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All the ideas for 'Intensional Logic', 'Causality: Production and Propagation' and 'Grundgesetze der Arithmetik 1 (Basic Laws)'

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19 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 / 2. Descriptions / b. Definite descriptions
Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn]
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 / G. Quantification / 4. Substitutional Quantification
Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers are ratios of quantities, such as lengths or masses [Frege]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright]
Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
My Basic Law V is a law of pure logic [Frege]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
Definite descriptions pick out different objects in different possible worlds [Fitting]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett]
Frege took the study of concepts to be part of logic [Frege, by Shapiro]
26. Natural Theory / C. Causation / 4. Naturalised causation
A causal interaction is when two processes intersect, and correlated modifications persist afterwards [Salmon]
26. Natural Theory / C. Causation / 5. Direction of causation
Cause must come first in propagations of causal interactions, but interactions are simultaneous [Salmon]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
Instead of localised events, I take enduring and extended processes as basic to causation [Salmon]