Combining Philosophers

All the ideas for Peter B. Lewis, Michael Potter and Charles Taylor

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25 ideas

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
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 / 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]
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 / 8. Parts of Objects / b. Sums of parts
Collections have fixed members, but fusions can be carved in innumerable ways [Potter]
10. Modality / A. Necessity / 1. Types of Modality
Priority is a modality, arising from collections and members [Potter]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
Fichte, Schelling and Hegel rejected transcendental idealism [Lewis,PB]
Fichte, Hegel and Schelling developed versions of Absolute Idealism [Lewis,PB]
16. Persons / A. Concept of a Person / 4. Persons as Agents
The modern self has disengaged reason, self-exploration, and personal commitment [Taylor,C]
16. Persons / B. Nature of the Self / 2. Ethical Self
My aim is to map the connections between our sense of self and our moral understanding [Taylor,C]
16. Persons / E. Rejecting the Self / 3. Narrative Self
I can only be aware of myself as a person who changes by means of my personal history [Taylor,C]
22. Metaethics / C. Ethics Foundations / 1. Nature of Ethics / b. Defining ethics
Selfhood and moral values are inextricably intertwined [Taylor,C]
23. Ethics / C. Virtue Theory / 3. Virtues / e. Honour
Willingness to risk life was the constitutive quality of the man of honour [Taylor,C]
23. Ethics / C. Virtue Theory / 3. Virtues / h. Respect
To have respect for people, you must feel their claims, or their injustices, or hold them in awe [Taylor,C]
23. Ethics / D. Deontological Ethics / 4. Categorical Imperative
Consistency presupposes intrinsic description [Taylor,C]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
In later utilitarianism the modern stress on freedom leads to the rejection of paternalism [Taylor,C]
28. God / A. Divine Nature / 6. Divine Morality / d. God decrees morality
Nominalists defended the sovereignty of God against the idea of natural existing good and evil [Taylor,C]