Combining Texts

All the ideas for 'Ars Magna', 'Model Theory' and 'My Philosophical Development'

expand these ideas     |    start again     |     specify just one area for these texts

33 ideas

1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
6420 Only by analysing is progress possible in philosophy [Russell]
6432 Analysis gives new knowledge, without destroying what we already have [Russell]
2. Reason / D. Definition / 7. Contextual Definition
10476 The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W]
2. Reason / F. Fallacies / 8. Category Mistake / a. Category mistakes
6437 The theory of types makes 'Socrates and killing are two' illegitimate [Russell]
3. Truth / A. Truth Problems / 5. Truth Bearers
6442 Truth belongs to beliefs, not to propositions and sentences [Russell]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
6436 I gradually replaced classes with properties, and they ended as a symbolic convenience [Russell]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
19369 Lull's combinatorial art would articulate all the basic concepts, then show how they combine [Lull, by Arthur,R]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10478 Since first-order languages are complete, |= and |- have the same meaning [Hodges,W]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10477 |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
7528 Leibniz bases everything on subject/predicate and substance/property propositions [Russell]
5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
6439 Names are meaningless unless there is an object which they designate [Russell]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
10474 |= should be read as 'is a model for' or 'satisfies' [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10475 A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]
10473 Model theory studies formal or natural language-interpretation using set-theory [Hodges,W]
10481 Models in model theory are structures, not sets of descriptions [Hodges,W]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
10480 First-order logic can't discriminate between one infinite cardinal and another [Hodges,W]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
6423 We tried to define all of pure maths using logical premisses and concepts [Russell]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
6424 Formalists say maths is merely conventional marks on paper, like the arbitrary rules of chess [Russell]
6425 Formalism can't apply numbers to reality, so it is an evasion [Russell]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
6426 Intuitionism says propositions are only true or false if there is a method of showing it [Russell]
7. Existence / C. Structure of Existence / 6. Fundamentals / d. Logical atoms
6419 In 1899-1900 I adopted the philosophy of logical atomism [Russell]
6438 Complex things can be known, but not simple things [Russell]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
6434 Facts are everything, except simples; they are either relations or qualities [Russell]
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
6440 Universals can't just be words, because words themselves are universals [Russell]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
6430 In epistemology we should emphasis the continuity between animal and human minds [Russell]
12. Knowledge Sources / D. Empiricism / 3. Pragmatism
6441 Pragmatism judges by effects, but I judge truth by causes [Russell]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
6431 Empiricists seem unclear what they mean by 'experience' [Russell]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / b. Gettier problem
6444 True belief about the time is not knowledge if I luckily observe a stopped clock at the right moment [Russell]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
6433 Behaviourists struggle to explain memory and imagination, because they won't admit images [Russell]
18. Thought / A. Modes of Thought / 6. Judgement / b. Error
6443 Surprise is a criterion of error [Russell]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
6427 Unverifiable propositions about the remote past are still either true or false [Russell]
19. Language / D. Propositions / 4. Mental Propositions
6435 You can believe the meaning of a sentence without thinking of the words [Russell]
28. God / A. Divine Nature / 3. Divine Perfections
19371 Nine principles of God: goodness, greatness, eternity, power, wisdom, will, virtue, truth and glory [Lull, by Arthur,R]