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All the ideas for 'Mahaprajnaparamitashastra', 'Foundations without Foundationalism' and 'The Republic'

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141 ideas

1. Philosophy / A. Wisdom / 2. Wise People
Philosophers become as divine and orderly as possible, by studying divinity and order [Plato]
     Full Idea: Because a philosopher's links are with a realm which is divine and orderly, he becomes as divine and orderly as is humanly possible.
     From: Plato (The Republic [c.374 BCE], 500d)
     A reaction: Can you be too orderly? Without order nothing of any interest (to gods or men) could ever happen.
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
The winds of the discussion should decide its destination [Plato]
     Full Idea: We must let our destination be decided by the winds of the discussion.
     From: Plato (The Republic [c.374 BCE], 394d)
     A reaction: Always loved that one. Had it on the wall of my teaching room. I take it that the aim is to follow reason, rather than the powerful rhetoric of some member of the group. The spirit of philosophy is to avoid prejudgement of your enquiry.
1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
It would be absurd to be precise about the small things, but only vague about the big things [Plato]
     Full Idea: It would be absurd to devote all our energies to securing the greatest possible precision and clarity in matters of little consequence, and not to demand the highest precision in the most important things of all.
     From: Plato (The Republic [c.374 BCE], 504e)
     A reaction: I offer this to modern analytic philosophers, who often strike me as having this priority the wrong way round. Their defence, of course, is that the important things depend on the things of little consequence - but they can lose the plot with big things.
2. Reason / C. Styles of Reason / 1. Dialectic
Dialectic is the only method of inquiry which uproots the things which it takes for granted [Plato]
     Full Idea: Dialectic is the only field of inquiry whose quest for certainty causes it to uproot the things it takes for granted in the course of its journey.
     From: Plato (The Republic [c.374 BCE], 533c)
The ability to take an overview is the distinguishing mark of a dialectician [Plato]
     Full Idea: The ability to take an overview is the distinguishing mark of a dialectician.
     From: Plato (The Republic [c.374 BCE], 537c)
For Plato, rationality is a vision of and love of a cosmic rational order [Plato, by Taylor,C]
     Full Idea: In Plato's theory, to be rational is to have a vision of rational order, and to love this order.
     From: report of Plato (The Republic [c.374 BCE], 537d) by Charles Taylor - Sources of the Self §4.1
     A reaction: There may be a worrying elitism in this, but it helps to pinpoint the sense in which 'all philosophers are Platonists'.
2. Reason / C. Styles of Reason / 2. Elenchus
You must never go against what you actually believe [Plato]
     Full Idea: You must never go against what you actually believe.
     From: Plato (The Republic [c.374 BCE], 350e)
2. Reason / C. Styles of Reason / 3. Eristic
People often merely practice eristic instead of dialectic, because they don't analyse the subject-matter [Plato]
     Full Idea: People often think they are practising dialectic when they are practising eristic; this is because of their inability to conduct the enquiry by dividing the subject-matter into its various aspects.
     From: Plato (The Republic [c.374 BCE], 454a)
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
Satisfaction is 'truth in a model', which is a model of 'truth' [Shapiro]
     Full Idea: In a sense, satisfaction is the notion of 'truth in a model', and (as Hodes 1984 elegantly puts it) 'truth in a model' is a model of 'truth'.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.1)
     A reaction: So we can say that Tarski doesn't offer a definition of truth itself, but replaces it with a 'model' of truth.
4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
Aristotelian logic is complete [Shapiro]
     Full Idea: Aristotelian logic is complete.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 2.5)
     A reaction: [He cites Corcoran 1972]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
In mathematics certain things have to be accepted without further explanation [Plato]
     Full Idea: The practitioners of maths take certain things as basic, and feel no further need to explain them.
     From: Plato (The Republic [c.374 BCE], 510c)
4. Formal Logic / F. Set Theory ST / 3. Types of Set / a. Types of set
A set is 'transitive' if contains every member of each of its members [Shapiro]
     Full Idea: If, for every b∈d, a∈b entails that a∈d, the d is said to be 'transitive'. In other words, d is transitive if it contains every member of each of its members.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.2)
     A reaction: The alternative would be that the members of the set are subsets, but the members of those subsets are not themselves members of the higher-level set.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
Choice is essential for proving downward Löwenheim-Skolem [Shapiro]
     Full Idea: The axiom of choice is essential for proving the downward Löwenheim-Skolem Theorem.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.1)
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
Are sets part of logic, or part of mathematics? [Shapiro]
     Full Idea: Is there a notion of set in the jurisdiction of logic, or does it belong to mathematics proper?
     From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref)
     A reaction: It immediately strikes me that they might be neither. I don't see that relations between well-defined groups of things must involve number, and I don't see that mapping the relations must intrinsically involve logical consequence or inference.
