### All the ideas for 'The Science of Knowing (Wissenschaftslehre) [1st ed]', 'Knowledge' and 'Intermediate Logic'

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

86 ideas

###### 2. Reason / A. Nature of Reason / 5. Objectivity
 22024 Fichte's subjectivity struggles to then give any account of objectivity [Pinkard on Fichte]
###### 4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
 13439 Venn Diagrams map three predicates into eight compartments, then look for the conclusion [Bostock]
###### 4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
 13422 'Conjunctive Normal Form' is ensuring that no disjunction has a conjunction within its scope [Bostock]
 13421 'Disjunctive Normal Form' is ensuring that no conjunction has a disjunction within its scope [Bostock]
###### 4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
 13355 'Disjunction' says that Γ,φ∨ψ|= iff Γ,φ|= and Γ,ψ|= [Bostock]
 13356 The 'conditional' is that Γ|=φ→ψ iff Γ,φ|=ψ [Bostock]
 13350 'Assumptions' says that a formula entails itself (φ|=φ) [Bostock]
 13351 'Thinning' allows that if premisses entail a conclusion, then adding further premisses makes no difference [Bostock]
 13352 'Cutting' allows that if x is proved, and adding y then proves z, you can go straight to z [Bostock]
 13353 'Negation' says that Γ,¬φ|= iff Γ|=φ [Bostock]
 13354 'Conjunction' says that Γ|=φ∧ψ iff Γ|=φ and Γ|=ψ [Bostock]
###### 4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
 13610 A logic with ¬ and → needs three axiom-schemas and one rule as foundation [Bostock]
###### 4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
 13846 A 'free' logic can have empty names, and a 'universally free' logic can have empty domains [Bostock]
###### 5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
 13346 Truth is the basic notion in classical logic [Bostock]
 13545 Elementary logic cannot distinguish clearly between the finite and the infinite [Bostock]
 13822 Fictional characters wreck elementary logic, as they have contradictions and no excluded middle [Bostock]
###### 5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
 13623 The syntactic turnstile |- φ means 'there is a proof of φ' or 'φ is a theorem' [Bostock]
###### 5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
 13349 Γ|=φ is 'entails'; Γ|= is 'is inconsistent'; |=φ is 'valid' [Bostock]
 13347 Validity is a conclusion following for premises, even if there is no proof [Bostock]
 13348 It seems more natural to express |= as 'therefore', rather than 'entails' [Bostock]
###### 5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
 13614 MPP: 'If Γ|=φ and Γ|=φ→ψ then Γ|=ψ' (omit Γs for Detachment) [Bostock]
 13617 MPP is a converse of Deduction: If Γ |- φ→ψ then Γ,φ|-ψ [Bostock]
###### 5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
 13799 The sign '=' is a two-place predicate expressing that 'a is the same thing as b' (a=b) [Bostock]
 13800 |= α=α and α=β |= φ(α/ξ ↔ φ(β/ξ) fix identity [Bostock]
 13803 If we are to express that there at least two things, we need identity [Bostock]
###### 5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
 13357 Truth-functors are usually held to be defined by their truth-tables [Bostock]
###### 5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
 22017 Normativity needs the possibility of negation, in affirmation and denial [Fichte, by Pinkard]
###### 5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
 13812 A 'zero-place' function just has a single value, so it is a name [Bostock]
 13811 A 'total' function ranges over the whole domain, a 'partial' function over appropriate inputs [Bostock]
###### 5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
 13360 In logic, a name is just any expression which refers to a particular single object [Bostock]
###### 5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
 13361 An expression is only a name if it succeeds in referring to a real object [Bostock]
###### 5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
 13813 Definite descriptions don't always pick out one thing, as in denials of existence, or errors [Bostock]
 13814 Definite desciptions resemble names, but can't actually be names, if they don't always refer [Bostock]
 13816 Because of scope problems, definite descriptions are best treated as quantifiers [Bostock]
 13817 Definite descriptions are usually treated like names, and are just like them if they uniquely refer [Bostock]
 13848 We are only obliged to treat definite descriptions as non-names if only the former have scope [Bostock]
###### 5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
 13815 Names do not have scope problems (e.g. in placing negation), but Russell's account does have that problem [Bostock]
###### 5. Theory of Logic / G. Quantification / 1. Quantification
 13438 'Prenex normal form' is all quantifiers at the beginning, out of the scope of truth-functors [Bostock]
###### 5. Theory of Logic / G. Quantification / 2. Domain of Quantification
 13818 If we allow empty domains, we must allow empty names [Bostock]
###### 5. Theory of Logic / H. Proof Systems / 1. Proof Systems
 13801 An 'informal proof' is in no particular system, and uses obvious steps and some ordinary English [Bostock]
###### 5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
 13619 Quantification adds two axiom-schemas and a new rule [Bostock]
 13622 Axiom systems from Frege, Russell, Church, Lukasiewicz, Tarski, Nicod, Kleene, Quine... [Bostock]
###### 5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
 13615 'Conditonalised' inferences point to the Deduction Theorem: If Γ,φ|-ψ then Γ|-φ→ψ [Bostock]
 13616 The Deduction Theorem greatly simplifies the search for proof [Bostock]
