Combining Texts

All the ideas for 'Parmenides', 'Grundgesetze der Arithmetik 2 (Basic Laws)' and 'A Conversation: what is it? What is it for?'

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


60 ideas

1. Philosophy / C. History of Philosophy / 1. History of Philosophy
The history of philosophy is an agent of power: how can you think if you haven't read the great names? [Deleuze]
     Full Idea: The history of philosophy has always been the agent of power in philosophy, and even in thought. It has played the oppressor's role: how can you think without having read Plato, Descartes, Kant and Heidegger.
     From: Gilles Deleuze (A Conversation: what is it? What is it for? [1977], I)
     A reaction: I find it hard to relate to this French 1960s obsession with everybody being oppressed in every conceivable way, so that 'liberation' is the only value that matters. If you ask why liberty is needed, you seem to have missed the point.
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
Thought should be thrown like a stone from a war-machine [Deleuze]
     Full Idea: Thought should be thrown like a stone by a war-machine. …Isn't this what Nietzsche does with an aphorism?
     From: Gilles Deleuze (A Conversation: what is it? What is it for? [1977], II)
     A reaction: It sounds as if philosophy should consist of nothing but aphorisms.
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
Philosophy aims to become the official language, supporting orthodoxy and the state [Deleuze]
     Full Idea: Philosophy is shot through with the project of becoming the official language of a Pure State. The exercise of thought thus conforms to the goals of the real State, to the dominant meanings and to the requirements of the established order.
     From: Gilles Deleuze (A Conversation: what is it? What is it for? [1977], I)
     A reaction: [He cites Nietzsche's 'Schopenhauer as Educator' as the source of this] Is Karl Marx included in this generalisation, or Diogenes of Sinope? Is conservative philosophy thereby invalidated?
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
When I meet objections I just move on; they never contribute anything [Deleuze]
     Full Idea: Not reflection, and objections are even worse. Every time someone puts an objection to me, I want to say: 'OK, OK, let's get on to something else'. Objections have never contributed anything.
     From: Gilles Deleuze (A Conversation: what is it? What is it for? [1977], I)
     A reaction: I know it is heresy in analytic philosophy, but I love this! In analytic seminars you can barely complete your first sentence before someone interrupts. It's like road range - the philosophical mind state is always poised to attack, attack.
1. Philosophy / H. Continental Philosophy / 1. Continental Philosophy
We must create new words, and treat them as normal, and as if designating real things. [Deleuze]
     Full Idea: Let us create extraordinary words, on condition that they be put to the most ordinary use and that the entity they designate be made to exist in the same way as the most common object.
     From: Gilles Deleuze (A Conversation: what is it? What is it for? [1977], I)
     A reaction: This sounds like the attitude of someone creating a computer game. A language game! The idea is to create concepts with which to 'palpitate' our conceptual scheme, in order to reveal it, and thus put it within our power.
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]
     Full Idea: Doubtful questions should not be discussed in terms of visible objects or in relation to them, but only with reference to ideas conceived by the intellect.
     From: Plato (Parmenides [c.364 BCE], 135e)
2. Reason / B. Laws of Thought / 5. Opposites
Opposites are as unlike as possible [Plato]
     Full Idea: Opposites are as unlike as possible.
     From: Plato (Parmenides [c.364 BCE], 159a)
2. Reason / C. Styles of Reason / 1. Dialectic
Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic [Hegel on Plato]
     Full Idea: Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic.
     From: comment on Plato (Parmenides [c.364 BCE]) by Georg W.F.Hegel - Phenomenology of Spirit Pref 71
     A reaction: It is a long way from the analytic tradition of philosophy to be singling out a classic text for its 'artistic' achievement. Eventually we may even look back on, say, Kripke's 'Naming and Necessity' and see it in that light.
Don't assess ideas for truth or justice; look for another idea, and establish a relationship with it [Deleuze]
     Full Idea: You should not try to find whether an idea is just or correct. You should look for a completely different idea, elsewhere, in another area, so that something passes between the two which is neither in one nor the other.
     From: Gilles Deleuze (A Conversation: what is it? What is it for? [1977], I)
     A reaction: Neither relativism nor dialectic. Sounds like just having fun with ideas, but a commentator tells me it is a strategy for liberating our thought, following an agenda created by Nietzsche.
Dualisms can be undone from within, by tracing connections, and drawing them to a new path [Deleuze]
     Full Idea: It is always possible to undo dualisms from the inside, by tracing the line of flight which passes between the two terms or the two sets …and which draws both into a non-parallel evolution. At least this does not belong to the dialectic.
