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All the ideas for 'poems', 'Truthmakers, Realism and Ontology' and 'Logic in Mathematics'

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35 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]
3. Truth / B. Truthmakers / 2. Truthmaker Relation
Moral realism doesn't seem to entail the existence of any things [Cameron]
3. Truth / B. Truthmakers / 3. Truthmaker Maximalism
Surely if some propositions are grounded in existence, they all are? [Cameron]
3. Truth / B. Truthmakers / 4. Truthmaker Necessitarianism
Orthodox Truthmaker applies to all propositions, and necessitates their truth [Cameron]
God fixes all the truths of the world by fixing what exists [Cameron]
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
What the proposition says may not be its truthmaker [Cameron]
Rather than what exists, some claim that the truthmakers are ways of existence, dispositions, modalities etc [Cameron]
Truthmaking doesn't require realism, because we can be anti-realist about truthmakers [Cameron]
3. Truth / B. Truthmakers / 6. Making Negative Truths
Without truthmakers, negative truths must be ungrounded [Cameron]
3. Truth / B. Truthmakers / 11. Truthmaking and Correspondence
I support the correspondence theory because I believe in truthmakers [Cameron]
Maybe truthmaking and correspondence stand together, and are interdefinable [Cameron]
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 / 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]
7. Existence / D. Theories of Reality / 2. Realism
For realists it is analytic that truths are grounded in the world [Cameron]
Realism says a discourse is true or false, and some of it is true [Cameron]
Realism says truths rest on mind-independent reality; truthmaking theories are about which features [Cameron]
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]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
We should reject distinct but indiscernible worlds [Cameron]
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]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
Nomos is king [Pindar]