 13620 Proof by Assumptions can always be reduced to Proof by Axioms, using the Deduction Theorem [Bostock]
 13621 The Deduction Theorem and Reductio can 'discharge' assumptions - they aren't needed for the new truth [Bostock]
###### 5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
 13754 Natural deduction rules for → are the Deduction Theorem (→I) and Modus Ponens (→E) [Bostock]
 13755 Excluded middle is an introduction rule for negation, and ex falso quodlibet will eliminate it [Bostock]
 13758 In natural deduction we work from the premisses and the conclusion, hoping to meet in the middle [Bostock]
 13753 Natural deduction takes proof from assumptions (with its rules) as basic, and axioms play no part [Bostock]
###### 5. Theory of Logic / H. Proof Systems / 5. Tableau Proof
 13756 A tree proof becomes too broad if its only rule is Modus Ponens [Bostock]
 13611 Tableau proofs use reduction - seeking an impossible consequence from an assumption [Bostock]
 13612 Non-branching rules add lines, and branching rules need a split; a branch with a contradiction is 'closed' [Bostock]
 13613 A completed open branch gives an interpretation which verifies those formulae [Bostock]
 13757 Unlike natural deduction, semantic tableaux have recipes for proving things [Bostock]
 13761 In a tableau proof no sequence is established until the final branch is closed; hypotheses are explored [Bostock]
 13762 Tableau rules are all elimination rules, gradually shortening formulae [Bostock]
###### 5. Theory of Logic / H. Proof Systems / 6. Sequent Calculi
 13759 Each line of a sequent calculus is a conclusion of previous lines, each one explicitly recorded [Bostock]
 13760 A sequent calculus is good for comparing proof systems [Bostock]
###### 5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
 13364 Interpretation by assigning objects to names, or assigning them to variables first [Bostock, by PG]
###### 5. Theory of Logic / I. Semantics of Logic / 5. Extensionalism
 13821 Extensionality is built into ordinary logic semantics; names have objects, predicates have sets of objects [Bostock]
 13362 If an object has two names, truth is undisturbed if the names are swapped; this is Extensionality [Bostock]
###### 5. Theory of Logic / K. Features of Logics / 2. Consistency
 13541 For 'negation-consistent', there is never |-(S)φ and |-(S)¬φ [Bostock]
 13542 A proof-system is 'absolutely consistent' iff we don't have |-(S)φ for every formula [Bostock]
 13540 A set of formulae is 'inconsistent' when there is no interpretation which can make them all true [Bostock]
###### 5. Theory of Logic / K. Features of Logics / 6. Compactness
 13544 Inconsistency or entailment just from functors and quantifiers is finitely based, if compact [Bostock]
 13618 Compactness means an infinity of sequents on the left will add nothing new [Bostock]
###### 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
 13359 Complete induction assumes for all numbers less than n, then also for n, and hence for all numbers [Bostock]
 13358 Ordinary or mathematical induction assumes for the first, then always for the next, and hence for all [Bostock]
###### 8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
 13802 Relations can be one-many (at most one on the left) or many-one (at most one on the right) [Bostock]
 13543 A relation is not reflexive, just because it is transitive and symmetrical [Bostock]
###### 9. Objects / F. Identity among Objects / 5. Self-Identity
 13847 If non-existent things are self-identical, they are just one thing - so call it the 'null object' [Bostock]
###### 10. Modality / A. Necessity / 6. Logical Necessity
 13820 The idea that anything which can be proved is necessary has a problem with empty names [Bostock]
###### 10. Modality / C. Sources of Modality / 4. Necessity from Concepts
 22018 Necessary truths from basic assertion and negation [Fichte, by Pinkard]
###### 11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
 22064 Fichte's logic is much too narrow, and doesn't deduce ethics, art, society or life [Schlegel,F on Fichte]
###### 11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
 22032 Fichte's key claim was that the subjective-objective distinction must itself be subjective [Fichte, by Pinkard]
###### 13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
 19724 Belief is knowledge if it is true, certain, and obtained by a reliable process [Ramsey]
###### 15. Nature of Minds / A. Nature of Mind / 4. Other Minds / a. Other minds
 22020 We only see ourselves as self-conscious and rational in relation to other rationalities [Fichte]
###### 16. Persons / B. Nature of the Self / 4. Presupposition of Self
 22060 The Self is the spontaneity, self-relatedness and unity needed for knowledge [Fichte, by Siep]
 22066 Novalis sought a much wider concept of the ego than Fichte's proposal [Novalis on Fichte]
 22016 The self is not a 'thing', but what emerges from an assertion of normativity [Fichte, by Pinkard]
###### 16. Persons / B. Nature of the Self / 6. Self as Higher Awareness
 22019 Consciousness of an object always entails awareness of the self [Fichte]
###### 18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
 22061 Judgement is distinguishing concepts, and seeing their relations [Fichte, by Siep]
###### 19. Language / C. Assigning Meanings / 3. Predicates
 13363 A (modern) predicate is the result of leaving a gap for the name in a sentence [Bostock]
###### 22. Metaethics / A. Value / 1. Nature of Value / d. Subjective value
 22023 Fichte's idea of spontaneity implied that nothing counts unless we give it status [Fichte, by Pinkard]
###### 26. Natural Theory / A. Speculations on Nature / 1. Nature
 22065 Fichte reduces nature to a lifeless immobility [Schlegel,F on Fichte]