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
It is central to the iterative conception that membership is well-founded, with no infinite descending chains [Shapiro]
     Full Idea: In set theory it is central to the iterative conception that the membership relation is well-founded, ...which means there are no infinite descending chains from any relation.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 5.1.4)
Russell's paradox shows that there are classes which are not iterative sets [Shapiro]
     Full Idea: The argument behind Russell's paradox shows that in set theory there are logical sets (i.e. classes) that are not iterative sets.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.3)
     A reaction: In his preface, Shapiro expresses doubts about the idea of a 'logical set'. Hence the theorists like the iterative hierarchy because it is well-founded and under control, not because it is comprehensive in scope. See all of pp.19-20.
Iterative sets are not Boolean; the complement of an iterative set is not an iterative sets [Shapiro]
     Full Idea: Iterative sets do not exhibit a Boolean structure, because the complement of an iterative set is not itself an iterative set.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.1)
4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
'Well-ordering' of a set is an irreflexive, transitive, and binary relation with a least element [Shapiro]
     Full Idea: A 'well-ordering' of a set X is an irreflexive, transitive, and binary relation on X in which every non-empty subset of X has a least element.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 5.1.3)
     A reaction: So there is a beginning, an ongoing sequence, and no retracing of steps.
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
There is no 'correct' logic for natural languages [Shapiro]
     Full Idea: There is no question of finding the 'correct' or 'true' logic underlying a part of natural language.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref)
     A reaction: One needs the context of Shapiro's defence of second-order logic to see his reasons for this. Call me romantic, but I retain faith that there is one true logic. The Kennedy Assassination problem - can't see the truth because drowning in evidence.
Logic is the ideal for learning new propositions on the basis of others [Shapiro]
     Full Idea: A logic can be seen as the ideal of what may be called 'relative justification', the process of coming to know some propositions on the basis of others.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 2.3.1)
     A reaction: This seems to be the modern idea of logic, as opposed to identification of a set of 'logical truths' from which eternal necessities (such as mathematics) can be derived. 'Know' implies that they are true - which conclusions may not be.
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
Bernays (1918) formulated and proved the completeness of propositional logic [Shapiro]
     Full Idea: Bernays (1918) formulated and proved the completeness of propositional logic, the first precise solution as part of the Hilbert programme.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.2.1)
Can one develop set theory first, then derive numbers, or are numbers more basic? [Shapiro]
     Full Idea: In 1910 Weyl observed that set theory seemed to presuppose natural numbers, and he regarded numbers as more fundamental than sets, as did Fraenkel. Dedekind had developed set theory independently, and used it to formulate numbers.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.2.2)
Skolem and Gödel championed first-order, and Zermelo, Hilbert, and Bernays championed higher-order [Shapiro]
     Full Idea: Skolem and Gödel were the main proponents of first-order languages. The higher-order language 'opposition' was championed by Zermelo, Hilbert, and Bernays.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.2)
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
First-order logic was an afterthought in the development of modern logic [Shapiro]
     Full Idea: Almost all the systems developed in the first part of the twentieth century are higher-order; first-order logic was an afterthought.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.1)
The 'triumph' of first-order logic may be related to logicism and the Hilbert programme, which failed [Shapiro]
     Full Idea: The 'triumph' of first-order logic may be related to the remnants of failed foundationalist programmes early this century - logicism and the Hilbert programme.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref)
     A reaction: Being complete must also be one of its attractions, and Quine seems to like it because of its minimal ontological commitment.
Maybe compactness, semantic effectiveness, and the Löwenheim-Skolem properties are desirable [Shapiro]
     Full Idea: Tharp (1975) suggested that compactness, semantic effectiveness, and the Löwenheim-Skolem properties are consequences of features one would want a logic to have.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 6.5)
     A reaction: I like this proposal, though Shapiro is strongly against. We keep extending our logic so that we can prove new things, but why should we assume that we can prove everything? That's just what Gödel suggests that we should give up on.
The notion of finitude is actually built into first-order languages [Shapiro]
     Full Idea: The notion of finitude is explicitly 'built in' to the systems of first-order languages in one way or another.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.1)
     A reaction: Personally I am inclined to think that they are none the worse for that. No one had even thought of all these lovely infinities before 1870, and now we are supposed to change our logic (our actual logic!) to accommodate them. Cf quantum logic.
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Second-order logic is better than set theory, since it only adds relations and operations, and nothing else [Shapiro, by Lavine]
     Full Idea: Shapiro preferred second-order logic to set theory because second-order logic refers only to the relations and operations in a domain, and not to the other things that set-theory brings with it - other domains, higher-order relations, and so forth.
