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All the ideas for 'Parmenides', 'Gentzen's Analysis of First-Order Proofs' and 'Language,Truth and Logic'

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80 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Philosophy is a department of logic [Ayer]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
Philosophers should abandon speculation, as philosophy is wholly critical [Ayer]
1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
Humeans rejected the a priori synthetic, and so rejected even Kantian metaphysics [Ayer, by Macdonald,C]
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
Critics say analysis can only show the parts, and not their distinctive configuration [Ayer]
1. Philosophy / G. Scientific Philosophy / 3. Scientism
Philosophy deals with the questions that scientists do not wish to handle [Ayer]
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]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
We cannot analyse the concept of 'truth', because it is simply a mark that a sentence is asserted [Ayer]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Logic is based on transitions between sentences [Prawitz]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Natural deduction introduction rules may represent 'definitions' of logical connectives [Prawitz]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
In natural deduction, inferences are atomic steps involving just one logical constant [Prawitz]
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 / 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]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Maths and logic are true universally because they are analytic or tautological [Ayer]
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 / 1. Ontologies
Positivists regard ontology as either meaningless or stipulated [Ayer, by Robinson,H]
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 / 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]
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]
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]
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]
Each idea is in all its participants at once, just as daytime is a unity but in many separate places at once [Plato]
Participation is not by means of similarity, so we are looking for some other method of participation [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 / 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]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
Only tautologies can be certain; other propositions can only be probable [Ayer]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
Logical positivists could never give the sense-data equivalent of 'there is a table next door' [Robinson,H on Ayer]
Material things are constructions from actual and possible occurrences of sense-contents [Ayer]
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
We could verify 'a thing can't be in two places at once' by destroying one of the things [Ierubino on Ayer]
12. Knowledge Sources / A. A Priori Knowledge / 5. A Priori Synthetic
Whether geometry can be applied to reality is an empirical question outside of geometry [Ayer]
12. Knowledge Sources / A. A Priori Knowledge / 7. A Priori from Convention
By changing definitions we could make 'a thing can't be in two places at once' a contradiction [Ayer]
12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
To say that a proposition is true a priori is to say that it is a tautology [Ayer]
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
Positivists prefer sense-data to objects, because the vocabulary covers both illusions and perceptions [Ayer, by Robinson,H]
12. Knowledge Sources / B. Perception / 7. Causal Perception
Causal and representative theories of perception are wrong as they refer to unobservables [Ayer]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
The main claim of rationalism is that thought is an independent source of knowledge [Ayer]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
Empiricism lacked a decent account of the a priori, until Ayer said it was entirely analytic [O'Grady on Ayer]
All propositions (especially 'metaphysics') must begin with the senses [Ayer]
My empiricism logically distinguishes analytic and synthetic propositions, and metaphysical verbiage [Ayer]
12. Knowledge Sources / D. Empiricism / 4. Pro-Empiricism
It is further sense-experience which informs us of the mistakes that arise out of sense-experience [Ayer]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
Empiricism, it is said, cannot account for our knowledge of necessary truths [Ayer]
14. Science / C. Induction / 2. Aims of Induction
The induction problem is to prove generalisations about the future based on the past [Ayer]
14. Science / C. Induction / 3. Limits of Induction
We can't use the uniformity of nature to prove induction, as that would be circular [Ayer]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / b. Scepticism of other minds
Other minds are 'metaphysical' objects, because I can never observe their experiences [Ayer]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
A conscious object is by definition one that behaves in a certain way, so behaviour proves consciousness [Ayer]
16. Persons / B. Nature of the Self / 5. Self as Associations
If the self is meaningful, it must be constructed from sense-experiences [Ayer]
16. Persons / B. Nature of the Self / 7. Self and Body / a. Self needs body
Two experiences belong to one self if their contents belong with one body [Ayer]
Empiricists can define personal identity as bodily identity, which consists of sense-contents [Ayer]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
The supposed 'gulf' between mind and matter is based on the senseless concept of 'substances' [Ayer]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
A sentence is factually significant to someone if they know how to verify its proposition [Ayer]
Factual propositions imply (in conjunction with a few other premises) possible experiences [Ayer]
Tautologies and empirical hypotheses form the entire class of significant propositions [Ayer]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
Moral intuition is worthless if there is no criterion to decide between intuitions [Ayer]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
Ayer defends the emotivist version of expressivism [Ayer, by Smith,M]
To say an act is wrong makes no further statement about it, but merely expresses disapproval [Ayer]
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 / A. Divine Nature / 4. Divine Contradictions
A person with non-empirical attributes is unintelligible. [Ayer]
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]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
When we ascribe an attribute to a thing, we covertly assert that it exists [Ayer]
28. God / C. Attitudes to God / 5. Atheism
If theism is non-sensical, then so is atheism. [Ayer]
29. Religion / D. Religious Issues / 1. Religious Commitment / c. Religious Verification
The 'truths' expressed by theists are not literally significant [Ayer]