Combining Philosophers

All the ideas for Hastings Rashdall, David Roochnik and Michal Walicki

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40 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
1606 You have to be a Platonist to debate about reality, so every philosopher is a Platonist [Roochnik]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / b. Philosophy as transcendent
1595 Philosophy aims to satisfy the chief human desire - the articulation of beauty itself [Roochnik]
2. Reason / A. Nature of Reason / 2. Logos
1571 'Logos' ranges from thought/reasoning, to words, to rational structures outside thought [Roochnik]
1572 In the seventeenth century the only acceptable form of logos was technical knowledge [Roochnik]
1573 The hallmark of a person with logos is that they give reasons why one opinion is superior to another [Roochnik]
1592 Logos cannot refute the relativist, and so must admit that it too is a matter of desire (for truth and agreement) [Roochnik]
1593 Human desire has an ordered structure, with logos at the pinnacle [Roochnik]
1603 Logos is not unconditionally good, but good if there is another person willing to engage with it [Roochnik]
2. Reason / A. Nature of Reason / 4. Aims of Reason
1598 We prefer reason or poetry according to whether basics are intelligible or not [Roochnik]
2. Reason / A. Nature of Reason / 8. Naturalising Reason
1584 Modern science, by aiming for clarity about the external world, has abandoned rationality in the human world [Roochnik]
2. Reason / A. Nature of Reason / 9. Limits of Reason
1591 Unfortunately for reason, argument can't be used to establish the value of argument [Roochnik]
1599 Attempts to suspend all presuppositions are hopeless, because a common ground must be agreed for the process [Roochnik]
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
17749 Post proved the consistency of propositional logic in 1921 [Walicki]
17765 Propositional language can only relate statements as the same or as different [Walicki]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
17764 Boolean connectives are interpreted as functions on the set {1,0} [Walicki]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
17752 The empty set is useful for defining sets by properties, when the members are not yet known [Walicki]
17753 The empty set avoids having to take special precautions in case members vanish [Walicki]
4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
17759 Ordinals play the central role in set theory, providing the model of well-ordering [Walicki]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
17741 To determine the patterns in logic, one must identify its 'building blocks' [Walicki]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
17747 A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17748 The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17761 A compact axiomatisation makes it possible to understand a field as a whole [Walicki]
17763 Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
17758 Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki]
17755 Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki]
17756 The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki]
17760 Two infinite ordinals can represent a single infinite cardinal [Walicki]
17757 Members of ordinals are ordinals, and also subsets of ordinals [Walicki]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
17762 In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
17754 Inductive proof depends on the choice of the ordering [Walicki]
7. Existence / D. Theories of Reality / 3. Reality
1605 Reality can be viewed neutrally, or as an object of desire [Roochnik]
10. Modality / A. Necessity / 2. Nature of Necessity
17742 Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki]
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
1577 Relativism is a disease which destroys the possibility of rational debate [Roochnik]
16. Persons / B. Nature of the Self / 2. Ethical Self
1457 Morality requires a minimum commitment to the self [Rashdall]
19. Language / F. Communication / 1. Rhetoric
1578 If relativism is the correct account of human values, then rhetoric is more important than reasoning [Roochnik]
1596 Reasoning aims not at the understanding of objects, but at the desire to give beautiful speeches [Roochnik]
22. Metaethics / B. Value / 1. Nature of Value / e. Means and ends
6674 All moral judgements ultimately concern the value of ends [Rashdall]
23. Ethics / E. Utilitarianism / 6. Ideal Utilitarianism
6673 Ideal Utilitarianism is teleological but non-hedonistic; the aim is an ideal end, which includes pleasure [Rashdall]
28. God / B. Proving God / 2. Proofs of Reason / c. Moral Argument
1458 Conduct is only reasonable or unreasonable if the world is governed by reason [Rashdall]
1459 Absolute moral ideals can't exist in human minds or material things, so their acceptance implies a greater Mind [Rashdall, by PG]