     From: report of Stewart Shapiro (Foundations without Foundationalism [1991]) by Shaughan Lavine - Understanding the Infinite VII.4
Broad standard semantics, or Henkin semantics with a subclass, or many-sorted first-order semantics? [Shapiro]
     Full Idea: Three systems of semantics for second-order languages: 'standard semantics' (variables cover all relations and functions), 'Henkin semantics' (relations and functions are a subclass) and 'first-order semantics' (many-sorted domains for variable-types).
     From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref)
     A reaction: [my summary]
Henkin semantics has separate variables ranging over the relations and over the functions [Shapiro]
     Full Idea: In 'Henkin' semantics, in a given model the relation variables range over a fixed collection of relations D on the domain, and the function variables range over a collection of functions F on the domain.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 3.3)
In standard semantics for second-order logic, a single domain fixes the ranges for the variables [Shapiro]
     Full Idea: In the standard semantics of second-order logic, by fixing a domain one thereby fixes the range of both the first-order variables and the second-order variables. There is no further 'interpreting' to be done.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 3.3)
     A reaction: This contrasts with 'Henkin' semantics (Idea 13650), or first-order semantics, which involve more than one domain of quantification.
Completeness, Compactness and Löwenheim-Skolem fail in second-order standard semantics [Shapiro]
     Full Idea: The counterparts of Completeness, Compactness and the Löwenheim-Skolem theorems all fail for second-order languages with standard semantics, but hold for Henkin or first-order semantics. Hence such logics are much like first-order logic.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.1)
     A reaction: Shapiro votes for the standard semantics, because he wants the greater expressive power, especially for the characterization of infinite structures.
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
Semantic consequence is ineffective in second-order logic [Shapiro]
     Full Idea: It follows from Gödel's incompleteness theorem that the semantic consequence relation of second-order logic is not effective. For example, the set of logical truths of any second-order logic is not recursively enumerable. It is not even arithmetic.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref)
     A reaction: I don't fully understand this, but it sounds rather major, and a good reason to avoid second-order logic (despite Shapiro's proselytising). See Peter Smith on 'effectively enumerable'.
If a logic is incomplete, its semantic consequence relation is not effective [Shapiro]
     Full Idea: Second-order logic is inherently incomplete, so its semantic consequence relation is not effective.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.2.1)
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
Finding the logical form of a sentence is difficult, and there are no criteria of correctness [Shapiro]
     Full Idea: It is sometimes difficult to find a formula that is a suitable counterpart of a particular sentence of natural language, and there is no acclaimed criterion for what counts as a good, or even acceptable, 'translation'.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.1)
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
We might reduce ontology by using truth of sentences and terms, instead of using objects satisfying models [Shapiro]
     Full Idea: The main role of substitutional semantics is to reduce ontology. As an alternative to model-theoretic semantics for formal languages, the idea is to replace the 'satisfaction' relation of formulas (by objects) with the 'truth' of sentences (using terms).
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.1.4)
     A reaction: I find this very appealing, and Ruth Barcan Marcus is the person to look at. My intuition is that logic should have no ontology at all, as it is just about how inference works, not about how things are. Shapiro offers a compromise.
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
'Satisfaction' is a function from models, assignments, and formulas to {true,false} [Shapiro]
     Full Idea: The 'satisfaction' relation may be thought of as a function from models, assignments, and formulas to the truth values {true,false}.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.1)
     A reaction: This at least makes clear that satisfaction is not the same as truth. Now you have to understand how Tarski can define truth in terms of satisfaction.
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Semantics for models uses set-theory [Shapiro]
     Full Idea: Typically, model-theoretic semantics is formulated in set theory.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 2.5.1)
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
An axiomatization is 'categorical' if its models are isomorphic, so there is really only one interpretation [Shapiro]
     Full Idea: An axiomatization is 'categorical' if all its models are isomorphic to one another; ..hence it has 'essentially only one' interpretation [Veblen 1904].
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.2.1)
Categoricity can't be reached in a first-order language [Shapiro]
     Full Idea: Categoricity cannot be attained in a first-order language.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.3)
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
The Löwenheim-Skolem theorems show an explosion of infinite models, so 1st-order is useless for infinity [Shapiro]
     Full Idea: The Löwenheim-Skolem theorems mean that no first-order theory with an infinite model is categorical. If Γ has an infinite model, then it has a model of every infinite cardinality. So first-order languages cannot characterize infinite structures.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.1)
     A reaction: So much of the debate about different logics hinges on characterizing 'infinite structures' - whatever they are! Shapiro is a leading structuralist in mathematics, so he wants second-order logic to help with his project.
