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All the ideas for 'Parmenides', 'God and Human Attributes' and 'Nature and Meaning of Numbers'

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60 ideas

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.
2. Reason / D. Definition / 9. Recursive Definition
Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter]
     Full Idea: Dedkind gave a rigorous proof of the principle of definition by recursion, permitting recursive definitions of addition and multiplication, and hence proofs of the familiar arithmetical laws.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 13 'Deriv'
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
An infinite set maps into its own proper subset [Dedekind, by Reck/Price]
     Full Idea: A set is 'Dedekind-infinite' iff there exists a one-to-one function that maps a set into a proper subset of itself.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], §64) by E Reck / M Price - Structures and Structuralism in Phil of Maths n 7
     A reaction: Sounds as if it is only infinite if it is contradictory, or doesn't know how big it is!
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter]
     Full Idea: Dedekind had an interesting proof of the Axiom of Infinity. He held that I have an a priori grasp of the idea of my self, and that every idea I can form the idea of that idea. Hence there are infinitely many objects available to me a priori.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], no. 66) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 12 'Numb'
     A reaction: Who said that Descartes' Cogito was of no use? Frege endorsed this, as long as the ideas are objective and not subjective.
4. Formal Logic / G. Formal Mereology / 1. Mereology
Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter]
     Full Idea: Dedekind plainly had fusions, not collections, in mind when he avoided the empty set and used the same symbol for membership and inclusion - two tell-tale signs of a mereological conception.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], 2-3) by Michael Potter - Set Theory and Its Philosophy 02.1
     A reaction: Potter suggests that mathematicians were torn between mereology and sets, and eventually opted whole-heartedly for sets. Maybe this is only because set theory was axiomatised by Zermelo some years before Lezniewski got to mereology.
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 / a. Numbers
Numbers are free creations of the human mind, to understand differences [Dedekind]
     Full Idea: Numbers are free creations of the human mind; they serve as a means of apprehending more easily and more sharply the difference of things.
     From: Richard Dedekind (Nature and Meaning of Numbers [1888], Pref)
     A reaction: Does this fit real numbers and complex numbers, as well as natural numbers? Frege was concerned by the lack of objectivity in this sort of view. What sort of arithmetic might the Martians have created? Numbers register sameness too.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman]
     Full Idea: It was primarily Dedekind's accomplishment to define the integers, rationals and reals, taking only the system of natural numbers for granted.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by A.George / D.J.Velleman - Philosophies of Mathematics Intro
Order, not quantity, is central to defining numbers [Dedekind, by Monk]
     Full Idea: Dedekind said that the notion of order, rather than that of quantity, is the central notion in the definition of number.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.4
     A reaction: Compare Aristotle's nice question in Idea 646. My intuition is that quantity comes first, because I'm not sure HOW you could count, if you didn't think you were changing the quantity each time. Why does counting go in THAT particular order? Cf. Idea 8661.
Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck]
     Full Idea: Dedekind and Cantor said the cardinals may be defined in terms of the ordinals: The cardinal number of a set S is the least ordinal onto whose predecessors the members of S can be mapped one-one.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 5
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell]
     Full Idea: Dedekind's ordinals are not essentially either ordinals or cardinals, but the members of any progression whatever.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - The Principles of Mathematics §243
     A reaction: This is part of Russell's objection to Dedekind's structuralism. The question is always why these beautiful structures should actually be considered as numbers. I say, unlike Russell, that the connection to counting is crucial.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell]
     Full Idea: Dedekind set up the axiom that the gap in his 'cut' must always be filled …The method of 'postulating' what we want has many advantages; they are the same as the advantages of theft over honest toil. Let us leave them to others.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - Introduction to Mathematical Philosophy VII
     A reaction: This remark of Russell's is famous, and much quoted in other contexts, but I have seen the modern comment that it is grossly unfair to Dedekind.
Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock]
     Full Idea: One view, favoured by Dedekind, is that the cut postulates a real number for each cut in the rationals; it does not identify real numbers with cuts. ....A view favoured by later logicists is simply to identify a real number with a cut.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by David Bostock - Philosophy of Mathematics 4.4
     A reaction: Dedekind is the patriarch of structuralism about mathematics, so he has little interest in the existenc of 'objects'.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
In counting we see the human ability to relate, correspond and represent [Dedekind]
     Full Idea: If we scrutinize closely what is done in counting an aggregate of things, we see the ability of the mind to relate things to things, to let a thing correspond to a thing, or to represent a thing by a thing, without which no thinking is possible.
     From: Richard Dedekind (Nature and Meaning of Numbers [1888], Pref)
     A reaction: I don't suppose it occurred to Dedekind that he was reasserting Hume's observation about the fundamental psychology of thought. Is the origin of our numerical ability of philosophical interest?
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / b. Mark of the infinite
A system S is said to be infinite when it is similar to a proper part of itself [Dedekind]
     Full Idea: A system S is said to be infinite when it is similar to a proper part of itself.
