Combining Texts

All the ideas for 'Through the Looking Glass', 'Frege philosophy of mathematics' and 'Ordinary Objects'

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49 ideas

2. Reason / D. Definition / 7. Contextual Definition
A contextual definition permits the elimination of the expression by a substitution [Dummett]
3. Truth / B. Truthmakers / 12. Rejecting Truthmakers
Maybe analytic truths do not require truth-makers, as they place no demands on the world [Thomasson]
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 / B. Logical Consequence / 6. Entailment
Analytical entailments arise from combinations of meanings and inference rules [Thomasson]
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 / 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 / d. Logicism critique
Set theory isn't part of logic, and why reduce to something more complex? [Dummett]
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Existence might require playing a role in explanation, or in a causal story, or being composed in some way [Thomasson]
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 / 11. Ontological Commitment / a. Ontological commitment
Rival ontological claims can both be true, if there are analytic relationships between them [Thomasson]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / d. Commitment of theories
Theories do not avoid commitment to entities by avoiding certain terms or concepts [Thomasson]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
Nominalism assumes unmediated mental contact with objects [Dummett]
9. Objects / A. Existence of Objects / 1. Physical Objects
Ordinary objects may be not indispensable, but they are nearly unavoidable [Thomasson]
The simple existence conditions for objects are established by our practices, and are met [Thomasson]
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
It is analytic that if simples are arranged chair-wise, then there is a chair [Thomasson, by Hofweber]
Eliminativists haven't found existence conditions for chairs, beyond those of the word 'chair' [Thomasson]
Ordinary objects are rejected, to avoid contradictions, or for greater economy in thought [Thomasson]
To individuate people we need conventions, but conventions are made up by people [Thomasson]
9. Objects / B. Unity of Objects / 1. Unifying an Object / c. Unity as conceptual
Wherever an object exists, there are intrinsic properties instantiating every modal profile [Thomasson]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
If the statue and the lump are two objects, they require separate properties, so we could add their masses [Thomasson]
Given the similarity of statue and lump, what could possibly ground their modal properties? [Thomasson]
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]
9. Objects / F. Identity among Objects / 6. Identity between Objects
Identity claims between objects are only well-formed if the categories are specified [Thomasson]
Identical entities must be of the same category, and meet the criteria for the category [Thomasson]
10. Modality / C. Sources of Modality / 3. Necessity by Convention
Modal Conventionalism says modality is analytic, not intrinsic to the world, and linguistic [Thomasson]
12. Knowledge Sources / E. Direct Knowledge / 1. Common Sense
A chief task of philosophy is making reflective sense of our common sense worldview [Thomasson]
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 / B. Reference / 3. Direct Reference / b. Causal reference
How can causal theories of reference handle nonexistence claims? [Thomasson]
Pure causal theories of reference have the 'qua problem', of what sort of things is being referred to [Thomasson]
19. Language / C. Assigning Meanings / 5. Fregean Semantics
Fregean semantics assumes a domain articulated into individual objects [Dummett]
19. Language / E. Analyticity / 1. Analytic Propositions
Analyticity is revealed through redundancy, as in 'He bought a house and a building' [Thomasson]
27. Natural Reality / C. Space / 3. Points in Space
Why should the limit of measurement be points, not intervals? [Dummett]