Substitutional semantics only has countably many terms, so Upward Löwenheim-Skolem trivially fails [Shapiro]
     Full Idea: The Upward Löwenheim-Skolem theorem fails (trivially) with substitutional semantics. If there are only countably many terms of the language, then there are no uncountable substitution models.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.1.4)
     A reaction: Better and better. See Idea 13674. Why postulate more objects than you can possibly name? I'm even suspicious of all real numbers, because you can't properly define them in finite terms. Shapiro objects that the uncountable can't be characterized.
Downward Löwenheim-Skolem: each satisfiable countable set always has countable models [Shapiro]
     Full Idea: A language has the Downward Löwenheim-Skolem property if each satisfiable countable set of sentences has a model whose domain is at most countable.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 6.5)
     A reaction: This means you can't employ an infinite model to represent a fact about a countable set.
Upward Löwenheim-Skolem: each infinite model has infinite models of all sizes [Shapiro]
     Full Idea: A language has the Upward Löwenheim-Skolem property if for each set of sentences whose model has an infinite domain, then it has a model at least as big as each infinite cardinal.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 6.5)
     A reaction: This means you can't have a countable model to represent a fact about infinite sets.
5. Theory of Logic / K. Features of Logics / 3. Soundness
'Weakly sound' if every theorem is a logical truth; 'sound' if every deduction is a semantic consequence [Shapiro]
     Full Idea: A logic is 'weakly sound' if every theorem is a logical truth, and 'strongly sound', or simply 'sound', if every deduction from Γ is a semantic consequence of Γ. Soundness indicates that the deductive system is faithful to the semantics.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.1)
     A reaction: Similarly, 'weakly complete' is when every logical truth is a theorem.
5. Theory of Logic / K. Features of Logics / 4. Completeness
We can live well without completeness in logic [Shapiro]
     Full Idea: We can live without completeness in logic, and live well.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref)
     A reaction: This is the kind of heady suggestion that American philosophers love to make. Sounds OK to me, though. Our ability to draw good inferences should be expected to outrun our ability to actually prove them. Completeness is for wimps.
5. Theory of Logic / K. Features of Logics / 6. Compactness
Non-compactness is a strength of second-order logic, enabling characterisation of infinite structures [Shapiro]
     Full Idea: It is sometimes said that non-compactness is a defect of second-order logic, but it is a consequence of a crucial strength - its ability to give categorical characterisations of infinite structures.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref)
     A reaction: The dispute between fans of first- and second-order may hinge on their attitude to the infinite. I note that Skolem, who was not keen on the infinite, stuck to first-order. Should we launch a new Skolemite Crusade?
Compactness is derived from soundness and completeness [Shapiro]
     Full Idea: Compactness is a corollary of soundness and completeness. If Γ is not satisfiable, then, by completeness, Γ is not consistent. But the deductions contain only finite premises. So a finite subset shows the inconsistency.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.1)
     A reaction: [this is abbreviated, but a proof of compactness] Since all worthwhile logics are sound, this effectively means that completeness entails compactness.
5. Theory of Logic / K. Features of Logics / 9. Expressibility
A language is 'semantically effective' if its logical truths are recursively enumerable [Shapiro]
     Full Idea: A logical language is 'semantically effective' if the collection of logically true sentences is a recursively enumerable set of strings.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 6.5)
6. Mathematics / A. Nature of Mathematics / 2. Geometry
Geometry can lead the mind upwards to truth and philosophy [Plato]
     Full Idea: Geometry can attract the mind towards truth. It can produce philosophical thought, in the sense that it can reverse the midguided downwards tendencies we currently have.
     From: Plato (The Republic [c.374 BCE], 527b)
     A reaction: Hence the Academy gate bore the inscription "Let no one enter here who is ignorant of geometry". He's not necessarily wrong. Something in early education must straighten out some of the kinks in the messy human mind.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
Complex numbers can be defined as reals, which are defined as rationals, then integers, then naturals [Shapiro]
     Full Idea: 'Definitions' of integers as pairs of naturals, rationals as pairs of integers, reals as Cauchy sequences of rationals, and complex numbers as pairs of reals are reductive foundations of various fields.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 2.1)
     A reaction: On p.30 (bottom) Shapiro objects that in the process of reduction the numbers acquire properties they didn't have before.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
Only higher-order languages can specify that 0,1,2,... are all the natural numbers that there are [Shapiro]
     Full Idea: The main problem of characterizing the natural numbers is to state, somehow, that 0,1,2,.... are all the numbers that there are. We have seen that this can be accomplished with a higher-order language, but not in a first-order language.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.1.4)
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
Natural numbers are the finite ordinals, and integers are equivalence classes of pairs of finite ordinals [Shapiro]
     Full Idea: By convention, the natural numbers are the finite ordinals, the integers are certain equivalence classes of pairs of finite ordinals, etc.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.3)
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The 'continuum' is the cardinality of the powerset of a denumerably infinite set [Shapiro]
     Full Idea: The 'continuum' is the cardinality of the powerset of a denumerably infinite set.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 5.1.2)
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
First-order arithmetic can't even represent basic number theory [Shapiro]
     Full Idea: Few theorists consider first-order arithmetic to be an adequate representation of even basic number theory.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 5 n28)
     A reaction: This will be because of Idea 13656. Even 'basic' number theory will include all sorts of vast infinities, and that seems to be where the trouble is.