     From: Richard Dedekind (Nature and Meaning of Numbers [1888], V.64)
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD]
     Full Idea: Dedekind's natural numbers: an object is in a set (0 is a number), a function sends the set one-one into itself (numbers have unique successors), the object isn't a value of the function (it isn't a successor), plus induction.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by William D. Hart - The Evolution of Logic 5
     A reaction: Hart notes that since this refers to sets of individuals, it is a second-order account of numbers, what we now call 'Second-Order Peano Arithmetic'.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock]
     Full Idea: Dedekind's idea is that the set of natural numbers has zero as a member, and also has as a member the successor of each of its members, and it is the smallest set satisfying this condition. It is the intersection of all sets satisfying the condition.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by David Bostock - Philosophy of Mathematics 4.4
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind]
     Full Idea: It is Dedekind's categoricity result that convinces most of us that he has articulated our implicit conception of the natural numbers, since it entitles us to speak of 'the' domain (in the singular, up to isomorphism) of natural numbers.
     From: comment on Richard Dedekind (Nature and Meaning of Numbers [1888]) by Ian Rumfitt - The Boundary Stones of Thought 9.1
     A reaction: The main rival is set theory, but that has an endlessly expanding domain. He points out that Dedekind needs second-order logic to achieve categoricity. Rumfitt says one could also add to the 1st-order version that successor is an ancestral relation.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell]
     Full Idea: Dedekind proves mathematical induction, while Peano regards it as an axiom, ...and Peano's method has the advantage of simplicity, and a clearer separation between the particular and the general propositions of arithmetic.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - The Principles of Mathematics §241
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride]
     Full Idea: Dedekind is the philosopher-mathematician with whom the structuralist conception originates.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], §3 n13) by Fraser MacBride - Structuralism Reconsidered
     A reaction: Hellman says the idea grew naturally out of modern mathematics, and cites Hilbert's belief that furniture would do as mathematical objects.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K]
     Full Idea: Dedekindian abstraction says mathematical objects are 'positions' in a model, while Cantorian abstraction says they are the result of abstracting on structurally similar objects.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Kit Fine - Cantorian Abstraction: Recon. and Defence §6
     A reaction: The key debate among structuralists seems to be whether or not they are committed to 'objects'. Fine rejects the 'austere' version, which says that objects have no properties. Either version of structuralism can have abstraction as its basis.
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.
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)
     A reaction: This seems to be rhetorical, rather a precise theory, given that the One is said to be eternal and unchanging. The One is not just what we call 'reality'.
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 / 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)
     A reaction: These seems to thoroughly pre-empt Plato's Theory of Forms a century before he created it. Which shows (as Simone Weil says) that Plato was just part of a long tradition.
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
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)
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)
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)
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)
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.
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]
     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)
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)
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 / A. Existence of Objects / 3. Objects in Thought
A thing is completely determined by all that can be thought concerning it [Dedekind]
     Full Idea: A thing (an object of our thought) is completely determined by all that can be affirmed or thought concerning it.
     From: Richard Dedekind (Nature and Meaning of Numbers [1888], I.1)
     A reaction: How could you justify this as an observation? Why can't there be unthinkable things (even by God)? Presumably Dedekind is offering a stipulative definition, but we may then be confusing epistemology with ontology.
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 / 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.
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett]
     Full Idea: By applying the operation of abstraction to a system of objects isomorphic to the natural numbers, Dedekind believed that we obtained the abstract system of natural numbers, each member having only properties consequent upon its position.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Michael Dummett - The Philosophy of Mathematics
     A reaction: Dummett is scornful of the abstractionism. He cites Benacerraf as a modern non-abstractionist follower of Dedekind's view. There seems to be a suspicion of circularity in it. How many objects will you abstract from to get seven?
We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind]
     Full Idea: If in an infinite system, set in order, we neglect the special character of the elements, simply retaining their distinguishability and their order-relations to one another, then the elements are the natural numbers, created by the human mind.
     From: Richard Dedekind (Nature and Meaning of Numbers [1888], VI.73)
     A reaction: [compressed] This is the classic abstractionist view of the origin of number, but with the added feature that the order is first imposed, so that ordinals remain after the abstraction. This, of course, sounds a bit circular, as well as subjective.
18. Thought / E. Abstraction / 8. Abstractionism Critique
Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait]
     Full Idea: Dedekind's conception is psychologistic only if that is the only way to understand the abstraction that is involved, which it is not.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by William W. Tait - Frege versus Cantor and Dedekind IV
     A reaction: This is a very important suggestion, implying that we can retain some notion of abstractionism, while jettisoning the hated subjective character of private psychologism, which seems to undermine truth and logic.
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)
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]
     Full Idea: Rachels argues 1) If any being is God, he must be a fitting object of worship, 2) No being could be a fitting object of worship, since worship requires the abandonment of one's role as an autonomous moral agent, so 3) There cannot be a being who is God.
     From: report of James Rachels (God and Human Attributes [1971], 7 p.334) by Brian Davies - Introduction to the Philosophy of Religion 9 'd morality'
     A reaction: Presumably Lionel Messi can be a fitting object of worship without being God. Since the problem is with being worshipful, rather than with being God, should I infer that Messi doesn't exist?