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All the ideas for 'Frege philosophy of mathematics', 'The Principles of Science' and 'Ontology and the Ambitions of Metaphysics'

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58 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]
2. Reason / D. Definition / 7. Contextual Definition
A contextual definition permits the elimination of the expression by a substitution [Dummett]
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 / 6. Classical Logic
In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett]
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 / 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
A prime number is one which is measured by a unit alone [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
A number is a multitude composed of units [Dummett]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett]
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 / 7. Mathematical Structuralism / e. Structuralism critique
The identity of a number may be fixed by something outside structure - by counting [Dummett]
Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
I hold that algebra and number are developments of logic [Jevons]
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
Set theory isn't part of logic, and why reduce to something more complex? [Dummett]
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 / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett]
7. Existence / D. Theories of Reality / 2. Realism
Realism is just the application of two-valued semantics to sentences [Dummett]
7. Existence / D. Theories of Reality / 3. Reality
Reality can be seen as the totality of facts, or as the totality of things [Hofweber]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
There are probably ineffable facts, systematically hidden from us [Hofweber]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
Nominalism assumes unmediated mental contact with objects [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
The existence of abstract objects is a pseudo-problem [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Abstract objects nowadays are those which are objective but not actual [Dummett]
It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett]
'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / d. Problems with abstracta
Abstract objects need the context principle, since they can't be encountered directly [Dummett]
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 / F. Identity among Objects / 2. Defining Identity
Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett]
Frege introduced criteria for identity, but thought defining identity was circular [Dummett]
10. Modality / B. Possibility / 9. Counterfactuals
Counterfactuals are essential for planning, and learning from mistakes [Hofweber]
18. Thought / D. Concepts / 4. Structure of Concepts / i. Conceptual priority
Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett]
An argument for conceptual priority is greater simplicity in explanation [Dummett]
18. Thought / E. Abstraction / 1. Abstract Thought
Abstract terms are acceptable as long as we know how they function linguistically [Dummett]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait]
We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett]
18. Thought / E. Abstraction / 8. Abstractionism Critique
To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett]
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 / C. Assigning Meanings / 5. Fregean Semantics
Fregean semantics assumes a domain articulated into individual objects [Dummett]
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]
27. Natural Reality / C. Space / 3. Points in Space
Why should the limit of measurement be points, not intervals? [Dummett]