Combining Texts

All the ideas for 'Explaining the A Priori', 'Thinking About Mechanisms' and 'Elements of Set Theory'

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22 ideas

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton]
The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
The empty set may look pointless, but many sets can be constructed from it [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
The singleton is defined using the pairing axiom (as {x,x}) [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
We can only define functions if Choice tells us which items are involved [Enderton]
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]
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 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]
Mechanisms are not just push-pull systems [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]
18. Thought / D. Concepts / 2. Origin of Concepts / a. Origin of concepts
The concept 'red' is tied to what actually individuates red things [Peacocke]
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
Laws of nature have very little application in biology [Machamer/Darden/Craver]