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All the ideas for 'Counterpart theory and Quant. Modal Logic', 'Logic in Mathematics' and 'Causality and Determinism'

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33 ideas

2. Reason / D. Definition / 3. Types of Definition
A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege]
2. Reason / D. Definition / 10. Stipulative Definition
Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta]
2. Reason / E. Argument / 6. Conclusive Proof
We must be clear about every premise and every law used in a proof [Frege]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Logic not only proves things, but also reveals logical relations between them [Frege]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege]
Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege]
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
'Theorems' are both proved, and used in proofs [Frege]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Tracing inference backwards closes in on a small set of axioms and postulates [Frege]
The essence of mathematics is the kernel of primitive truths on which it rests [Frege]
A truth can be an axiom in one system and not in another [Frege]
Axioms are truths which cannot be doubted, and for which no proof is needed [Frege]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
To create order in mathematics we need a full system, guided by patterns of inference [Frege]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
If principles are provable, they are theorems; if not, they are axioms [Frege]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege]
9. Objects / D. Essence of Objects / 1. Essences of Objects
Aristotelian essentialism says essences are not relative to specification [Lewis]
10. Modality / A. Necessity / 7. Natural Necessity
Causal necessities hold in all worlds compatible with the laws of nature [Lewis]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
It doesn't take the whole of a possible Humphrey to win the election [Lewis]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
Counterpart theory is bizarre, as no one cares what happens to a mere counterpart [Kripke on Lewis]
Counterparts are not the original thing, but resemble it more than other things do [Lewis]
If the closest resembler to you is in fact quite unlike you, then you have no counterpart [Lewis]
Essential attributes are those shared with all the counterparts [Lewis]
16. Persons / F. Free Will / 3. Constraints on the will
Freedom involves acting according to an idea [Anscombe]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
To believe in determinism, one must believe in a system which determines events [Anscombe]
18. Thought / B. Mechanics of Thought / 5. Mental Files
We need definitions to cram retrievable sense into a signed receptacle [Frege]
We use signs to mark receptacles for complex senses [Frege]
19. Language / A. Nature of Meaning / 6. Meaning as Use
A sign won't gain sense just from being used in sentences with familiar components [Frege]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
Thoughts are not subjective or psychological, because some thoughts are the same for us all [Frege]
A thought is the sense expressed by a sentence, and is what we prove [Frege]
19. Language / D. Propositions / 5. Unity of Propositions
The parts of a thought map onto the parts of a sentence [Frege]
26. Natural Theory / C. Causation / 5. Direction of causation
With diseases we easily trace a cause from an effect, but we cannot predict effects [Anscombe]
26. Natural Theory / C. Causation / 6. Causation as primitive
The word 'cause' is an abstraction from a group of causal terms in a language (scrape, push..) [Anscombe]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
Causation is relative to how we describe the primary relata [Anscombe, by Schaffer,J]
26. Natural Theory / C. Causation / 8. Particular Causation / c. Conditions of causation
Since Mill causation has usually been explained by necessary and sufficient conditions [Anscombe]