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All the ideas for 'Thinking About Mathematics', 'Ontology and the Ambitions of Metaphysics' and 'Ideas: intro to pure phenomenology'

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71 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Metaphysics is (supposedly) first the ontology, then in general what things are like [Hofweber]
1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
'Fundamentality' is either a superficial idea, or much too obscure [Hofweber]
1. Philosophy / H. Continental Philosophy / 2. Phenomenology
Phenomenology studies different types of correlation between consciousness and its objects [Husserl, by Bernet]
Phenomenology needs absolute reflection, without presuppositions [Husserl]
There can only be a science of fluctuating consciousness if it focuses on stable essences [Husserl, by Bernet]
Phenomenology aims to validate objects, on the basis of intentional intuitive experience [Husserl, by Bernet]
Husserl saw transcendental phenomenology as idealist, in its construction of objects [Husserl, by Bernet]
Start philosophising with no preconceptions, from the intuitively non-theoretical self-given [Husserl]
Epoché or 'bracketing' is refraining from judgement, even when some truths are certain [Husserl]
'Bracketing' means no judgements at all about spatio-temporal existence [Husserl]
After everything is bracketed, consciousness still has a unique being of its own [Husserl]
Phenomenology describes consciousness, in the light of pure experiences [Husserl]
2. Reason / D. Definition / 13. Against Definition
The use of mathematical-style definitions in philosophy is fruitless and harmful [Husserl]
3. Truth / H. Deflationary Truth / 1. Redundant Truth
'It's true that Fido is a dog' conjures up a contrast class, of 'it's false' or 'it's unlikely' [Hofweber]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Since properties can have properties, some theorists rank them in 'types' [Hofweber]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
Maybe not even names are referential, but are just by used by speakers to refer [Hofweber]
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
'Singular terms' are not found in modern linguistics, and are not the same as noun phrases [Hofweber]
If two processes are said to be identical, that doesn't make their terms refer to entities [Hofweber]
5. Theory of Logic / G. Quantification / 1. Quantification
The inferential quantifier focuses on truth; the domain quantifier focuses on reality [Hofweber]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
Numbers are used as singular terms, as adjectives, and as symbols [Hofweber]
The Amazonian Piraha language is said to have no number words [Hofweber]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
Cauchy gave a formal definition of a converging sequence. [Shapiro]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
The fundamental theorem of arithmetic is that all numbers are composed uniquely of primes [Hofweber]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
How can words be used for counting if they are objects? [Hofweber]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Categories are the best foundation for mathematics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Logicism makes sense of our ability to know arithmetic just by thought [Hofweber]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Neo-Fregeans are dazzled by a technical result, and ignore practicalities [Hofweber]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
'Impredicative' definitions refer to the thing being described [Shapiro]
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
Our goal is to reveal a new hidden region of Being [Husserl]
7. Existence / A. Nature of Existence / 3. Being / h. Dasein (being human)
As a thing and its perception are separated, two modes of Being emerge [Husserl]
7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
Supervenience offers little explanation for things which necessarily go together [Hofweber]
7. Existence / D. Theories of Reality / 3. Reality
Reality can be seen as the totality of facts, or as the totality of things [Hofweber]
The World is all experiencable objects [Husserl]
7. Existence / D. Theories of Reality / 4. Anti-realism
Absolute reality is an absurdity [Husserl]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
There are probably ineffable facts, systematically hidden from us [Hofweber]
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
Our perceptual beliefs are about ordinary objects, not about simples arranged chair-wise [Hofweber]
9. Objects / D. Essence of Objects / 5. Essence as Kind
The sense of anything contingent has a purely apprehensible essence or Eidos [Husserl]
9. Objects / D. Essence of Objects / 9. Essence and Properties
Imagine an object's properties varying; the ones that won't vary are the essential ones [Husserl, by Vaidya]
10. Modality / B. Possibility / 9. Counterfactuals
Counterfactuals are essential for planning, and learning from mistakes [Hofweber]
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
The physical given, unlike the mental given, could be non-existing [Husserl]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
Feelings of self-evidence (and necessity) are just the inventions of theory [Husserl]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Direct 'seeing' by consciousness is the ultimate rational legitimation [Husserl]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
The phenomena of memory are given in the present, but as being past [Husserl, by Bernet]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
Natural science has become great by just ignoring ancient scepticism [Husserl]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
We know another's mind via bodily expression, while also knowing it is inaccessible [Husserl, by Bernet]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / b. Essence of consciousness
Pure consciousness is a sealed off system of actual Being [Husserl]
16. Persons / C. Self-Awareness / 2. Knowing the Self
We never meet the Ego, as part of experience, or as left over from experience [Husserl]
19. Language / A. Nature of Meaning / 1. Meaning
The "Fido"-Fido theory of meaning says every expression in a language has a referent [Hofweber]
19. Language / A. Nature of Meaning / 7. Meaning Holism / c. Meaning by Role
Inferential role semantics is an alternative to semantics that connects to the world [Hofweber]
19. Language / C. Assigning Meanings / 1. Syntax
Syntactic form concerns the focus of the sentence, as well as the truth-conditions [Hofweber]
19. Language / C. Assigning Meanings / 3. Predicates
Properties can be expressed in a language despite the absence of a single word for them [Hofweber]
'Being taller than this' is a predicate which can express many different properties [Hofweber]
19. Language / C. Assigning Meanings / 4. Compositionality
Compositonality is a way to build up the truth-conditions of a sentence [Hofweber]
19. Language / D. Propositions / 1. Propositions
Proposition have no content, because they are content [Hofweber]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
Without propositions there can be no beliefs or desires [Hofweber]
19. Language / D. Propositions / 3. Concrete Propositions
Do there exist thoughts which we are incapable of thinking? [Hofweber]
19. Language / F. Communication / 5. Pragmatics / a. Contextual meaning
'Semantic type coercion' is selecting the reading of a word to make the best sense [Hofweber]
19. Language / F. Communication / 5. Pragmatics / b. Implicature
'Background deletion' is appropriately omitting background from an answer [Hofweber]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
Only facts follow from facts [Husserl]