Combining Texts

All the ideas for 'fragments/reports', 'An Inquiry into Meaning and Truth' and 'First-order Logic, 2nd-order, Completeness'

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26 ideas

3. Truth / A. Truth Problems / 7. Falsehood
16477 Asserting not-p is saying p is false [Russell]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / e. Existential quantifier ∃
16484 There are four experiences that lead us to talk of 'some' things [Russell]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
16486 The physical world doesn't need logic, but the mental world does [Russell]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10757 Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg]
10751 Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg]
10759 There are at least seven possible systems of semantics for second-order logic [Rossberg]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10753 Logical consequence is intuitively semantic, and captured by model theory [Rossberg]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
10752 Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
2947 Questions wouldn't lead anywhere without the law of excluded middle [Russell]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
10754 In proof-theory, logical form is shown by the logical constants [Rossberg]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / e. or
16479 'Or' expresses hesitation, in a dog at a crossroads, or birds risking grabbing crumbs [Russell]
16480 A disjunction expresses indecision [Russell]
16483 Disjunction may also arise in practice if there is imperfect memory. [Russell]
16481 'Or' expresses a mental state, not something about the world [Russell]
16487 Maybe the 'or' used to describe mental states is not the 'or' of logic [Russell]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10756 A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
10758 If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10761 Completeness can always be achieved by cunning model-design [Rossberg]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
10755 A deductive system is only incomplete with respect to a formal semantics [Rossberg]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / c. Grelling's paradox
16475 A 'heterological' predicate can't be predicated of itself; so is 'heterological' heterological? Yes=no! [Russell]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
16482 All our knowledge (if verbal) is general, because all sentences contain general words [Russell]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / a. Naïve realism
4758 Naïve realism leads to physics, but physics then shows that naïve realism is false [Russell]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
16476 For simple words, a single experience can show that they are true [Russell]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
16485 Perception can't prove universal generalisations, so abandon them, or abandon empiricism? [Russell]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
16478 A mother cat is paralysed if equidistant between two needy kittens [Russell]
23. Ethics / A. Egoism / 1. Ethical Egoism
3031 The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius]