Combining Texts

All the ideas for 'works', 'Set Theory and Its Philosophy' and 'Guide to Ground'

expand these ideas     |    start again     |     specify just one area for these texts


60 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
There is practical wisdom (for action), and theoretical wisdom (for deep understanding) [Aristotle, by Whitcomb]
1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
Realist metaphysics concerns what is real; naive metaphysics concerns natures of things [Fine,K]
2. Reason / A. Nature of Reason / 2. Logos
For Aristotle logos is essentially the ability to talk rationally about questions of value [Roochnik on Aristotle]
2. Reason / A. Nature of Reason / 4. Aims of Reason
Aristotle is the supreme optimist about the ability of logos to explain nature [Roochnik on Aristotle]
2. Reason / D. Definition / 4. Real Definition
Aristotelian definitions aim to give the essential properties of the thing defined [Aristotle, by Quine]
2. Reason / D. Definition / 5. Genus and Differentia
Aristotelian definition involves first stating the genus, then the differentia of the thing [Aristotle, by Urmson]
3. Truth / B. Truthmakers / 3. Truthmaker Maximalism
Truths need not always have their source in what exists [Fine,K]
3. Truth / B. Truthmakers / 7. Making Modal Truths
If the truth-making relation is modal, then modal truths will be grounded in anything [Fine,K]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
Usually the only reason given for accepting the empty set is convenience [Potter]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Infinity: There is at least one limit level [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
Nowadays we derive our conception of collections from the dependence between them [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter]
4. Formal Logic / G. Formal Mereology / 1. Mereology
Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki]
Mereology elides the distinction between the cards in a pack and the suits [Potter]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
We can formalize second-order formation rules, but not inference rules [Potter]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
Logical consequence is verification by a possible world within a truth-set [Fine,K]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady]
5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
If set theory didn't found mathematics, it is still needed to count infinite sets [Potter]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
2+2=4 is necessary if it is snowing, but not true in virtue of the fact that it is snowing [Fine,K]
If you say one thing causes another, that leaves open that the 'other' has its own distinct reality [Fine,K]
An immediate ground is the next lower level, which gives the concept of a hierarchy [Fine,K]
'Strict' ground moves down the explanations, but 'weak' ground can move sideways [Fine,K]
We learn grounding from what is grounded, not what does the grounding [Fine,K]
7. Existence / C. Structure of Existence / 1. Grounding / b. Relata of grounding
Ground is best understood as a sentence operator, rather than a relation between predicates [Fine,K]
If grounding is a relation it must be between entities of the same type, preferably between facts [Fine,K]
7. Existence / C. Structure of Existence / 1. Grounding / c. Grounding and explanation
Only metaphysical grounding must be explained by essence [Fine,K]
Philosophical explanation is largely by ground (just as cause is used in science) [Fine,K]
7. Existence / C. Structure of Existence / 1. Grounding / d. Grounding and reduction
We can only explain how a reduction is possible if we accept the concept of ground [Fine,K]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
Facts, such as redness and roundness of a ball, can be 'fused' into one fact [Fine,K]
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
A relation is a set consisting entirely of ordered pairs [Potter]
9. Objects / B. Unity of Objects / 2. Substance / b. Need for substance
If dependence is well-founded, with no infinite backward chains, this implies substances [Potter]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
The unmoved mover and the soul show Aristotelian form as the ultimate mereological atom [Aristotle, by Koslicki]
9. Objects / C. Structure of Objects / 2. Hylomorphism / d. Form as unifier
The 'form' is the recipe for building wholes of a particular kind [Aristotle, by Koslicki]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
Collections have fixed members, but fusions can be carved in innumerable ways [Potter]
9. Objects / E. Objects over Time / 5. Temporal Parts
Even a three-dimensionalist might identify temporal parts, in their thinking [Fine,K]
10. Modality / A. Necessity / 1. Types of Modality
Priority is a modality, arising from collections and members [Potter]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
Every necessary truth is grounded in the nature of something [Fine,K]
Each basic modality has its 'own' explanatory relation [Fine,K]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
For Aristotle, knowledge is of causes, and is theoretical, practical or productive [Aristotle, by Code]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
The notion of a priori truth is absent in Aristotle [Aristotle, by Politis]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Aristotle is a rationalist, but reason is slowly acquired through perception and experience [Aristotle, by Frede,M]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Aristotle wants to fit common intuitions, and therefore uses language as a guide [Aristotle, by Gill,ML]
14. Science / B. Scientific Theories / 1. Scientific Theory
Plato says sciences are unified around Forms; Aristotle says they're unified around substance [Aristotle, by Moravcsik]
14. Science / D. Explanation / 1. Explanation / a. Explanation
Aristotelian explanations are facts, while modern explanations depend on human conceptions [Aristotle, by Politis]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
Is there metaphysical explanation (as well as causal), involving a constitutive form of determination? [Fine,K]
Aristotle's standard analysis of species and genus involves specifying things in terms of something more general [Aristotle, by Benardete,JA]
We explain by identity (what it is), or by truth (how things are) [Fine,K]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
Aristotle regularly says that essential properties explain other significant properties [Aristotle, by Kung]
17. Mind and Body / D. Property Dualism / 5. Supervenience of mind
If mind supervenes on the physical, it may also explain the physical (and not vice versa) [Fine,K]
18. Thought / A. Modes of Thought / 5. Rationality / c. Animal rationality
Aristotle and the Stoics denied rationality to animals, while Platonists affirmed it [Aristotle, by Sorabji]
19. Language / E. Analyticity / 2. Analytic Truths
The notion of analytic truth is absent in Aristotle [Aristotle, by Politis]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Aristotle never actually says that man is a rational animal [Aristotle, by Fogelin]
25. Social Practice / E. Policies / 5. Education / a. Aims of education
It is the mark of an educated mind to be able to entertain an idea without accepting it [Aristotle]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Aristotle said the educated were superior to the uneducated as the living are to the dead [Aristotle, by Diog. Laertius]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / a. Greek matter
Aristotle's matter can become any other kind of matter [Aristotle, by Wiggins]
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
The concepts of gods arose from observing the soul, and the cosmos [Aristotle, by Sext.Empiricus]