Combining Texts

All the ideas for 'works', 'Logic in Mathematics' and 'Necessity, Essence and Individuation'

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67 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 / 6. Metaphysics as Conceptual
Metaphysics is clarifying how we speak and think (and possibly improving it) [Sidelle]
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 / 3. Types of Definition
A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege]
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]
2. Reason / D. Definition / 10. Stipulative Definition
Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta]
2. Reason / E. Argument / 6. Conclusive Proof
We must be clear about every premise and every law used in a proof [Frege]
2. Reason / E. Argument / 7. Thought Experiments
We seem to base necessities on thought experiments and imagination [Sidelle]
4. Formal Logic / G. Formal Mereology / 1. Mereology
Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Logic not only proves things, but also reveals logical relations between them [Frege]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege]
The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege]
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 / E. Structures of Logic / 8. Theories in Logic
'Theorems' are both proved, and used in proofs [Frege]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Tracing inference backwards closes in on a small set of axioms and postulates [Frege]
The essence of mathematics is the kernel of primitive truths on which it rests [Frege]
A truth can be an axiom in one system and not in another [Frege]
Axioms are truths which cannot be doubted, and for which no proof is needed [Frege]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
To create order in mathematics we need a full system, guided by patterns of inference [Frege]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
If principles are provable, they are theorems; if not, they are axioms [Frege]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / d. Dispositions as occurrent
There doesn't seem to be anything in the actual world that can determine modal facts [Sidelle]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege]
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 / D. Essence of Objects / 2. Types of Essence
Causal reference presupposes essentialism if it refers to modally extended entities [Sidelle]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / c. Essentials are necessary
Clearly, essential predications express necessary properties [Sidelle]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
Being a deepest explanatory feature is an actual, not a modal property [Sidelle]
9. Objects / D. Essence of Objects / 15. Against Essentialism
That the essence of water is its microstructure is a convention, not a discovery [Sidelle]
9. Objects / F. Identity among Objects / 3. Relative Identity
We aren't clear about 'same stuff as this', so a principle of individuation is needed to identify it [Sidelle]
10. Modality / A. Necessity / 4. De re / De dicto modality
Evaluation of de dicto modalities does not depend on the identity of its objects [Sidelle]
10. Modality / C. Sources of Modality / 3. Necessity by Convention
Necessary a posteriori is conventional for necessity and nonmodal for a posteriority [Sidelle, by Sider]
To know empirical necessities, we need empirical facts, plus conventions about which are necessary [Sidelle]
10. Modality / D. Knowledge of Modality / 3. A Posteriori Necessary
The necessary a posteriori is statements either of identity or of essence [Sidelle]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
Empiricism explores necessities and concept-limits by imagining negations of truths [Sidelle]
Contradictoriness limits what is possible and what is imaginable [Sidelle]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
The individuals and kinds involved in modality are also a matter of convention [Sidelle]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
A thing doesn't need transworld identity prior to rigid reference - that could be a convention of the reference [Sidelle]
'Dthat' operates to make a singular term into a rigid term [Sidelle]
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 / A. A Priori Knowledge / 8. A Priori as Analytic
A priori knowledge is entirely of analytic truths [Sidelle]
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
Aristotle's standard analysis of species and genus involves specifying things in terms of something more general [Aristotle, by Benardete,JA]
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]
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]
18. Thought / B. Mechanics of Thought / 5. Mental Files
We need definitions to cram retrievable sense into a signed receptacle [Frege]
We use signs to mark receptacles for complex senses [Frege]
18. Thought / C. Content / 5. Twin Earth
That water is essentially H2O in some way concerns how we use 'water' [Sidelle]
19. Language / A. Nature of Meaning / 6. Meaning as Use
A sign won't gain sense just from being used in sentences with familiar components [Frege]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
Causal reference seems to get directly at the object, thus leaving its nature open [Sidelle]
19. Language / B. Reference / 5. Speaker's Reference
Because some entities overlap, reference must have analytic individuation principles [Sidelle]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
Thoughts are not subjective or psychological, because some thoughts are the same for us all [Frege]
A thought is the sense expressed by a sentence, and is what we prove [Frege]
19. Language / D. Propositions / 5. Unity of Propositions
The parts of a thought map onto the parts of a sentence [Frege]
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]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
Can anything in science reveal the necessity of what it discovers? [Sidelle]
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
The concepts of gods arose from observing the soul, and the cosmos [Aristotle, by Sext.Empiricus]