Combining Texts

All the ideas for 'fragments/reports', 'What Numbers Could Not Be' and 'Lectures 1930-32 (student notes)'

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61 ideas

1. Philosophy / C. History of Philosophy / 1. History of Philosophy
The history of philosophy only matters if the subject is a choice between rival theories [Wittgenstein]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / d. Philosophy as puzzles
Philosophy tries to be rid of certain intellectual puzzles, irrelevant to daily life [Wittgenstein]
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
Philosophers express puzzlement, but don't clearly state the puzzle [Wittgenstein]
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
We don't need a theory of truth, because we use the word perfectly well [Wittgenstein]
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
We already know what we want to know, and analysis gives us no new facts [Wittgenstein]
2. Reason / F. Fallacies / 8. Category Mistake / a. Category mistakes
Words of the same kind can be substituted in a proposition without producing nonsense [Wittgenstein]
2. Reason / F. Fallacies / 8. Category Mistake / b. Category mistake as syntactic
Talking nonsense is not following the rules [Wittgenstein]
Grammar says that saying 'sound is red' is not false, but nonsense [Wittgenstein]
3. Truth / A. Truth Problems / 2. Defining Truth
There is no theory of truth, because it isn't a concept [Wittgenstein]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
All thought has the logical form of reality [Wittgenstein]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
In logic nothing is hidden [Wittgenstein]
5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention
Laws of logic are like laws of chess - if you change them, it's just a different game [Wittgenstein]
5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
Contradiction is between two rules, not between rule and reality [Wittgenstein]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
We may correctly use 'not' without making the rule explicit [Wittgenstein]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
Saying 'and' has meaning is just saying it works in a sentence [Wittgenstein]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
A person's name doesn't mean their body; bodies don't sit down, and their existence can be denied [Wittgenstein]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
There are no such things as numbers [Benacerraf]
Numbers can't be sets if there is no agreement on which sets they are [Benacerraf]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Benacerraf says numbers are defined by their natural ordering [Benacerraf, by Fine,K]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
To understand finite cardinals, it is necessary and sufficient to understand progressions [Benacerraf, by Wright,C]
A set has k members if it one-one corresponds with the numbers less than or equal to k [Benacerraf]
To explain numbers you must also explain cardinality, the counting of things [Benacerraf]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
We don't get 'nearer' to something by adding decimals to 1.1412... (root-2) [Wittgenstein]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
We can count intransitively (reciting numbers) without understanding transitive counting of items [Benacerraf]
Someone can recite numbers but not know how to count things; but not vice versa [Benacerraf]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
The application of a system of numbers is counting and measurement [Benacerraf]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Infinity is not a number, so doesn't say how many; it is the property of a law [Wittgenstein]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
For Zermelo 3 belongs to 17, but for Von Neumann it does not [Benacerraf]
The successor of x is either x and all its members, or just the unit set of x [Benacerraf]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
Disputes about mathematical objects seem irrelevant, and mathematicians cannot resolve them [Benacerraf, by Friend]
No particular pair of sets can tell us what 'two' is, just by one-to-one correlation [Benacerraf, by Lowe]
If ordinal numbers are 'reducible to' some set-theory, then which is which? [Benacerraf]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
If any recursive sequence will explain ordinals, then it seems to be the structure which matters [Benacerraf]
The job is done by the whole system of numbers, so numbers are not objects [Benacerraf]
The number 3 defines the role of being third in a progression [Benacerraf]
Number words no more have referents than do the parts of a ruler [Benacerraf]
Mathematical objects only have properties relating them to other 'elements' of the same structure [Benacerraf]
How can numbers be objects if order is their only property? [Benacerraf, by Putnam]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
Number-as-objects works wholesale, but fails utterly object by object [Benacerraf]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
Number words are not predicates, as they function very differently from adjectives [Benacerraf]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
The set-theory paradoxes mean that 17 can't be the class of all classes with 17 members [Benacerraf]
7. Existence / D. Theories of Reality / 8. Facts / b. Types of fact
There are no positive or negative facts; these are just the forms of propositions [Wittgenstein]
8. Modes of Existence / D. Universals / 5. Universals as Concepts
Using 'green' is a commitment to future usage of 'green' [Wittgenstein]
9. Objects / F. Identity among Objects / 6. Identity between Objects
Identity statements make sense only if there are possible individuating conditions [Benacerraf]
10. Modality / C. Sources of Modality / 3. Necessity by Convention
For each necessity in the world there is an arbitrary rule of language [Wittgenstein]
11. Knowledge Aims / A. Knowledge / 2. Understanding
Understanding is translation, into action or into other symbols [Wittgenstein]
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
We live in sense-data, but talk about physical objects [Wittgenstein]
12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems
Part of what we mean by stating the facts is the way we tend to experience them [Wittgenstein]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
If you remember wrongly, then there must be some other criterion than your remembering [Wittgenstein]
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
Explanation and understanding are the same [Wittgenstein]
Explanation gives understanding by revealing the full multiplicity of the thing [Wittgenstein]
14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism
A machine strikes us as being a rule of movement [Wittgenstein]
14. Science / D. Explanation / 3. Best Explanation / a. Best explanation
If an explanation is good, the symbol is used properly in the future [Wittgenstein]
18. Thought / A. Modes of Thought / 1. Thought
Thought is an activity which we perform by the expression of it [Wittgenstein]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
A proposition draws a line around the facts which agree with it [Wittgenstein]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
The meaning of a proposition is the mode of its verification [Wittgenstein]
19. Language / A. Nature of Meaning / 7. Meaning Holism / a. Sentence meaning
Words function only in propositions, like levers in a machine [Wittgenstein]
19. Language / D. Propositions / 1. Propositions
A proposition is any expression which can be significantly negated [Wittgenstein]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
Laws of nature are an aspect of the phenomena, and are just our mode of description [Wittgenstein]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]