Combining Texts

All the ideas for 'Thinking About Mathematics', 'On the Happy Life' and 'Truth and Truthmakers'

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55 ideas

1. Philosophy / A. Wisdom / 2. Wise People
A wise man is not subservient to anything [Seneca]
1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
All metaphysical discussion should be guided by a quest for truthmakers [Armstrong]
3. Truth / B. Truthmakers / 4. Truthmaker Necessitarianism
Truth-making can't be entailment, because truthmakers are portions of reality [Armstrong]
Armstrong says truthmakers necessitate their truth, where 'necessitate' is a primitive relation [Armstrong, by MacBride]
3. Truth / B. Truthmakers / 6. Making Negative Truths
Negative truths have as truthmakers all states of affairs relevant to the truth [Armstrong]
The nature of arctic animals is truthmaker for the absence of penguins there [Armstrong]
3. Truth / B. Truthmakers / 7. Making Modal Truths
In mathematics, truthmakers are possible instantiations of structures [Armstrong]
One truthmaker will do for a contingent truth and for its contradictory [Armstrong]
The truthmakers for possible unicorns are the elements in their combination [Armstrong]
What is the truthmaker for 'it is possible that there could have been nothing'? [Armstrong]
3. Truth / B. Truthmakers / 8. Making General Truths
Necessitating general truthmakers must also specify their limits [Armstrong]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
The set theory brackets { } assert that the member is a unit [Armstrong]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
For 'there is a class with no members' we don't need the null set as truthmaker [Armstrong]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
Cauchy gave a formal definition of a converging sequence. [Shapiro]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
Classes have cardinalities, so their members must all be treated as units [Armstrong]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Categories are the best foundation for mathematics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
'Impredicative' definitions refer to the thing being described [Shapiro]
7. Existence / C. Structure of Existence / 6. Fundamentals / d. Logical atoms
Logical atomism builds on the simple properties, but are they the only possible properties? [Armstrong]
7. Existence / D. Theories of Reality / 5. Naturalism
'Naturalism' says only the world of space-time exists [Armstrong]
7. Existence / D. Theories of Reality / 9. States of Affairs
Truthmaking needs states of affairs, to unite particulars with tropes or universals. [Armstrong]
8. Modes of Existence / B. Properties / 2. Need for Properties
We need properties, as minimal truthmakers for the truths about objects [Armstrong]
8. Modes of Existence / B. Properties / 3. Types of Properties
The determinates of a determinable must be incompatible with each other [Armstrong]
Length is a 'determinable' property, and one mile is one its 'determinates' [Armstrong]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
If tropes are non-transferable, then they necessarily belong to their particular substance [Armstrong]
8. Modes of Existence / C. Powers and Dispositions / 5. Powers and Properties
Properties are not powers - they just have powers [Armstrong]
8. Modes of Existence / C. Powers and Dispositions / 7. Against Powers
Powers must result in some non-powers, or there would only be potential without result [Armstrong]
How does the power of gravity know the distance it acts over? [Armstrong]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
The class of similar things is much too big a truthmaker for the feature of a particular [Armstrong]
9. Objects / F. Identity among Objects / 1. Concept of Identity
When entities contain entities, or overlap with them, there is 'partial' identity [Armstrong]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Possible worlds don't fix necessities; intrinsic necessities imply the extension in worlds [Armstrong]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
General truths are a type of negative truth, saying there are no more ravens than black ones [Armstrong]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
For all being, there is a potential proposition which expresses its existence and nature [Armstrong]
A realm of abstract propositions is causally inert, so has no explanatory value [Armstrong]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / a. Idealistic ethics
The supreme good is harmony of spirit [Seneca]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
I seek virtue, because it is its own reward [Seneca]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / j. Unity of virtue
Virtue is always moderate, so excess need not be feared [Seneca]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
It is shameful to not even recognise your own slaves [Seneca]
23. Ethics / C. Virtue Theory / 4. External Goods / c. Wealth
There is far more scope for virtue if you are wealthy; poverty only allows endurance [Seneca]
Why does your wife wear in her ears the income of a wealthy house? [Seneca]
If wealth was a good, it would make men good [Seneca]
24. Political Theory / D. Ideologies / 5. Democracy / f. Against democracy
Unfortunately the majority do not tend to favour what is best [Seneca]
26. Natural Theory / C. Causation / 4. Naturalised causation
Negative causations supervene on positive causations plus their laws? [Armstrong]
27. Natural Reality / D. Time / 3. Parts of Time / e. Present moment
The pure present moment is too brief to be experienced [Armstrong]