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All the ideas for 'fragments/reports', 'Lectures 1930-32 (student notes)' and 'Model Theory'

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66 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 / D. Definition / 7. Contextual Definition
The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W]
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 / A. Overview of Logic / 5. First-Order Logic
Since first-order languages are complete, |= and |- have the same meaning [Hodges,W]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
|= in model-theory means 'logical consequence' - it holds in all models [Hodges,W]
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]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
|= should be read as 'is a model for' or 'satisfies' [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Model theory studies formal or natural language-interpretation using set-theory [Hodges,W]
A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]
Models in model theory are structures, not sets of descriptions [Hodges,W]
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 / 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 / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
First-order logic can't discriminate between one infinite cardinal and another [Hodges,W]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
Things get smaller without end [Anaxagoras]
7. Existence / A. Nature of Existence / 1. Nature of Existence
Nothing is created or destroyed; there is only mixing and separation [Anaxagoras]
7. Existence / A. Nature of Existence / 3. Being / f. Primary being
Anaxagoras's concept of supreme Mind has a simple First and a multiple One [Anaxagoras, by Plotinus]
7. Existence / C. Structure of Existence / 6. Fundamentals / a. Fundamental reality
Basic is the potentially perceptible, then comes the contrary qualities, and finally the 'elements' [Anaxagoras]
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]
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 / 1. Perception
Snow is not white, and doesn't even appear white, because it is made of black water [Anaxagoras, by Cicero]
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 / D. Empiricism / 5. Empiricism Critique
The senses are too feeble to determine the truth [Anaxagoras]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
If you remember wrongly, then there must be some other criterion than your remembering [Wittgenstein]
13. Knowledge Criteria / D. Scepticism / 2. Types of Scepticism
We reveal unreliability in the senses when we cannot discriminate a slow change of colour [Anaxagoras, by Sext.Empiricus]
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]
15. Nature of Minds / A. Nature of Mind / 1. Mind / a. Mind
Nous is unlimited, self-ruling and pure; it is the finest thing, with great discernment and strength [Anaxagoras]
15. Nature of Minds / A. Nature of Mind / 1. Mind / c. Features of mind
Mind is self-ruling, pure, ordering and ubiquitous [Anaxagoras, by Plato]
16. Persons / F. Free Will / 1. Nature of Free Will
Anaxagoras says mind remains pure, and so is not affected by what it changes [Anaxagoras, by Aristotle]
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]
23. Ethics / C. Virtue Theory / 3. Virtues / g. Contemplation
Anaxagoras said a person would choose to be born to contemplate the ordered heavens [Anaxagoras]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / a. Final purpose
For Anaxagoras the Good Mind has no opposite, and causes all movement, for a higher reason [Anaxagoras, by Aristotle]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / a. Greek matter
Mind creates the world from a mixture of pure substances [Anaxagoras, by ]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
Anaxagoras said that the number of principles was infinite [Anaxagoras, by Aristotle]
The ultimate constituents of reality are the homoeomeries [Anaxagoras, by Vlastos]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
Anaxagoreans regard the homoeomeries as elements, which compose earth, air, fire and water [Anaxagoras, by Aristotle]
26. Natural Theory / C. Causation / 1. Causation
Anaxagoras says mind produces order and causes everything [Anaxagoras, by Plato]
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 / 1. Biology
Germs contain microscopic organs, which become visible as they grow [Anaxagoras]
28. God / A. Divine Nature / 1. God
When things were unified, Mind set them in order [Anaxagoras]
Anaxagoras was the first to say that the universe is directed by an intelligence [Anaxagoras, by Cicero]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
Past, present and future, and the movements of the heavens, were arranged by Mind [Anaxagoras]
28. God / C. Attitudes to God / 5. Atheism
Anaxagoras was charged with impiety for calling the sun a lump of stone [Anaxagoras, by Plutarch]
Anaxagoras was the first recorded atheist [Anaxagoras, by Watson]