Combining Texts

All the ideas for 'Parmenides', 'Mere Possibilities' and 'On Second-Order Logic'

expand these ideas     |    start again     |     specify just one area for these texts


70 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
I don't think Lewis's cost-benefit reflective equilibrium approach offers enough guidance [Stalnaker]
2. Reason / A. Nature of Reason / 1. On Reason
When questions are doubtful we should concentrate not on objects but on ideas of the intellect [Plato]
2. Reason / B. Laws of Thought / 5. Opposites
Opposites are as unlike as possible [Plato]
2. Reason / C. Styles of Reason / 1. Dialectic
Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic [Hegel on Plato]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
Non-S5 can talk of contingent or necessary necessities [Stalnaker]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
In modal set theory, sets only exist in a possible world if that world contains all of its members [Stalnaker]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
We regiment to get semantic structure, for evaluating arguments, and understanding complexities [Stalnaker]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / e. or
In 'S was F or some other than S was F', the disjuncts need S, but the whole disjunction doesn't [Stalnaker]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
'∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]
5. Theory of Logic / K. Features of Logics / 4. Completeness
Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
5. Theory of Logic / K. Features of Logics / 6. Compactness
Why should compactness be definitive of logic? [Boolos, by Hacking]
5. Theory of Logic / L. Paradox / 3. Antinomies
Plato found antinomies in ideas, Kant in space and time, and Bradley in relations [Plato, by Ryle]
Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Many concepts can only be expressed by second-order logic [Boolos]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato]
7. Existence / A. Nature of Existence / 1. Nature of Existence
A nominalist view says existence is having spatio-temporal location [Stalnaker]
Some say what exists must do so, and nothing else could possible exist [Stalnaker]
7. Existence / A. Nature of Existence / 3. Being / c. Becoming
The one was and is and will be and was becoming and is becoming and will become [Plato]
7. Existence / A. Nature of Existence / 3. Being / f. Primary being
Plato's Parmenides has a three-part theory, of Primal One, a One-Many, and a One-and-Many [Plato, by Plotinus]
7. Existence / D. Theories of Reality / 3. Reality
Absolute ideas, such as the Good and the Beautiful, cannot be known by us [Plato]
8. Modes of Existence / B. Properties / 1. Nature of Properties
Properties are modal, involving possible situations where they are exemplified [Stalnaker]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
I accept a hierarchy of properties of properties of properties [Stalnaker]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / a. Dispositions
Dispositions have modal properties, of which properties things would have counterfactually [Stalnaker]
8. Modes of Existence / D. Universals / 2. Need for Universals
If you deny that each thing always stays the same, you destroy the possibility of discussion [Plato]
You must always mean the same thing when you utter the same name [Plato]
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
Greatness and smallness must exist, to be opposed to one another, and come into being in things [Plato]
It would be absurd to think there were abstract Forms for vile things like hair, mud and dirt [Plato]
The concept of a master includes the concept of a slave [Plato]
If admirable things have Forms, maybe everything else does as well [Plato]
If absolute ideas existed in us, they would cease to be absolute [Plato]
Plato moves from Forms to a theory of genera and principles in his later work [Plato, by Frede,M]
8. Modes of Existence / D. Universals / 6. Platonic Forms / b. Partaking
The whole idea of each Form must be found in each thing which participates in it [Plato]
If things are made alike by participating in something, that thing will be the absolute idea [Plato]
If things partake of ideas, this implies either that everything thinks, or that everything actually is thought [Plato]
Participation is not by means of similarity, so we are looking for some other method of participation [Plato]
Each idea is in all its participants at once, just as daytime is a unity but in many separate places at once [Plato]
8. Modes of Existence / D. Universals / 6. Platonic Forms / c. Self-predication
If absolute greatness and great things are seen as the same, another thing appears which makes them seem great [Plato]
Nothing can be like an absolute idea, because a third idea intervenes to make them alike (leading to a regress) [Plato]
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
Parts must belong to a created thing with a distinct form [Plato]
9. Objects / C. Structure of Objects / 5. Composition of an Object
In Parmenides, if composition is identity, a whole is nothing more than its parts [Plato, by Harte,V]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
Plato says only a one has parts, and a many does not [Plato, by Harte,V]
Anything which has parts must be one thing, and parts are of a one, not of a many [Plato]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
It seems that the One must be composed of parts, which contradicts its being one [Plato]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
'Socrates is essentially human' seems to say nothing could be Socrates if it was not human [Stalnaker]
9. Objects / F. Identity among Objects / 6. Identity between Objects
Two things relate either as same or different, or part of a whole, or the whole of the part [Plato]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
The bundle theory makes the identity of indiscernibles a necessity, since the thing is the properties [Stalnaker]
10. Modality / A. Necessity / 3. Types of Necessity
Strong necessity is always true; weak necessity is cannot be false [Stalnaker]
10. Modality / C. Sources of Modality / 2. Necessity as Primitive
Necessity and possibility are fundamental, and there can be no reductive analysis of them [Stalnaker]
10. Modality / C. Sources of Modality / 5. Modality from Actuality
Modal concepts are central to the actual world, and shouldn't need extravagant metaphysics [Stalnaker]
10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism
Given actualism, how can there be possible individuals, other than the actual ones? [Stalnaker]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
Possible worlds are properties [Stalnaker]
Possible worlds don't reduce modality, they regiment it to reveal its structure [Stalnaker]
I think of worlds as cells (rather than points) in logical space [Stalnaker]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
Modal properties depend on the choice of a counterpart, which is unconstrained by metaphysics [Stalnaker]
10. Modality / E. Possible worlds / 3. Transworld Objects / d. Haecceitism
Anti-haecceitism says there is no more to an individual than meeting some qualitative conditions [Stalnaker]
18. Thought / C. Content / 6. Broad Content
How can we know what we are thinking, if content depends on something we don't know? [Stalnaker]
19. Language / C. Assigning Meanings / 2. Semantics
We still lack an agreed semantics for quantifiers in natural language [Stalnaker]
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
Possible world semantics may not reduce modality, but it can explain it [Stalnaker]
19. Language / D. Propositions / 1. Propositions
I take propositions to be truth conditions [Stalnaker]
A theory of propositions at least needs primitive properties of consistency and of truth [Stalnaker]
19. Language / D. Propositions / 3. Concrete Propositions
Propositions presumably don't exist if the things they refer to don't exist [Stalnaker]
25. Social Practice / E. Policies / 5. Education / c. Teaching
Only a great person can understand the essence of things, and an even greater person can teach it [Plato]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / d. The unlimited
The unlimited has no shape and is endless [Plato]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / e. The One
Everything partakes of the One in some way [Plato]
The only movement possible for the One is in space or in alteration [Plato]
Some things do not partake of the One [Plato]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
We couldn't discuss the non-existence of the One without knowledge of it [Plato]