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Some sets of natural numbers are definable in set-theory but not in arithmetic [Shapiro]
     Full Idea: There are sets of natural numbers definable in set-theory but not in arithmetic.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 5.3.3)
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
We aim for elevated discussion of pure numbers, not attaching them to physical objects [Plato]
     Full Idea: Our discussion of numbers leads the soul forcibly upward and compels it to discuss the numbers themselves, never permitting anyone to propose for discussion numbers attached to visible or tangible bodies.
     From: Plato (The Republic [c.374 BCE], 525d)
     A reaction: This strikes me as very important, because it shows that the platonist view of numbers places little or no importance on counting, inviting the question of whether they could be understood in complete ignorance of the process of counting.
In pure numbers, all ones are equal, with no internal parts [Plato]
     Full Idea: With those numbers that can be grasped only in thought, ..each one is equal to every other, without the least difference and containing no internal parts.
     From: Plato (The Republic [c.374 BCE], 526a)
     A reaction: [Two voices in the conversation are elided] Intriguing and tantalising. Does 13 have internal parts, in the platonist view? If so, is it more than the sum of its parts? Is Plato committed to numbers being built from indistinguishable abstract units/
Geometry is not an activity, but the study of unchanging knowledge [Plato]
     Full Idea: Geometers talk as if they were actually doing something, and the point of their theorems is to have some effect (like 'squaring'). ...But the sole purpose is knowledge, of things which exist forever, not coming into existence and passing away.
     From: Plato (The Republic [c.374 BCE], 527a)
     A reaction: Modern Constructivism defends the view which Plato is attacking. The existence of real infinities can be doubted simply because we have not got enough time to construct them.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
The same thing is both one and an unlimited number at the same time [Plato]
     Full Idea: We see the same thing to be both one and an unlimited number at the same time.
     From: Plato (The Republic [c.374 BCE], 525a)
     A reaction: Frege makes the same point, that a pair of boots is both two and one. The point is at its strongest in opposition to empirical accounts of arithmetic. However, Mill observes that pebbles can be both 5 and 3+2, without contradiction.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Logicism is distinctive in seeking a universal language, and denying that logic is a series of abstractions [Shapiro]
     Full Idea: It is claimed that aiming at a universal language for all contexts, and the thesis that logic does not involve a process of abstraction, separates the logicists from algebraists and mathematicians, and also from modern model theory.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.1)
     A reaction: I am intuitively drawn to the idea that logic is essentially the result of a series of abstractions, so this gives me a further reason not to be a logicist. Shapiro cites Goldfarb 1979 and van Heijenoort 1967. Logicists reduce abstraction to logic.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Mathematics and logic have no border, and logic must involve mathematics and its ontology [Shapiro]
     Full Idea: I extend Quinean holism to logic itself; there is no sharp border between mathematics and logic, especially the logic of mathematics. One cannot expect to do logic without incorporating some mathematics and accepting at least some of its ontology.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref)
     A reaction: I have strong sales resistance to this proposal. Mathematics may have hijacked logic and warped it for its own evil purposes, but if logic is just the study of inferences then it must be more general than to apply specifically to mathematics.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
Some reject formal properties if they are not defined, or defined impredicatively [Shapiro]
     Full Idea: Some authors (Poincaré and Russell, for example) were disposed to reject properties that are not definable, or are definable only impredicatively.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.1)
     A reaction: I take Quine to be the culmination of this line of thought, with his general rejection of 'attributes' in logic and in metaphysics.
7. Existence / A. Nature of Existence / 3. Being / c. Becoming
To become rational, philosophers must rise from becoming into being [Plato]
     Full Idea: Philosophers must rise up out of becoming and grasp being, if they are ever to become rational.
     From: Plato (The Republic [c.374 BCE], 525b)
     A reaction: I am never quite sure what 'being' means in such contexts, and it seems suffused with mysticism. In Plato's case, it is obviously related to what is unchanging, but why would something lack 'being', just because it underwent change?
7. Existence / A. Nature of Existence / 3. Being / f. Primary being
Being depends on the Good, which is not itself being, but superior to being [Plato]
     Full Idea: Not only do the objects of knowledge owe their being known to the good, but their being is also due to it, although the good is not being, but superior to it in rank and power.
