Combining Philosophers

All the ideas for Iamblichus, Fraser MacBride and John von Neumann

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36 ideas

3. Truth / A. Truth Problems / 2. Defining Truth
We might define truth as arising from the truth-maker relation [MacBride]
3. Truth / B. Truthmakers / 1. For Truthmakers
Phenomenalists, behaviourists and presentists can't supply credible truth-makers [MacBride]
3. Truth / B. Truthmakers / 2. Truthmaker Relation
If truthmaking is classical entailment, then anything whatsoever makes a necessary truth [MacBride]
3. Truth / B. Truthmakers / 3. Truthmaker Maximalism
'Maximalism' says every truth has an actual truthmaker [MacBride]
Maximalism follows Russell, and optimalism (no negative or universal truthmakers) follows Wittgenstein [MacBride]
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
The main idea of truth-making is that what a proposition is about is what matters [MacBride]
3. Truth / B. Truthmakers / 6. Making Negative Truths
There are different types of truthmakers for different types of negative truth [MacBride]
There aren't enough positive states out there to support all the negative truths [MacBride]
3. Truth / B. Truthmakers / 8. Making General Truths
Optimalists say that negative and universal are true 'by default' from the positive truths [MacBride]
3. Truth / B. Truthmakers / 12. Rejecting Truthmakers
Does 'this sentence has no truth-maker' have a truth-maker? Reductio suggests it can't have [MacBride]
Even idealists could accept truthmakers, as mind-dependent [MacBride]
Maybe 'makes true' is not an active verb, but just a formal connective like 'because'? [MacBride]
Truthmaker talk of 'something' making sentences true, which presupposes objectual quantification [MacBride]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Connectives link sentences without linking their meanings [MacBride]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
'A is F' may not be positive ('is dead'), and 'A is not-F' may not be negative ('is not blind') [MacBride]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
Numbers are identified by their main properties and relations, involving the successor function [MacBride]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone]
A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
All the axioms for mathematics presuppose set theory [Neumann]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
For mathematical objects to be positions, positions themselves must exist first [MacBride]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Maybe it only exists if it is a truthmaker (rather than the value of a variable)? [MacBride]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
Different types of 'grounding' seem to have no more than a family resemblance relation [MacBride]
Which has priority - 'grounding' or 'truth-making'? [MacBride]
7. Existence / C. Structure of Existence / 6. Fundamentals / d. Logical atoms
Russell allows some complex facts, but Wittgenstein only allows atomic facts [MacBride]
8. Modes of Existence / A. Relations / 1. Nature of Relations
It may be that internal relations like proportion exist, because we directly perceive it [MacBride]
8. Modes of Existence / A. Relations / 2. Internal Relations
Internal relations are fixed by existences, or characters, or supervenience on characters [MacBride]
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
'Multigrade' relations are those lacking a fixed number of relata [MacBride]
10. Modality / A. Necessity / 6. Logical Necessity
Wittgenstein's plan to show there is only logical necessity failed, because of colours [MacBride]
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
Pythagoreans believe it is absurd to seek for goodness anywhere except with the gods [Iamblichus]