Combining Texts

All the ideas for 'fragments/reports', 'The Tarskian Turn' and 'Coming-to-be and Passing-away (Gen/Corr)'

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72 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Philosophy is the most general intellectual discipline [Horsten]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
Unobservant thinkers tend to dogmatise using insufficient facts [Aristotle]
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
Semantic theories of truth seek models; axiomatic (syntactic) theories seek logical principles [Horsten]
Truth is a property, because the truth predicate has an extension [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's hierarchy lacks uniform truth, and depends on contingent factors [Horsten]
Tarski Bi-conditional: if you'll assert φ you'll assert φ-is-true - and also vice versa [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
Axiomatic approaches avoid limiting definitions to avoid the truth predicate, and limited sizes of models [Horsten]
Axiomatic approaches to truth avoid the regress problem of semantic theories [Horsten]
An axiomatic theory needs to be of maximal strength, while being natural and sound [Horsten]
'Reflexive' truth theories allow iterations (it is T that it is T that p) [Horsten]
A good theory of truth must be compositional (as well as deriving biconditionals) [Horsten]
The Naďve 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]
By adding truth to Peano Arithmetic we increase its power, so truth has mathematical content! [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
Inferential deflationism says truth has no essence because no unrestricted logic governs the concept [Horsten]
Deflationism skips definitions and models, and offers just accounts of basic laws of truth [Horsten]
Deflationism concerns the nature and role of truth, but not its laws [Horsten]
This deflationary account says truth has a role in generality, and in inference [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]
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 / 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 / A. Nature of Mathematics / 5. The Infinite / c. Potential infinite
Infinity is only potential, never actual [Aristotle]
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 / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
Predicativism says mathematical definitions must not include the thing being defined [Horsten]
7. Existence / A. Nature of Existence / 2. Types of Existence
Existence is either potential or actual [Aristotle]
7. Existence / B. Change in Existence / 1. Nature of Change
True change is in a thing's logos or its matter, not in its qualities [Aristotle]
A change in qualities is mere alteration, not true change [Aristotle]
If the substratum persists, it is 'alteration'; if it doesn't, it is 'coming-to-be' or 'passing-away' [Aristotle]
7. Existence / B. Change in Existence / 2. Processes
All comings-to-be are passings-away, and vice versa [Aristotle]
7. Existence / D. Theories of Reality / 8. Facts / b. Types of fact
We may believe in atomic facts, but surely not complex disjunctive ones? [Horsten]
7. Existence / D. Theories of Reality / 10. 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]
9. Objects / C. Structure of Objects / 3. Matter of an Object
Matter is the substratum, which supports both coming-to-be and alteration [Aristotle]
9. Objects / E. Objects over Time / 10. Beginning of an Object
Does the pure 'this' come to be, or the 'this-such', or 'so-great', or 'somewhere'? [Aristotle]
Philosophers have worried about coming-to-be from nothing pre-existing [Aristotle]
The substratum changing to a contrary is the material cause of coming-to-be [Aristotle]
If a perceptible substratum persists, it is 'alteration'; coming-to-be is a complete change [Aristotle]
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]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / b. Primary/secondary
Which of the contrary features of a body are basic to it? [Aristotle]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
By nature people are close to one another, but culture drives them apart [Hippias]
19. Language / C. Assigning Meanings / 1. Syntax
A theory of syntax can be based on Peano arithmetic, thanks to the translation by Gödel coding [Horsten]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / a. Greek matter
Matter is the limit of points and lines, and must always have quality and form [Aristotle]
The primary matter is the substratum for the contraries like hot and cold [Aristotle]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
There couldn't be just one element, which was both water and air at the same time [Aristotle]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
The Four Elements must change into one another, or else alteration is impossible [Aristotle]
Fire is hot and dry; Air is hot and moist; Water is cold and moist; Earth is cold and dry [Aristotle]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
Bodies are endlessly divisible [Aristotle]
Wood is potentially divided through and through, so what is there in the wood besides the division? [Aristotle]
If a body is endlessly divided, is it reduced to nothing - then reassembled from nothing? [Aristotle]
27. Natural Reality / D. Time / 1. Nature of Time / b. Relative time
There is no time without movement [Aristotle]
27. Natural Reality / E. Cosmology / 2. Eternal Universe
If each thing can cease to be, why hasn't absolutely everything ceased to be long ago? [Aristotle]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
Being is better than not-being [Aristotle]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
An Order controls all things [Aristotle]