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All the ideas for 'Thinking About Mathematics', 'Outline of a Theory of Truth' and 'Person and Object'

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52 ideas

1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
Many philosophers aim to understand metaphysics by studying ourselves [Chisholm]
1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
I use variables to show that each item remains the same entity throughout [Chisholm]
3. Truth / F. Semantic Truth / 2. Semantic Truth
Kripke's semantic theory has actually inspired promising axiomatic theories [Kripke, by Horsten]
Kripke offers a semantic theory of truth (involving models) [Kripke, by Horsten]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
The Tarskian move to a metalanguage may not be essential for truth theories [Kripke, by Gupta]
Certain three-valued languages can contain their own truth predicates [Kripke, by Gupta]
3. Truth / G. Axiomatic Truth / 3. KF Truth Axioms
Kripke classified fixed points, and illuminated their use for clarifications [Kripke, by Halbach]
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 / 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 / B. Change in Existence / 4. Events / a. Nature of events
Events are states of affairs that occur at certain places and times [Chisholm]
7. Existence / D. Theories of Reality / 9. States of Affairs
The mark of a state of affairs is that it is capable of being accepted [Chisholm]
A state of affairs pertains to a thing if it implies that it has some property [Chisholm]
I propose that events and propositions are two types of states of affairs [Chisholm]
8. Modes of Existence / B. Properties / 1. Nature of Properties
Some properties can never be had, like being a round square [Chisholm]
Some properties, such as 'being a widow', can be seen as 'rooted outside the time they are had' [Chisholm]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
If some dogs are brown, that entails the properties of 'being brown' and 'being canine' [Chisholm]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
Maybe we can only individuate things by relating them to ourselves [Chisholm]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
Being the tallest man is an 'individual concept', but not a haecceity [Chisholm]
A haecceity is a property had necessarily, and strictly confined to one entity [Chisholm]
9. Objects / C. Structure of Objects / 7. Substratum
A peach is sweet and fuzzy, but it doesn't 'have' those qualities [Chisholm]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
If x is ever part of y, then y is necessarily such that x is part of y at any time that y exists [Chisholm, by Simons]
9. Objects / D. Essence of Objects / 3. Individual Essences
A traditional individual essence includes all of a thing's necessary characteristics [Chisholm]
9. Objects / E. Objects over Time / 7. Intermittent Objects
Intermittence is seen in a toy fort, which is dismantled then rebuilt with the same bricks [Chisholm, by Simons]
9. Objects / F. Identity among Objects / 5. Self-Identity
The property of being identical with me is an individual concept [Chisholm]
9. Objects / F. Identity among Objects / 9. Sameness
There is 'loose' identity between things if their properties, or truths about them, might differ [Chisholm]
12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems
Do sense-data have structure, location, weight, and constituting matter? [Chisholm]
12. Knowledge Sources / B. Perception / 8. Adverbial Theory
'I feel depressed' is more like 'he runs slowly' than like 'he has a red book' [Chisholm]
If we can say a man senses 'redly', why not also 'rectangularly'? [Chisholm]
So called 'sense-data' are best seen as 'modifications' of the person experiencing them [Chisholm]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
14. Science / D. Explanation / 1. Explanation / a. Explanation
Explanations have states of affairs as their objects [Chisholm]
16. Persons / B. Nature of the Self / 3. Self as Non-physical
I am picked out uniquely by my individual essence, which is 'being identical with myself' [Chisholm]
16. Persons / C. Self-Awareness / 3. Limits of Introspection
Sartre says the ego is 'opaque'; I prefer to say that it is 'transparent' [Chisholm]
16. Persons / D. Continuity of the Self / 3. Reference of 'I'
People use 'I' to refer to themselves, with the meaning of their own individual essence [Chisholm]
16. Persons / E. Rejecting the Self / 1. Self as Indeterminate
Bad theories of the self see it as abstract, or as a bundle, or as a process [Chisholm]
16. Persons / F. Free Will / 5. Against Free Will
Determinism claims that every event has a sufficient causal pre-condition [Chisholm]
20. Action / C. Motives for Action / 5. Action Dilemmas / c. Omissions
There are mere omissions (through ignorance, perhaps), and people can 'commit an omission' [Chisholm]
26. Natural Theory / A. Speculations on Nature / 1. Nature
The concept of physical necessity is basic to both causation, and to the concept of nature [Chisholm]
26. Natural Theory / C. Causation / 2. Types of cause
Some propose a distinct 'agent causation', as well as 'event causation' [Chisholm]
26. Natural Theory / D. Laws of Nature / 7. Strictness of Laws
A 'law of nature' is just something which is physically necessary [Chisholm]