Combining Texts

All the ideas for 'Meno', 'Thinking About Mechanisms' and 'Set Theory'

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36 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
Spiritual qualities only become advantageous with the growth of wisdom [Plato]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
Choice: ∀A ∃R (R well-orders A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
Set Existence: ∃x (x = x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
Constructibility: V = L (all sets are constructible) [Kunen]
5. Theory of Logic / L. Paradox / 2. Aporiai
How can you seek knowledge of something if you don't know it? [Plato]
7. Existence / B. Change in Existence / 2. Processes
Activities have place, rate, duration, entities, properties, modes, direction, polarity, energy and range [Machamer/Darden/Craver]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
Penicillin causes nothing; the cause is what penicillin does [Machamer/Darden/Craver]
11. Knowledge Aims / A. Knowledge / 2. Understanding
We understand something by presenting its low-level entities and activities [Machamer/Darden/Craver]
11. Knowledge Aims / A. Knowledge / 3. Value of Knowledge
True opinions only become really valuable when they are tied down by reasons [Plato]
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / b. Recollection doctrine
Seeking and learning are just recollection [Plato]
The slave boy learns geometry from questioning, not teaching, so it is recollection [Plato]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / b. Need for justification
As a guide to action, true opinion is as good as knowledge [Plato]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
You don't need to learn what you know, and how do you seek for what you don't know? [Plato]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
The explanation is not the regularity, but the activity sustaining it [Machamer/Darden/Craver]
14. Science / D. Explanation / 2. Types of Explanation / h. Explanations by function
Functions are not properties of objects, they are activities contributing to mechanisms [Machamer/Darden/Craver]
14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism
Mechanisms are not just push-pull systems [Machamer/Darden/Craver]
Mechanisms are systems organised to produce regular change [Machamer/Darden/Craver]
A mechanism explains a phenomenon by showing how it was produced [Machamer/Darden/Craver]
Our account of mechanism combines both entities and activities [Machamer/Darden/Craver]
Descriptions of explanatory mechanisms have a bottom level, where going further is irrelevant [Machamer/Darden/Craver]
14. Science / D. Explanation / 3. Best Explanation / b. Ultimate explanation
There are four types of bottom-level activities which will explain phenomena [Machamer/Darden/Craver]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
We can abstract by taking an exemplary case and ignoring the detail [Machamer/Darden/Craver]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
Is virtue taught, or achieved by practice, or a natural aptitude, or what? [Plato]
If virtue is a type of knowledge then it ought to be taught [Plato]
It seems that virtue is neither natural nor taught, but is a divine gift [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / j. Unity of virtue
How can you know part of virtue without knowing the whole? [Plato]
Even if virtues are many and various, they must have something in common to make them virtues [Plato]
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
Laws of nature have very little application in biology [Machamer/Darden/Craver]