Combining Philosophers

All the ideas for James Rachels, Dale Jacquette and Graham Priest

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71 ideas

2. Reason / B. Laws of Thought / 3. Non-Contradiction
Someone standing in a doorway seems to be both in and not-in the room [Priest,G, by Sorensen]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
Modal logic is multiple systems, shown in the variety of accessibility relations between worlds [Jacquette]
4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
The modal logic of C.I.Lewis was only interpreted by Kripke and Hintikka in the 1960s [Jacquette]
4. Formal Logic / E. Nonclassical Logics / 5. Relevant Logic
A logic is 'relevant' if premise and conclusion are connected, and 'paraconsistent' allows contradictions [Priest,G, by Friend]
4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
Free logic is one of the few first-order non-classical logics [Priest,G]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / a. Symbols of ST
X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets [Priest,G]
<a,b&62; is a set whose members occur in the order shown [Priest,G]
a ∈ X says a is an object in set X; a ∉ X says a is not in X [Priest,G]
{x; A(x)} is a set of objects satisfying the condition A(x) [Priest,G]
{a1, a2, ...an} indicates that a set comprising just those objects [Priest,G]
Φ indicates the empty set, which has no members [Priest,G]
{a} is the 'singleton' set of a (not the object a itself) [Priest,G]
X⊂Y means set X is a 'proper subset' of set Y [Priest,G]
X⊆Y means set X is a 'subset' of set Y [Priest,G]
X = Y means the set X equals the set Y [Priest,G]
X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets [Priest,G]
X∪Y indicates the 'union' of all the things in sets X and Y [Priest,G]
Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X [Priest,G]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
The 'relative complement' is things in the second set not in the first [Priest,G]
The 'intersection' of two sets is a set of the things that are in both sets [Priest,G]
The 'union' of two sets is a set containing all the things in either of the sets [Priest,G]
The 'induction clause' says complex formulas retain the properties of their basic formulas [Priest,G]
An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order [Priest,G]
A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets [Priest,G]
A 'set' is a collection of objects [Priest,G]
The 'empty set' or 'null set' has no members [Priest,G]
A set is a 'subset' of another set if all of its members are in that set [Priest,G]
A 'proper subset' is smaller than the containing set [Priest,G]
A 'singleton' is a set with only one member [Priest,G]
A 'member' of a set is one of the objects in the set [Priest,G]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST
The empty set Φ is a subset of every set (including itself) [Priest,G]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
The two main views in philosophy of logic are extensionalism and intensionalism [Jacquette]
Logic describes inferences between sentences expressing possible properties of objects [Jacquette]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
Classical logic is bivalent, has excluded middle, and only quantifies over existent objects [Jacquette]
5. Theory of Logic / C. Ontology of Logic / 2. Platonism in Logic
Logic is not just about signs, because it relates to states of affairs, objects, properties and truth-values [Jacquette]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
On Russell's analysis, the sentence "The winged horse has wings" comes out as false [Jacquette]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
Nominalists like substitutional quantification to avoid the metaphysics of objects [Jacquette]
Substitutional universal quantification retains truth for substitution of terms of the same type [Jacquette]
5. Theory of Logic / I. Semantics of Logic / 5. Extensionalism
Extensionalists say that quantifiers presuppose the existence of their objects [Jacquette]
5. Theory of Logic / I. Semantics of Logic / 6. Intensionalism
Intensionalists say meaning is determined by the possession of properties [Jacquette]
5. Theory of Logic / L. Paradox / 1. Paradox
Typically, paradoxes are dealt with by dividing them into two groups, but the division is wrong [Priest,G]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / b. König's paradox
The 'least indefinable ordinal' is defined by that very phrase [Priest,G]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / c. Berry's paradox
'x is a natural number definable in less than 19 words' leads to contradiction [Priest,G]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / d. Richard's paradox
By diagonalization we can define a real number that isn't in the definable set of reals [Priest,G]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox
The least ordinal greater than the set of all ordinals is both one of them and not one of them [Priest,G]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
Can a Barber shave all and only those persons who do not shave themselves? [Jacquette]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / e. Mirimanoff's paradox
The next set up in the hierarchy of sets seems to be both a member and not a member of it [Priest,G]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
If you know that a sentence is not one of the known sentences, you know its truth [Priest,G]
There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar [Priest,G]
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
To grasp being, we must say why something exists, and why there is one world [Jacquette]
7. Existence / A. Nature of Existence / 5. Reason for Existence
Being is maximal consistency [Jacquette]
Existence is completeness and consistency [Jacquette]
7. Existence / D. Theories of Reality / 1. Ontologies
Ontology is the same as the conceptual foundations of logic [Jacquette]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
Ontology must include the minimum requirements for our semantics [Jacquette]
7. Existence / E. Categories / 3. Proposed Categories
Logic is based either on separate objects and properties, or objects as combinations of properties [Jacquette]
Reduce states-of-affairs to object-property combinations, and possible worlds to states-of-affairs [Jacquette]
8. Modes of Existence / B. Properties / 11. Properties as Sets
If classes can't be eliminated, and they are property combinations, then properties (universals) can't be either [Jacquette]
9. Objects / A. Existence of Objects / 1. Physical Objects
An object is a predication subject, distinguished by a distinctive combination of properties [Jacquette]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Numbers, sets and propositions are abstract particulars; properties, qualities and relations are universals [Jacquette]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
The actual world is a consistent combination of states, made of consistent property combinations [Jacquette]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
The actual world is a maximally consistent combination of actual states of affairs [Jacquette]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / c. Worlds as propositions
Do proposition-structures not associated with the actual world deserve to be called worlds? [Jacquette]
We must experience the 'actual' world, which is defined by maximally consistent propositions [Jacquette]
15. Nature of Minds / B. Features of Minds / 5. Qualia / c. Explaining qualia
If qualia supervene on intentional states, then intentional states are explanatorily fundamental [Jacquette]
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
Reduction of intentionality involving nonexistent objects is impossible, as reduction must be to what is actual [Jacquette]
19. Language / C. Assigning Meanings / 7. Extensional Semantics
Extensionalist semantics forbids reference to nonexistent objects [Jacquette]
Extensionalist semantics is circular, as we must know the extension before assessing 'Fa' [Jacquette]
19. Language / D. Propositions / 1. Propositions
The extreme views on propositions are Frege's Platonism and Quine's extreme nominalism [Jacquette]
25. Social Practice / F. Life Issues / 2. Euthanasia
If it is desirable that a given patient die, then moral objections to killing them do not apply [Rachels]
It has become normal to consider passive euthanasia while condemning active euthanasia [Rachels]
28. God / B. Proving God / 2. Proofs of Reason / c. Moral Argument
God must be fit for worship, but worship abandons morally autonomy, but there is no God [Rachels, by Davies,B]