     From: Gilles Deleuze (A Conversation: what is it? What is it for? [1977], II)
     A reaction: Deleuze disliked Hegel's version of the dialectic. Not clear what he means here, but he is evidently groping for an alternative account of the reasoning process, which is interesting. Deleuze hates rigid dualisms.
2. Reason / D. Definition / 2. Aims of Definition
Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C]
     Full Idea: Frege later became fastidious about definitions, and demanded that they must provide for every possible case, and that no function is properly determined unless its value is fixed for every conceivable object as argument.
     From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Crispin Wright - Frege's Concept of Numbers as Objects 3.xiv
     A reaction: Presumably definitions come in degrees of completeness, but it seems harsh to describe a desire for the perfect definition as 'fastidious', especially if we are talking about mathematics, rather than defining 'happiness'.
2. Reason / D. Definition / 7. Contextual Definition
We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege]
     Full Idea: Given the reference (bedeutung) of an expression and a part of it, obviously the reference of the remaining part is not always determined. So we may not define a symbol or word by defining an expression in which it occurs, whose remaining parts are known
     From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §66)
     A reaction: Dummett cites this as Frege's rejection of contextual definitions, which he had employed in the Grundlagen. I take it not so much that they are wrong, as that Frege decided to set the bar a bit higher.
2. Reason / D. Definition / 11. Ostensive Definition
Only what is logically complex can be defined; what is simple must be pointed to [Frege]
     Full Idea: Only what is logically complex can be defined; what is simple can only be pointed to.
     From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §180), quoted by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.137
     A reaction: Frege presumably has in mind his treasured abstract objects, such as cardinal numbers. It is hard to see how you could 'point to' anything in the phenomenal world that had atomic simplicity. Hodes calls this a 'desperate Kantian move'.
5. Theory of Logic / L. Paradox / 2. Aporiai
Before we seek solutions, it is important to invent problems [Deleuze]
     Full Idea: The art of constructing a problem is very important: you invent a problem, a problem-position, before finding a solution.
     From: Gilles Deleuze (A Conversation: what is it? What is it for? [1977], I)
     A reaction: I get the impression that Deleuze prefers problems to solutions, so the activity of exploring the problem is all that really matters. Sceptics accuse philosophers of inventing pseudo-problems. We must first know why 'problematising' is good.
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]
     Full Idea: Plato (in 'Parmenides') shows that the theory that 'Eide' are substances, and Kant that space and time are substances, and Bradley that relations are substances, all lead to aninomies.
     From: report of Plato (Parmenides [c.364 BCE]) by Gilbert Ryle - Are there propositions? 'Objections'
Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato]
     Full Idea: Plato's 'Parmenides' is perhaps the best collection of antinomies ever made.
     From: comment on Plato (Parmenides [c.364 BCE]) by Bertrand Russell - The Principles of Mathematics §337
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
Cardinals say how many, and reals give measurements compared to a unit quantity [Frege]
     Full Idea: The cardinals and the reals are completely disjoint domains. The cardinal numbers answer the question 'How many objects of a given kind are there?', but the real numbers are for measurement, saying how large a quantity is compared to a unit quantity.
     From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §157), quoted by Michael Dummett - Frege philosophy of mathematics Ch.19
     A reaction: We might say that cardinals are digital and reals are analogue. Frege is unusual in totally separating them. They map onto one another, after all. Cardinals look like special cases of reals. Reals are dreams about the gaps between cardinals.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers are ratios of quantities [Frege, by Dummett]
     Full Idea: Frege fixed on construing real numbers as ratios of quantities (in agreement with Newton).
     From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Michael Dummett - Frege philosophy of mathematics Ch.20
     A reaction: If 3/4 is the same real number as 6/8, which is the correct ratio? Why doesn't the square root of 9/16 also express it? Why should irrationals be so utterly different from rationals? In what sense are they both 'numbers'?
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
A number is a class of classes of the same cardinality [Frege, by Dummett]
     Full Idea: For Frege, in 'Grundgesetze', a number is a class of classes of the same cardinality.
     From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14
Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege]
     Full Idea: The inconsistency of Grundgesetze was only a minor flaw. Its fundamental flaw was its inability to account for the way in which the senses of number terms are determined. It leaves the reference-magnetic nature of the standard numberer a mystery.
     From: comment on Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.139
     A reaction: A point also made by Hofweber. As a logician, Frege was only concerned with the inferential role of number terms, and he felt he had captured their logical form, but it is when you come to look at numbers in natural language that he seem in trouble.
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]
     Full Idea: If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it.
