Combining Texts

All the ideas for 'The Science of Knowing (Wissenschaftslehre) [1st ed]', 'Structuralism and the Notion of Dependence' and 'The Tarskian Turn'

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68 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Philosophy is the most general intellectual discipline [Horsten]
2. Reason / A. Nature of Reason / 5. Objectivity
Fichte's subjectivity struggles to then give any account of objectivity [Pinkard on Fichte]
2. Reason / D. Definition / 2. Aims of Definition
A definition should allow the defined term to be eliminated [Horsten]
3. Truth / A. Truth Problems / 1. Truth
Truth is a property, because the truth predicate has an extension [Horsten]
Semantic theories of truth seek models; axiomatic (syntactic) theories seek logical principles [Horsten]
3. Truth / A. Truth Problems / 2. Defining Truth
Truth has no 'nature', but we should try to describe its behaviour in inferences [Horsten]
3. Truth / A. Truth Problems / 5. Truth Bearers
Propositions have sentence-like structures, so it matters little which bears the truth [Horsten]
3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
Modern correspondence is said to be with the facts, not with true propositions [Horsten]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
The correspondence 'theory' is too vague - about both 'correspondence' and 'facts' [Horsten]
3. Truth / D. Coherence Truth / 2. Coherence Truth Critique
The coherence theory allows multiple coherent wholes, which could contradict one another [Horsten]
3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
The pragmatic theory of truth is relative; useful for group A can be useless for group B [Horsten]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Tarski Bi-conditional: if you'll assert φ you'll assert φ-is-true - and also vice versa [Horsten]
Tarski's hierarchy lacks uniform truth, and depends on contingent factors [Horsten]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
Semantic theories have a regress problem in describing truth in the languages for the models [Horsten]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
The Nave Theory takes the bi-conditionals as axioms, but it is inconsistent, and allows the Liar [Horsten]
Axiomatic theories take truth as primitive, and propose some laws of truth as axioms [Horsten]
A good theory of truth must be compositional (as well as deriving biconditionals) [Horsten]
An axiomatic theory needs to be of maximal strength, while being natural and sound [Horsten]
By adding truth to Peano Arithmetic we increase its power, so truth has mathematical content! [Horsten]
'Reflexive' truth theories allow iterations (it is T that it is T that p) [Horsten]
Axiomatic approaches to truth avoid the regress problem of semantic theories [Horsten]
Axiomatic approaches avoid limiting definitions to avoid the truth predicate, and limited sizes of models [Horsten]
3. Truth / G. Axiomatic Truth / 2. FS Truth Axioms
Friedman-Sheard theory keeps classical logic and aims for maximum strength [Horsten]
3. Truth / G. Axiomatic Truth / 3. KF Truth Axioms
Kripke-Feferman has truth gaps, instead of classical logic, and aims for maximum strength [Horsten]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Deflationism concerns the nature and role of truth, but not its laws [Horsten]
Deflationism says truth isn't a topic on its own - it just concerns what is true [Horsten]
Deflation: instead of asserting a sentence, we can treat it as an object with the truth-property [Horsten]
This deflationary account says truth has a role in generality, and in inference [Horsten]
Deflationism skips definitions and models, and offers just accounts of basic laws of truth [Horsten]
Inferential deflationism says truth has no essence because no unrestricted logic governs the concept [Horsten]
4. Formal Logic / E. Nonclassical Logics / 1. Nonclassical Logics
Nonclassical may accept T/F but deny applicability, or it may deny just T or F as well [Horsten]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
Doubt is thrown on classical logic by the way it so easily produces the liar paradox [Horsten]
5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
Deduction Theorem: ψ only derivable from φ iff φ→ψ are axioms [Horsten]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
Normativity needs the possibility of negation, in affirmation and denial [Fichte, by Pinkard]
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
A theory is 'non-conservative' if it facilitates new mathematical proofs [Horsten]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
It is easier to imagine truth-value gaps (for the Liar, say) than for truth-value gluts (both T and F) [Horsten]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
Satisfaction is a primitive notion, and very liable to semantical paradoxes [Horsten]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
The first incompleteness theorem means that consistency does not entail soundness [Horsten]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
Strengthened Liar: 'this sentence is not true in any context' - in no context can this be evaluated [Horsten]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
English expressions are denumerably infinite, but reals are nondenumerable, so many are unnameable [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
ZFC showed that the concept of set is mathematical, not logical, because of its existence claims [Horsten]
Set theory is substantial over first-order arithmetic, because it enables new proofs [Horsten]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo]
'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo]
'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo]
Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
Structuralism is right about algebra, but wrong about sets [Linnebo]
In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
Predicativism says mathematical definitions must not include the thing being defined [Horsten]
7. Existence / C. Structure of Existence / 4. Ontological Dependence
There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo]
7. Existence / D. Theories of Reality / 7. Facts / b. Types of fact
We may believe in atomic facts, but surely not complex disjunctive ones? [Horsten]
7. Existence / D. Theories of Reality / 9. Vagueness / f. Supervaluation for vagueness
In the supervaluationist account, disjunctions are not determined by their disjuncts [Horsten]
If 'Italy is large' lacks truth, so must 'Italy is not large'; but classical logic says it's large or it isn't [Horsten]
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo]
10. Modality / C. Sources of Modality / 4. Necessity from Concepts
Necessary truths from basic assertion and negation [Fichte, by Pinkard]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
Some claim that indicative conditionals are believed by people, even though they are not actually held true [Horsten]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
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
Fichte's key claim was that the subjective-objective distinction must itself be subjective [Fichte, by Pinkard]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / a. Other minds
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
The Self is the spontaneity, self-relatedness and unity needed for knowledge [Fichte, by Siep]
Novalis sought a much wider concept of the ego than Fichte's proposal [Novalis on Fichte]
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
Consciousness of an object always entails awareness of the self [Fichte]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
Judgement is distinguishing concepts, and seeing their relations [Fichte, by Siep]
19. Language / C. Assigning Meanings / 1. Syntax
A theory of syntax can be based on Peano arithmetic, thanks to the translation by Gdel coding [Horsten]
22. Metaethics / A. Value / 1. Nature of Value / d. Subjective value
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
Fichte reduces nature to a lifeless immobility [Schlegel,F on Fichte]