     From: Plato (The Republic [c.374 BCE], 509b)
     A reaction: I was surprised to find that in Plotinus the One is not being, because it is the source of being, and thus superior to being. Then a footnote sent me here, and I realise that Plato thought that the Form of the Good is superior to Being.
7. Existence / B. Change in Existence / 1. Nature of Change
The best things (gods, healthy bodies, good souls) are least liable to change [Plato]
     Full Idea: The best things (such as a god, a healthy body, or a good soul) are least liable to alteration or change.
     From: Plato (The Republic [c.374 BCE], 380e)
7. Existence / D. Theories of Reality / 3. Reality
Plato's reality has unchanging Parmenidean forms, and Heraclitean flux [Plato, by Fogelin]
     Full Idea: For Plato, the intelligible world - the world of eternal and unchanging forms - is Parmenidean; the world of appearances - the world of flux we inhabit - is Heraclitean.
     From: report of Plato (The Republic [c.374 BCE]) by Robert Fogelin - Walking the Tightrope of Reason Ch.1
     A reaction: Parmenides said reality is 'One'; Heraclitus said reality is 'flux'. This is a nice summary of Plato's view, and encapsulates two key influences on Plato, though the mathematical reality of Pythagoras should also be mentioned on the 'forms' side.
8. Modes of Existence / B. Properties / 10. Properties as Predicates
Properties are often seen as intensional; equiangular and equilateral are different, despite identity of objects [Shapiro]
     Full Idea: Properties are often taken to be intensional; equiangular and equilateral are thought to be different properties of triangles, even though any triangle is equilateral if and only if it is equiangular.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.3)
     A reaction: Many logicians seem to want to treat properties as sets of objects (red being just the set of red things), but this looks like a desperate desire to say everything in first-order logic, where only objects are available to quantify over.
8. Modes of Existence / D. Universals / 2. Need for Universals
The plurality of beautiful things must belong to a single class, because they have a single particular character [Plato]
     Full Idea: All the things we refer to as pluralities (e.g. beautiful things) we also count as belonging to a single class by virtue of the fact that they have a single particular character.
     From: Plato (The Republic [c.374 BCE], 507b)
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
Plato's Forms are said to have no location in space [Plato, by Aristotle]
     Full Idea: Plato claims that the Forms are not beyond the heavens, because they are not anywhere.
     From: report of Plato (The Republic [c.374 BCE]) by Aristotle - Physics 203a09
     A reaction: This is an important corrective to caricature accounts of Plato's Forms (encouraged, I'm afraid, by 'Phaedrus'), when critics talk about 'Platonic Heaven'. Forms are not part of space-time. I like the view that they are hypothetical truths.
Forms are not universals, as they don't cover every general term [Plato, by Annas]
     Full Idea: Despite a widely misinterpreted passage in the Republic, Plato does not think that there is a Form for every general term; Forms are not what came to be called universals.
     From: report of Plato (The Republic [c.374 BCE]) by Julia Annas - Ancient Philosophy: very short introduction Ch.5
     A reaction: Hm. This is a bit of a blow to someone who has catalogued Platonic Forms under 'Universals'. See also Idea 12042, for what Annas thinks Plato may really have had in mind.
Craftsmen making furniture refer to the form, but no one manufactures the form of furniture [Plato]
     Full Idea: The manufacture of beds and tables involves the craftsman looking to the form and then making the furniture. The form itself is not manufactured by anyone.
     From: Plato (The Republic [c.374 BCE], 596b)
8. Modes of Existence / D. Universals / 6. Platonic Forms / b. Partaking
A Form applies to a set of particular things with the same name [Plato]
     Full Idea: We always postulate a single form for each set of particular things, to which we apply the same name.
     From: Plato (The Republic [c.374 BCE], 596a)
     A reaction: This implies that the Forms have a great deal in common with the things, but also hints at the possibility of the Form being quite different from the particular things.
8. Modes of Existence / D. Universals / 6. Platonic Forms / d. Forms critiques
Plato mistakenly thought forms were totally abstracted away from matter [Bacon on Plato]
     Full Idea: Plato lost the real fruit of his opinion, by considering forms as absolutely abstracted from matter, and not confined and determined by matter.
     From: comment on Plato (The Republic [c.374 BCE]) by Francis Bacon - The Advancement of Learning II.VII.5
     A reaction: This thought is roughly what got me interested in abstraction, on which you will find many ideas in this database. Research into Bacon's thought is hampered by that fact that the logicians have hijacked abstraction in recent philosophy.
Plato's Forms not only do not come from the senses, but they are beyond possibility of sensing [Plato, by Kant]
     Full Idea: In Plato's use of the expression 'idea' we can see that he understood by it something that not only could never be borrowed from the senses, but even goes beyond the concepts of the understanding, since nothing in experience could be congruent to it.
