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All the ideas for 'Frege philosophy of mathematics', 'Types and Ontology' and 'Intro to the Philosophy of Time'

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64 ideas

2. Reason / D. Definition / 7. Contextual Definition
A contextual definition permits the elimination of the expression by a substitution [Dummett]
2. Reason / F. Fallacies / 2. Infinite Regress
Vicious regresses force you to another level; non-vicious imply another level [Baron/Miller]
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 / L. Paradox / 7. Paradoxes of Time
A traveller takes a copy of a picture into the past, gives it the artist, who then creates the original! [Baron/Miller]
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 / C. Structure of Existence / 1. Grounding / a. Nature of grounding
Grounding is intended as a relation that fits dependences between things [Baron/Miller]
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 / E. Categories / 1. Categories
Categories can't overlap; they are either disjoint, or inclusive [Sommers, by Westerhoff]
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 / E. Objects over Time / 2. Objects that Change
How does a changing object retain identity or have incompatible properties over time? [Baron/Miller]
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]
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 / C. Assigning Meanings / 5. Fregean Semantics
Fregean semantics assumes a domain articulated into individual objects [Dummett]
26. Natural Theory / C. Causation / 1. Causation
Modern accounts of causation involve either processes or counterfactuals [Baron/Miller]
26. Natural Theory / C. Causation / 4. Naturalised causation
The main process theory of causation says it is transference of mass, energy, momentum or charge [Baron/Miller]
If causes are processes, what is causation by omission? (Distinguish legal from scientific causes?) [Baron/Miller]
26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation
The counterfactual theory of causation handles the problem no matter what causes actually are [Baron/Miller]
Counterfactual theories struggle with pre-emption by a causal back-up system [Baron/Miller]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / d. Entropy
There is no second 'law' of thermodynamics; it just reflects probabilities of certain microstates [Baron/Miller]
27. Natural Reality / C. Space / 3. Points in Space
Why should the limit of measurement be points, not intervals? [Dummett]
27. Natural Reality / C. Space / 6. Space-Time
In relativity space and time depend on one's motion, but spacetime gives an invariant metric [Baron/Miller]
27. Natural Reality / D. Time / 1. Nature of Time / f. Eternalism
The block universe theory says entities of all times exist, and time is the B-series [Baron/Miller]
27. Natural Reality / D. Time / 1. Nature of Time / g. Growing block
How can we know this is the present moment, if other times are real? [Baron/Miller]
If we are actually in the past then we shouldn't experience time passing [Baron/Miller]
27. Natural Reality / D. Time / 1. Nature of Time / h. Presentism
Erzatz Presentism allows the existence of other times, with only the present 'actualised' [Baron/Miller]
How do presentists explain relations between things existing at different times? [Baron/Miller]
Presentism needs endurantism, because other theories imply most of the object doesn't exist [Baron/Miller]
How can presentists move to the next future moment, if that doesn't exist? [Baron/Miller]
27. Natural Reality / D. Time / 1. Nature of Time / i. Denying time
Most of the sciences depend on the concept of time [Baron/Miller]
27. Natural Reality / D. Time / 2. Passage of Time / a. Experience of time
For abstractionists past times might still exist, althought their objects don't [Baron/Miller]
The error theory of time's passage says it is either a misdescription or a false inference [Baron/Miller]
27. Natural Reality / D. Time / 2. Passage of Time / b. Rate of time
It is meaningless to measure the rate of time using time itself, and without a rate there is no flow [Baron/Miller]
27. Natural Reality / D. Time / 2. Passage of Time / d. Time series
The C-series rejects A and B, and just sees times as order by betweenness, without direction [Baron/Miller]
27. Natural Reality / D. Time / 2. Passage of Time / e. Tensed (A) series
The A-series has to treat being past, present or future as properties [Baron/Miller]
27. Natural Reality / D. Time / 2. Passage of Time / f. Tenseless (B) series
The B-series can have a direction, as long as it does not arise from temporal flow [Baron/Miller]
27. Natural Reality / D. Time / 2. Passage of Time / g. Time's arrow
Static theories cannot account for time's obvious asymmetry, so time must be dynamic [Baron/Miller]
The direction of time is either primitive, or reducible to something else [Baron/Miller]
The kaon does not seem to be time-reversal invariant, unlike the rest of nature [Baron/Miller]
Maybe the past is just the direction of decreasing entropy [Baron/Miller]
We could explain time's direction by causation: past is the direction of causes, future of effects [Baron/Miller]
27. Natural Reality / D. Time / 2. Passage of Time / h. Change in time
Static time theory presents change as one property at t1, and a different property at t2 [Baron/Miller]
27. Natural Reality / D. Time / 2. Passage of Time / j. Time travel
If a time traveller kills his youthful grandfather, he both exists and fails to exist [Baron/Miller]
Presentism means there no existing past for a time traveller to visit [Baron/Miller]
27. Natural Reality / D. Time / 2. Passage of Time / k. Temporal truths
The past (unlike the future) is fixed, along with truths about it, by the existence of past objects [Baron/Miller]
27. Natural Reality / D. Time / 3. Parts of Time / e. Present moment
The moving spotlight says entities can have properties of being present, past or future [Baron/Miller]
The present moment is a matter of existence, not of acquiring a property [Baron/Miller]