite descriptions pick out different objects in different possible worlds [Fitting]
12. Knowledge Sources / B. Perception / 3. Representation
Descartes said images can refer to objects without resembling them (as words do) [Descartes, by Tuck]
16. Persons / F. Free Will / 4. For Free Will
We have inner awareness of our freedom [Descartes]
17. Mind and Body / A. Mind-Body Dualism / 2. Interactionism
Descartes discussed the interaction problem, and compared it with gravity [Descartes, by Lycan]
26. Natural Theory / A. Speculations on Nature / 1. Nature
Nature is devoid of thought [Descartes, by Meillassoux]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / c. Matter as extension
Matter can't just be Descartes's geometry, because a filler of the spaces is needed [Robinson,H on Descartes]