     From: report of Plato (The Republic [c.374 BCE]) by Immanuel Kant - Critique of Pure Reason B370
     A reaction: This is why Kant is not a Platonist - because he thinks the limits of our world are the limits of our capacity for possible experience, and Platonic Forms exceed that limit. Personally I am with Plato. I'll never experience a quark either.
11. Knowledge Aims / A. Knowledge / 1. Knowledge
Knowledge must be of the permanent unchanging nature of things [Plato]
     Full Idea: Those who can see each thing in itself, in its permanent and unvarying nature, we'll say they have knowledge and are not merely entertaining beliefs.
     From: Plato (The Republic [c.374 BCE], 479e)
12. Knowledge Sources / C. Rationalism / 1. Rationalism
If theory and practice conflict, the best part of the mind accepts theory, so the other part is of lower grade [Plato]
     Full Idea: When appearance and measure conflict…it is the best part of the mind which accepts measurements and calculations, and the part which opposes them, therefore, must be a low-grade part of the mind.
     From: Plato (The Republic [c.374 BCE], 603a)
13. Knowledge Criteria / A. Justification Problems / 1. Justification / b. Need for justification
True belief without knowledge is like blind people on the right road [Plato]
     Full Idea: Don't people who have a correct belief but no knowledge strike you as exactly like blind people who happen to be taking the right road?
     From: Plato (The Republic [c.374 BCE], 506c)
     A reaction: Good. I love the style of this. Most philosophical points can be made in one concise sentence, and it is only the industry of journals and academe that forces points to be extended so much.
15. Nature of Minds / A. Nature of Mind / 1. Mind / e. Questions about mind
Is the function of the mind management, authority and planning - or is it one's whole way of life? [Plato]
     Full Idea: Does the mind have a function - say, management, authority and planning? And isn't one's way of life a function of the mind?
     From: Plato (The Republic [c.374 BCE], 353d)
     A reaction: Note that this is Plato, not some Darwinian materialist. This strikes me as the correct starting point - what does a mind appear to be for (with or without the help of Darwin)? Plato's proposals seem good (though we could cut 'authority').
15. Nature of Minds / A. Nature of Mind / 2. Psuche
Psychic conflict is clear if appetite is close to the body and reason fairly separate [Plato, by Modrak]
     Full Idea: Plato makes psychic conflict intelligible by appeal to a conception of the soul such that the soul is closely connected to the body at the level of appetite and relatively separate from the body at the level of reason.
     From: report of Plato (The Republic [c.374 BCE], 339b) by Deborah K.W. Modrak - Classical theories of Mind
     A reaction: I'm not sure about this at the level of biology or ontology, but at the phenomenal level this is obviously right. Hunger makes consciousness feel like a physical event, but doing arithmetic doesn't seem remotely physical.
There is a third element to the mind - spirit - lying between reason and appetite [Plato]
     Full Idea: Is the third element of the mind a form of reason, so that there are only two elements to it, reason and appetite? There must be a third element, if spirit ('thumos') can be shown to be distinct - and you can see it in children when they are born.
     From: Plato (The Republic [c.374 BCE], 441a)
     A reaction: This is Plato's famous tripartite doctrine of the soul, though in other dialogues he says that there is only reason and appetite. The suspicion is that he fixed the soul having three parts, to match the three parts of his republic's social structure.
15. Nature of Minds / A. Nature of Mind / 5. Unity of Mind
The mind has parts, because we have inner conflicts [Plato]
     Full Idea: If someone is thirsty but something is making the mind resist the pull of its thirst, isn't this bound to be a different part of the mind from the thirsty part?
     From: Plato (The Republic [c.374 BCE], 439b)
     A reaction: For Descartes there is one mind pulled by appetite and the 'natural light'. For Hume they don't seem to be 'parts' of anything. For Fodor there is an integrated team of modules. I like Fodor, and good integration is virtue.
The soul seems to have an infinity of parts [Aristotle on Plato]
     Full Idea: There seem in a way to be an infinity of parts of the soul, and not only those that some have given, distinguishing the reasoning, spirited and desiderative parts, or with others the rational and irrational.
     From: comment on Plato (The Republic [c.374 BCE], 439b) by Aristotle - De Anima 432a25
     A reaction: This seems a nice response to Plato's proposal that the psuché has two or three parts. He could have said that the soul was a unity, and has no parts, but the proposal of infinite parts seems much closer to the modern neurological view of the mind.
19. Language / F. Communication / 1. Rhetoric
The 'Republic' is a great work of rhetorical theory [Lawson-Tancred on Plato]
     Full Idea: The 'Republic' is the greatest single achievement of ancient rhetorical theory.