     From: Plato (Parmenides [c.364 BCE], 144a)
     A reaction: This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed.
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett]
     Full Idea: Frege's three main objections to radical formalism are that it cannot account for the application of mathematics, that it confuses a formal theory with its metatheory, and it cannot explain an infinite sequence.
     From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §86-137) by Michael Dummett - Frege philosophy of mathematics
     A reaction: The application is because we don't design maths randomly, but to be useful. The third objection might be dealt with by potential infinities (from formal rules). The second objection sounds promising.
Only applicability raises arithmetic from a game to a science [Frege]
     Full Idea: It is applicability alone which elevates arithmetic from a game to the rank of a science.
     From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §91), quoted by Stewart Shapiro - Thinking About Mathematics 6.1.2
     A reaction: This is the basic objection to Formalism. It invites the question of why it is applicable, which platonists like Frege don't seem to answer (though Plato himself has reality modelled on the Forms). This is why I like structuralism.
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]
     Full Idea: The one was and is and will be and was becoming and is becoming and will become.
     From: Plato (Parmenides [c.364 BCE], 155d)
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]
     Full Idea: The Platonic Parmenides is more exact [than Parmenides himself]; the distinction is made between the Primal One, a strictly pure Unity, and a secondary One which is a One-Many, and a third which is a One-and-Many.
     From: report of Plato (Parmenides [c.364 BCE]) by Plotinus - The Enneads 5.1.08
     A reaction: Plotinus approves of this three-part theory. Parmenides has the problem that the highest Being contains no movement. By placing the One outside Being you can give it powers which an existent thing cannot have. Cf the concept of God.
7. Existence / A. Nature of Existence / 3. Being / i. Deflating being
Before Being there is politics [Deleuze]
     Full Idea: Before Being there is politics.
     From: Gilles Deleuze (A Conversation: what is it? What is it for? [1977], I)
     A reaction: [He says he is quoting Felix Guattari] I can only think that this is a very Marxist view - that politics permeates and dictates everything. This seems to tell me that I am forever controlled by something so deep and vast that I can never understand it.
7. Existence / D. Theories of Reality / 3. Reality
Absolute ideas, such as the Good and the Beautiful, cannot be known by us [Plato]
     Full Idea: The absolute good and the beautiful and all which we conceive to be absolute ideas are unknown to us.
     From: Plato (Parmenides [c.364 BCE], 134c)
8. Modes of Existence / D. Universals / 2. Need for Universals
You must always mean the same thing when you utter the same name [Plato]
     Full Idea: You must always mean the same thing when you utter the same name.
     From: Plato (Parmenides [c.364 BCE], 147d)
If you deny that each thing always stays the same, you destroy the possibility of discussion [Plato]
     Full Idea: If a person denies that the idea of each thing is always the same, he will utterly destroy the power of carrying on discussion.
     From: Plato (Parmenides [c.364 BCE], 135c)
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
If admirable things have Forms, maybe everything else does as well [Plato]
     Full Idea: It is troubling that if admirable things have abstract ideas, then perhaps everything else must have ideas as well.
     From: Plato (Parmenides [c.364 BCE], 130d)
If absolute ideas existed in us, they would cease to be absolute [Plato]
     Full Idea: None of the absolute ideas exists in us, because then it would no longer be absolute.
     From: Plato (Parmenides [c.364 BCE], 133c)
Greatness and smallness must exist, to be opposed to one another, and come into being in things [Plato]
     Full Idea: These two ideas, greatness and smallness, exist, do they not? For if they did not exist, they could not be opposites of one another, and could not come into being in things.
     From: Plato (Parmenides [c.364 BCE], 149e)
Plato moves from Forms to a theory of genera and principles in his later work [Plato, by Frede,M]
     Full Idea: It seems to me that Plato in the later dialogues, beginning with the second half of 'Parmenides', wants to substitute a theory of genera and theory of principles that constitute these genera for the earlier theory of forms.
     From: report of Plato (Parmenides [c.364 BCE]) by Michael Frede - Title, Unity, Authenticity of the 'Categories' V
     A reaction: My theory is that the later Plato came under the influence of the brilliant young Aristotle, and this idea is a symptom of it. The theory of 'principles' sounds like hylomorphism to me.
It would be absurd to think there were abstract Forms for vile things like hair, mud and dirt [Plato]
     Full Idea: Are there abstract ideas for such things as hair, mud and dirt, which are particularly vile and worthless? That would be quite absurd.
     From: Plato (Parmenides [c.364 BCE], 130d)
The concept of a master includes the concept of a slave [Plato]
     Full Idea: Mastership in the abstract is mastership of slavery in the abstract.
