Combining Texts

All the ideas for 'Structures and Structuralism in Phil of Maths', 'Essays on Intellectual Powers 6: Judgement' and 'Tarski's Theory of Truth'

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


38 ideas

1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
The existence of tensed verbs shows that not all truths are necessary truths [Reid]
2. Reason / F. Fallacies / 7. Ad Hominem
An ad hominem argument is good, if it is shown that the man's principles are inconsistent [Reid]
3. Truth / A. Truth Problems / 4. Uses of Truth
The notion of truth is to help us make use of the utterances of others [Field,H]
3. Truth / A. Truth Problems / 9. Rejecting Truth
In the early 1930s many philosophers thought truth was not scientific [Field,H]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Tarski reduced truth to reference or denotation [Field,H, by Hart,WD]
Tarski really explained truth in terms of denoting, predicating and satisfied functions [Field,H]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
Tarski just reduced truth to some other undefined semantic notions [Field,H]
3. Truth / F. Semantic Truth / 2. Semantic Truth
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
Tarski gives us the account of truth needed to build a group of true sentences in a model [Field,H]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Model theory is unusual in restricting the range of the quantifiers [Field,H]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
'Analysis' is the theory of the real numbers [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Mereological arithmetic needs infinite objects, and function definitions [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory gives a unified and an explicit basis for mathematics [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price]
There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price]
Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
If someone denies that he is thinking when he is conscious of it, we can only laugh [Reid]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / b. Direct realism
The existence of ideas is no more obvious than the existence of external objects [Reid]
11. Knowledge Aims / C. Knowing Reality / 4. Solipsism
We are only aware of other beings through our senses; without that, we are alone in the universe [Reid]
12. Knowledge Sources / E. Direct Knowledge / 1. Common Sense
In obscure matters the few must lead the many, but the many usually lead in common sense [Reid]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
The theory of ideas, popular with philosophers, means past existence has to be proved [Reid]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / a. Consciousness
Consciousness is an indefinable and unique operation [Reid]
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
'Valence' and 'gene' had to be reduced to show their compatibility with physicalism [Field,H]
18. Thought / A. Modes of Thought / 8. Human Thought
The structure of languages reveals a uniformity in basic human opinions [Reid]
18. Thought / E. Abstraction / 2. Abstracta by Selection
If you can't distinguish the features of a complex object, your notion of it would be a muddle [Reid]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
Field says reference is a causal physical relation between mental states and objects [Field,H, by Putnam]
21. Aesthetics / A. Aesthetic Experience / 3. Taste
There are axioms of taste - such as a general consensus about a beautiful face [Reid]