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All the ideas for 'Thinking About Mathematics', 'The Thought: a Logical Enquiry' and 'The Inessential Indexical'

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47 ideas

2. Reason / A. Nature of Reason / 5. Objectivity
There exists a realm, beyond objects and ideas, of non-spatio-temporal thoughts [Frege, by Weiner]
2. Reason / E. Argument / 1. Argument
A 'teepee' argument has several mutually supporting planks to it [Cappelen/Dever]
3. Truth / A. Truth Problems / 2. Defining Truth
The word 'true' seems to be unique and indefinable [Frege]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
There cannot be complete correspondence, because ideas and reality are quite different [Frege]
3. Truth / H. Deflationary Truth / 1. Redundant Truth
The property of truth in 'It is true that I smell violets' adds nothing to 'I smell violets' [Frege]
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 / A. Nature of Existence / 2. Types of Existence
Thoughts in the 'third realm' cannot be sensed, and do not need an owner to exist [Frege]
7. Existence / D. Theories of Reality / 8. Facts / c. Facts and truths
A fact is a thought that is true [Frege]
9. Objects / A. Existence of Objects / 3. Objects in Thought
Late Frege saw his non-actual objective objects as exclusively thoughts and senses [Frege, by Dummett]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
16. Persons / C. Self-Awareness / 2. Knowing the Self
Prioprioception focuses on your body parts, not on your self, or indexicality [Cappelen/Dever]
We can acquire self-knowledge with mirrors, not just with proprioception and introspection [Cappelen/Dever]
Proprioception is only immune from error if you are certain that it represents the agent [Cappelen/Dever]
17. Mind and Body / C. Functionalism / 1. Functionalism
Folk Functionalism is a Ramsification of our folk psychology [Cappelen/Dever]
18. Thought / A. Modes of Thought / 1. Thought
We grasp thoughts (thinking), decide they are true (judgement), and manifest the judgement (assertion) [Frege]
Thoughts have their own realm of reality - 'sense' (as opposed to the realm of 'reference') [Frege, by Dummett]
A thought is distinguished from other things by a capacity to be true or false [Frege, by Dummett]
18. Thought / A. Modes of Thought / 9. Indexical Thought
Thoughts about myself are understood one way to me, and another when communicated [Frege]
It is assumed that indexical content is needed to represent the perspective of perception [Cappelen/Dever]
All information is objective, and purely indexical information is not much use [Cappelen/Dever]
If some of our thought is tied to its context, it will be hard to communicate it [Cappelen/Dever]
You don't remember your house interior just from an experienced viewpoint [Cappelen/Dever]
Our beliefs and desires are not organised around ourselves, but around the world [Cappelen/Dever]
Indexicality is not significantly connected to agency [Cappelen/Dever]
19. Language / C. Assigning Meanings / 5. Fregean Semantics
Fregeans can't agree on what 'senses' are [Cappelen/Dever]
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
Possible worlds accounts of content are notoriously coarse-grained [Cappelen/Dever]
19. Language / C. Assigning Meanings / 9. Indexical Semantics
Indexicals are just non-constant in meaning, and don't involve any special concepts [Cappelen/Dever]
Fregeans say 'I' differs in reference, so it must also differ in sense [Cappelen/Dever]
All indexicals can be expressed non-indexically [Cappelen/Dever]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
A 'thought' is something for which the question of truth can arise; thoughts are senses of sentences [Frege]
19. Language / D. Propositions / 5. Unity of Propositions
A sentence is only a thought if it is complete, and has a time-specification [Frege]
19. Language / F. Communication / 5. Pragmatics / a. Contextual meaning
The basic Kaplan view is that there is truth-conditional content, and contextual character [Cappelen/Dever]
It is proposed that a huge range of linguistic items are context-sensitive [Cappelen/Dever]
20. Action / C. Motives for Action / 2. Acting on Beliefs / b. Action cognitivism
We deny that action involves some special class of beliefs [Cappelen/Dever]