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All the ideas for '', 'The Essence of Reference' and 'Logic in Mathematics'

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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 / 1. Overview of Logic
If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
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
Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege]
The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
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 / F. Referring in Logic / 1. Naming / e. Empty names
It is best to say that a name designates iff there is something for it to designate [Sainsbury]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Definite descriptions may not be referring expressions, since they can fail to refer [Sainsbury]
Definite descriptions are usually rigid in subject, but not in predicate, position [Sainsbury]
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]
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 / B. Reference / 3. Direct Reference / b. Causal reference
A new usage of a name could arise from a mistaken baptism of nothing [Sainsbury]
19. Language / B. Reference / 5. Speaker's Reference
Even a quantifier like 'someone' can be used referentially [Sainsbury]
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]
19. Language / F. Communication / 3. Denial
We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]
26. Natural Theory / A. Speculations on Nature / 3. Natural Function
Things are thought to have a function, even when they can't perform them [Sainsbury]