     From: Plato (Parmenides [c.364 BCE], 133e)
8. Modes of Existence / D. Universals / 6. Platonic Forms / b. Partaking
Participation is not by means of similarity, so we are looking for some other method of participation [Plato]
     Full Idea: Participation is not by means of likeness, so we must seek some other method of participation.
     From: Plato (Parmenides [c.364 BCE], 133a)
The whole idea of each Form must be found in each thing which participates in it [Plato]
     Full Idea: The whole idea of each form (of beauty, justice etc) must be found in each thing which participates in it.
     From: Plato (Parmenides [c.364 BCE], 131a)
Each idea is in all its participants at once, just as daytime is a unity but in many separate places at once [Plato]
     Full Idea: Just as day is in many places at once, but not separated from itself, so each idea might be in all its participants at once.
     From: Plato (Parmenides [c.364 BCE], 131b)
If things are made alike by participating in something, that thing will be the absolute idea [Plato]
     Full Idea: That by participation in which like things are made like, will be the absolute idea, will it not?
     From: Plato (Parmenides [c.364 BCE], 132e)
If things partake of ideas, this implies either that everything thinks, or that everything actually is thought [Plato]
     Full Idea: If all things partake of ideas, must either everything be made of thoughts and everything thinks, or everything is thought, and so can't think?
     From: Plato (Parmenides [c.364 BCE], 132c)
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]
     Full Idea: If you regard the absolute great and the many great things in the same way, will not another appear beyond, by which all these must appear to be great?
     From: Plato (Parmenides [c.364 BCE], 132a)
Nothing can be like an absolute idea, because a third idea intervenes to make them alike (leading to a regress) [Plato]
     Full Idea: It is impossible for anything to be like an absolute idea, because a third idea will appear to make them alike, and if that is like anything, it will lead to another idea, and so on.
     From: Plato (Parmenides [c.364 BCE], 133a)
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]
     Full Idea: The part would not be the part of many things or all, but of some one character ['ideas'] and of some one thing, which we call a 'whole', since it has come to be one complete [perfected] thing composed [created] of all.
     From: Plato (Parmenides [c.364 BCE], 157d)
     A reaction: A serious shot by Plato at what identity is. Harte quotes it (125) and shows that 'character' is Gk 'idea', and 'composed' will translate as 'created'. 'Form' links this Platonic passage to Aristotle's hylomorphism.
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
The first demand of logic is of a sharp boundary [Frege]
     Full Idea: The first demand of logic is of a sharp boundary.
     From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §160), quoted by Michael Dummett - Frege philosophy of mathematics Ch.22
     A reaction: Nothing I have read about vagueness has made me doubt Frege's view of this, although precisification might allow you to do logic with vague concepts without having to finally settle where the actual boundaries are.
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]
     Full Idea: At the heart of the 'Parmenides' puzzles about composition is the thesis that composition is identity. Considered thus, a whole adds nothing to an ontology that already includes its parts
     From: report of Plato (Parmenides [c.364 BCE]) by Verity Harte - Plato on Parts and Wholes 2.5
     A reaction: There has to be more to a unified identity that mere proximity of the parts. When do parts come together, and when do they actually 'compose' something?
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]
     Full Idea: In 'Parmenides' it is argued that a part cannot be part of a many, but must be part of something one.
     From: report of Plato (Parmenides [c.364 BCE], 157c) by Verity Harte - Plato on Parts and Wholes 3.2
     A reaction: This looks like the right way to go with the term 'part'. We presuppose a unity before we even talk of its parts, so we can't get into contradictions and paradoxes about their relationships.
Anything which has parts must be one thing, and parts are of a one, not of a many [Plato]
     Full Idea: The whole of which the parts are parts must be one thing composed of many; for each of the parts must be part, not of a many, but of a whole.
     From: Plato (Parmenides [c.364 BCE], 157c)
     A reaction: This is a key move of metaphysics, and we should hang on to it. The other way madness lies.
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]
     Full Idea: The One must be composed of parts, both being a whole and having parts. So on both grounds the One would thus be many and not one. But it must be not many, but one. So if the One will be one, it will neither be a whole, nor have parts.
     From: Plato (Parmenides [c.364 BCE], 137c09), quoted by Kathrin Koslicki - The Structure of Objects 5.2
     A reaction: This is the starting point for Plato's metaphysical discussion of objects. It seems to begin a line of thought which is completed by Aristotle, surmising that only an essential structure can bestow identity on a bunch of parts.
