Combining Texts

All the ideas for 'Set Theory', 'Letters to Wolff' and 'Action'

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46 ideas

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]
9. Objects / D. Essence of Objects / 9. Essence and Properties
The properties of a thing flow from its essence [Leibniz]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
Evolutionary explanations look to the past or the group, not to the individual [Stout,R]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
Not all explanation is causal. We don't explain a painting's beauty, or the irrationality of root-2, that way [Stout,R]
20. Action / A. Definition of Action / 1. Action Theory
Philosophy of action studies the nature of agency, and of deliberate actions [Stout,R]
Agency is causal processes that are sensitive to justification [Stout,R]
20. Action / A. Definition of Action / 2. Duration of an Action
Mental states and actions need to be separate, if one is to cause the other [Stout,R]
Are actions bodily movements, or a sequence of intention-movement-result? [Stout,R]
If one action leads to another, does it cause it, or is it part of it? [Stout,R]
20. Action / A. Definition of Action / 3. Actions and Events
I do actions, but not events, so actions are not events [Stout,R]
20. Action / A. Definition of Action / 4. Action as Movement
Bicycle riding is not just bodily movement - you also have to be on the bicycle [Stout,R]
20. Action / B. Preliminaries of Action / 1. Intention to Act / a. Nature of intentions
The rationalistic approach says actions are intentional when subject to justification [Stout,R]
The causal theory says that actions are intentional when intention (or belief-desire) causes the act [Stout,R]
Deciding what to do usually involves consulting the world, not our own minds [Stout,R]
Should we study intentions in their own right, or only as part of intentional action? [Stout,R]
You can have incompatible desires, but your intentions really ought to be consistent [Stout,R]
The normativity of intentions would be obvious if they were internal promises [Stout,R]
20. Action / B. Preliminaries of Action / 1. Intention to Act / b. Types of intention
Intentional agency is seen in internal precursors of action, and in external reasons for the act [Stout,R]
Speech needs sustained intentions, but not prior intentions [Stout,R]
20. Action / B. Preliminaries of Action / 1. Intention to Act / d. Group intentions
Bratman has to treat shared intentions as interrelated individual intentions [Stout,R]
A request to pass the salt shares an intention that the request be passed on [Stout,R]
An individual cannot express the intention that a group do something like moving a piano [Stout,R]
An intention is a goal to which behaviour is adapted, for an individual or for a group [Stout,R]
20. Action / B. Preliminaries of Action / 2. Willed Action / b. Volitionism
If the action of walking is just an act of will, then movement of the legs seems irrelevant [Stout,R]
20. Action / B. Preliminaries of Action / 2. Willed Action / c. Agent causation
Most philosophers see causation as by an event or state in the agent, rather than the whole agent [Stout,R]
If you don't mention an agent, you aren't talking about action [Stout,R]
20. Action / B. Preliminaries of Action / 2. Willed Action / d. Weakness of will
If you can judge one act as best, then do another, this supports an inward-looking view of agency [Stout,R]
20. Action / C. Motives for Action / 1. Acting on Desires
Maybe your emotions arise from you motivations, rather than being their cause [Stout,R]
For an ascetic a powerful desire for something is a reason not to implement it [Stout,R]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
Beliefs, desires and intentions are not events, so can't figure in causal relations [Stout,R]
A standard view says that the explanation of an action is showing its rational justification [Stout,R]
In order to be causal, an agent's reasons must be internalised as psychological states [Stout,R]
20. Action / C. Motives for Action / 4. Responsibility for Actions
An action is only yours if you produce it, rather than some state or event within you [Stout,R]
There may be a justification relative to a person's view, and yet no absolute justification [Stout,R]
20. Action / C. Motives for Action / 5. Action Dilemmas / b. Double Effect
Describing a death as a side-effect rather than a goal may just be good public relations [Stout,R]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
Aristotelian causation involves potentiality inputs into processes (rather than a pair of events) [Stout,R]