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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Nature's Metaphysics' and 'Truth'

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68 ideas

1. Philosophy / F. Analytic Philosophy / 3. Analysis of Preconditions
In "if and only if" (iff), "if" expresses the sufficient condition, and "only if" the necessary condition [Engel]
3. Truth / A. Truth Problems / 5. Truth Bearers
Are truth-bearers propositions, or ideas/beliefs, or sentences/utterances? [Engel]
3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
The redundancy theory gets rid of facts, for 'it is a fact that p' just means 'p' [Engel]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
We can't explain the corresponding structure of the world except by referring to our thoughts [Engel]
3. Truth / D. Coherence Truth / 1. Coherence Truth
The coherence theory says truth is an internal relationship between groups of truth-bearers [Engel]
3. Truth / D. Coherence Truth / 2. Coherence Truth Critique
Any coherent set of beliefs can be made more coherent by adding some false beliefs [Engel]
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]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Deflationism seems to block philosophers' main occupation, asking metatheoretical questions [Engel]
Deflationism cannot explain why we hold beliefs for reasons [Engel]
3. Truth / H. Deflationary Truth / 3. Minimalist Truth
Maybe there is no more to be said about 'true' than there is about the function of 'and' in logic [Engel]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
The plausible Barcan formula implies modality in the actual world [Bird]
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 / D. Assumptions for Logic / 1. Bivalence
Deflationism must reduce bivalence ('p is true or false') to excluded middle ('p or not-p') [Engel]
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]
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]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
If all existents are causally active, that excludes abstracta and causally isolated objects [Bird]
7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
If naturalism refers to supervenience, that leaves necessary entities untouched [Bird]
8. Modes of Existence / B. Properties / 3. Types of Properties
There might be just one fundamental natural property [Bird]
8. Modes of Existence / B. Properties / 6. Categorical Properties
Categorical properties are not modally fixed, but change across possible worlds [Bird]
The categoricalist idea is that a property is only individuated by being itself [Bird]
If we abstractly define a property, that doesn't mean some object could possess it [Bird]
Categoricalists take properties to be quiddities, with no essential difference between them [Bird]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
To name an abundant property is either a Fregean concept, or a simple predicate [Bird]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
Only real powers are fundamental [Bird, by Mumford/Anjum]
8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived
If all properties are potencies, and stimuli and manifestation characterise them, there is a regress [Bird]
The essence of a potency involves relations, e.g. mass, to impressed force and acceleration [Bird]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / c. Dispositions as conditional
A disposition is finkish if a time delay might mean the manifestation fizzles out [Bird]
A robust pot attached to a sensitive bomb is not fragile, but if struck it will easily break [Bird]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / d. Dispositions as occurrent
Megarian actualists deny unmanifested dispositions [Bird]
8. Modes of Existence / D. Universals / 3. Instantiated Universals
Why should a universal's existence depend on instantiation in an existing particular? [Bird]
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
Resemblance itself needs explanation, presumably in terms of something held in common [Bird]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
10. Modality / A. Necessity / 3. Types of Necessity
If the laws necessarily imply p, that doesn't give a new 'nomological' necessity [Bird]
10. Modality / A. Necessity / 6. Logical Necessity
Logical necessitation is not a kind of necessity; George Orwell not being Eric Blair is not a real possibility [Bird]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
Empiricist saw imaginability and possibility as close, but now they seem remote [Bird]
10. Modality / E. Possible worlds / 3. Transworld Objects / d. Haecceitism
Haecceitism says identity is independent of qualities and without essence [Bird]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
The Humean theory of motivation is that beliefs may be motivators as well as desires [Engel]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
Our beliefs are meant to fit the world (i.e. be true), where we want the world to fit our desires [Engel]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
'Evidentialists' say, and 'voluntarists' deny, that we only believe on the basis of evidence [Engel]
12. Knowledge Sources / D. Empiricism / 3. Pragmatism
Pragmatism is better understood as a theory of belief than as a theory of truth [Engel]
13. Knowledge Criteria / C. External Justification / 5. Controlling Beliefs
We cannot directly control our beliefs, but we can control the causes of our involuntary beliefs [Engel]
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
We can't reject all explanations because of a regress; inexplicable A can still explain B [Bird]
17. Mind and Body / C. Functionalism / 1. Functionalism
Mental states as functions are second-order properties, realised by first-order physical properties [Engel]
26. Natural Theory / C. Causation / 4. Naturalised causation
We should explain causation by powers, not powers by causation [Bird]
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
Singularism about causes is wrong, as the universals involved imply laws [Bird]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
Laws are explanatory relationships of things, which supervene on their essences [Bird]
26. Natural Theory / D. Laws of Nature / 2. Types of Laws
Laws are either disposition regularities, or relations between properties [Bird]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
That other diamonds are hard does not explain why this one is [Bird]
Dispositional essentialism says laws (and laws about laws) are guaranteed regularities [Bird]
26. Natural Theory / D. Laws of Nature / 5. Laws from Universals
Laws cannot offer unified explanations if they don't involve universals [Bird]
If the universals for laws must be instantiated, a vanishing particular could destroy a law [Bird]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / b. Scientific necessity
Salt necessarily dissolves in water, because of the law which makes the existence of salt possible [Bird]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
Most laws supervene on fundamental laws, which are explained by basic powers [Bird, by Friend/Kimpton-Nye]
26. Natural Theory / D. Laws of Nature / 9. Counterfactual Claims
Essentialism can't use conditionals to explain regularities, because of possible interventions [Bird]
27. Natural Reality / D. Time / 1. Nature of Time / b. Relative time
The relational view of space-time doesn't cover times and places where things could be [Bird]