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]
     Full Idea: Everything is surely related to everything as follows: either it is the same or different; or, if it is not the same or different, it would be related as part to whole or as whole to part.
     From: Plato (Parmenides [c.364 BCE], 146b)
     A reaction: This strikes me as a really helpful first step in trying to analyse the nature of identity. Two things are either two or (actually) one, or related mereologically.
15. Nature of Minds / A. Nature of Mind / 1. Mind / d. Location of mind
A meeting of man and animal can be deterritorialization (like a wasp with an orchid) [Deleuze]
     Full Idea: The wasp becomes part of the orchid's reproductive apparatus at the same time as the orchid becomes the sexual organ of the wasp. …There are becomings where a man and an animal only meet on the trajectory of a common but asymmetrical deterritorialization.
     From: Gilles Deleuze (A Conversation: what is it? What is it for? [1977], I)
     A reaction: [second bit compressed] The point here is to illustrate 'deterritorialization', a term which Deleuze got from Guattari. It seems to be where the margins of your being become unclear. Recall the externalist, anti-individualist view of mind.
16. Persons / E. Rejecting the Self / 1. Self as Indeterminate
People consist of many undetermined lines, some rigid, some supple, some 'lines of flight' [Deleuze]
     Full Idea: Things, people, are made up of varied lines, and they do not necessarily know which line they are on or where they should make the line which they are tracing pass; there is a whole geography in people, with rigid lines, supple lines, lines of flight etc.
     From: Gilles Deleuze (A Conversation: what is it? What is it for? [1977], I)
     A reaction: An example of Deleuze creating a novel concept, in order to generate a liberating way of seeing our lives. His big focus is on 'lines of flight' (which, I think, are less restrained by local culture than the others).
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
The modern account of real numbers detaches a ratio from its geometrical origins [Frege]
     Full Idea: From geometry we retain the interpretation of a real number as a ratio of quantities or measurement-number; but in more recent times we detach it from geometrical quantities, and from all particular types of quantity.
     From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §159), quoted by Michael Dummett - Frege philosophy of mathematics
     A reaction: Dummett glosses the 'recent' version as by Cantor and Dedekind in 1872. This use of 'detach' seems to me startlingly like the sort of psychological abstractionism which Frege was so desperate to avoid.
18. Thought / E. Abstraction / 8. Abstractionism Critique
If we abstract the difference between two houses, they don't become the same house [Frege]
     Full Idea: If abstracting from the difference between my house and my neighbour's, I were to regard both houses as mine, the defect of the abstraction would soon be made clear. It may, though, be possible to obtain a concept by means of abstraction...
     From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §99)
     A reaction: Note the important concession at the end, which shows Frege could never deny the abstraction process, despite all the modern protests by Geach and Dummett that he totally rejected it.
25. Social Practice / A. Freedoms / 2. Freedom of belief
Some lines (of flight) are becomings which escape the system [Deleuze]
     Full Idea: There are lines which do not amount to the path of a point, which break free from structure - lines of flight, becomings, without future or past, without memory, which resist the binary machine. …The rhizome is all this.
     From: Gilles Deleuze (A Conversation: what is it? What is it for? [1977], II)
     A reaction: The binary machine enforces simplistic either/or choices. I assume the 'lines' are to replace the Self, with something much more indeterminate, active and changing.
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]
     Full Idea: Only a man of very great natural gifts will be able to understand that everything has a class and absolute essence, and an even more wonderful man can teach this.
     From: Plato (Parmenides [c.364 BCE], 135a)
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / d. The unlimited
The unlimited has no shape and is endless [Plato]
     Full Idea: The unlimited partakes neither of the round nor of the straight, because it has no ends nor edges.
     From: Plato (Parmenides [c.364 BCE], 137e)
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / e. The One
Some things do not partake of the One [Plato]
     Full Idea: The others cannot partake of the one in any way; they can neither partake of it nor of the whole.
     From: Plato (Parmenides [c.364 BCE], 159d)
     A reaction: Compare Idea 231
The only movement possible for the One is in space or in alteration [Plato]
     Full Idea: If the One moves it either moves spatially or it is altered, since these are the only motions.
     From: Plato (Parmenides [c.364 BCE], 138b)
Everything partakes of the One in some way [Plato]
     Full Idea: The others are not altogether deprived of the one, for they partake of it in some way.
     From: Plato (Parmenides [c.364 BCE], 157c)
     A reaction: Compare Idea 233.
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]
     Full Idea: There must be knowledge of the one, or else not even the meaning of the words 'if the one does not exist' would be known.
     From: Plato (Parmenides [c.364 BCE], 160d)