     From: comment on Plato (The Republic [c.374 BCE]) by Hugh Lawson-Tancred - Plato's Republic and Greek Enlightenment Ch.9
     A reaction: A lovely inversion of our normal reading of Plato! Is the real aim of philosophy the making of good speeches? Is the great aim to display the true beauty of the human mind, as the Olympics display the beauty of the body?
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
For Plato and Aristotle there is no will; there is only rational desire for what is seen as good [Plato, by Frede,M]
     Full Idea: Neither Plato nor Aristotle has a notion of the will. …Willing is a form of desire which is specific to reason. If reason perceives something as good, it wills or desires it.
     From: report of Plato (The Republic [c.374 BCE], 577e) by Michael Frede - A Free Will 1
     A reaction: [Frede cites 577e, Aris. 413c8, 1113a15-, 1136b6] How do they explain the apparent decisions of non-rational animals? No modern neuroscientist thinks there is a physical object called a person's 'will'.
20. Action / C. Motives for Action / 2. Acting on Beliefs / a. Acting on beliefs
We avoid evil either through a natural aversion, or because we have acquired knowledge [Plato]
     Full Idea: Unless a man is born with a heaven-sent aversion to wrong-doing, or acquires the knowledge to refrain from it, he will never do right of his own free will.
     From: Plato (The Republic [c.374 BCE], 366c)
     A reaction: This is the territory explored so carefully by Aristotle (after he had read Republic!). It is hard to see what the knowledge could be, other than awareness of consequences.
21. Aesthetics / B. Nature of Art / 8. The Arts / b. Literature
Without the surface decoration, poetry shows only appearances and nothing of what is real [Plato]
     Full Idea: If you strip a poet's works of their musical colorings and take them by themselves, I think you know what they look like. …We say that a maker of an image - an imitator - knows nothing about that which is but only about its appearance.
     From: Plato (The Republic [c.374 BCE], 601a)
     A reaction: Knowing the appearances well is more than most people can manage, and aspirations to know the true reality may be an idle dream. Poets are, I presume, welcome in the Cave.
21. Aesthetics / C. Artistic Issues / 3. Artistic Representation
Representation is two steps removed from the truth [Plato]
     Full Idea: The province of representation is indeed two steps removed from the truth.
     From: Plato (The Republic [c.374 BCE], 602c)
21. Aesthetics / C. Artistic Issues / 6. Value of Art
Artists should be excluded from a law-abiding community, because they destroy the rational mind [Plato]
     Full Idea: We are right to refuse admission to artists in any community which is going to respect convention, because he destroys the rational mind and feeds the irrational - it is like destroying good citizens by giving ruffians power.
     From: Plato (The Republic [c.374 BCE], 605b)
Truth is closely related to proportion [Plato]
     Full Idea: Truth is closely related to proportion.
     From: Plato (The Republic [c.374 BCE], 486d)
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / b. Defining ethics
I suggest that we forget about trying to define goodness itself for the time being [Plato]
     Full Idea: I suggest that we forget about trying to define goodness itself for the time being.
     From: Plato (The Republic [c.374 BCE], 506e)
     A reaction: This was a source of some humour in the ancient world (in the theatre). Goodness is like some distant glow, which can never be approached in order to learn of its source.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / a. Idealistic ethics
The good cannot be expressed in words, but imprints itself upon the soul [Plato, by Celsus]
     Full Idea: Plato points to the truth about the highest good when he says that it cannot be expressed in words, but rather comes from familiarity - like a flash from the blue, imprinting itself upon the soul.
     From: report of Plato (The Republic [c.374 BCE]) by Celsus - On the True Doctrine (Against Christians) VII
     A reaction: It is reasonable to be drawn to something inexpressible, such as an appealing piece of music, but not good philosophy to build a system around something so obscure.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / f. Übermensch
Plato found that he could only enforce rational moral justification by creating an authoritarian society [Williams,B on Plato]
     Full Idea: For Plato, the problem of making the ethical into a force was the problem of making society embody rational justification, and that problem could only have an authoritarian solution.
     From: comment on Plato (The Republic [c.374 BCE]) by Bernard Williams - Ethics and the Limits of Philosophy Ch. 2
     A reaction: Plato's citizens were largely illiterate. We can be more carrot and less stick.
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
Plato measured the degree of reality by the degree of value [Nietzsche on Plato]
     Full Idea: Plato measured the degree of reality by the degree of value.
     From: comment on Plato (The Republic [c.374 BCE], 518d) by Friedrich Nietzsche - The Will to Power (notebooks) §572
     A reaction: A most interesting comment. It epitomises the Nietzschean reading of Plato, in which the will to power leads the sense of value, which in turn creates the metaphysics.
22. Metaethics / B. Value / 2. Values / b. Successful function
A thing's function is what it alone can do, or what it does better than other things [Plato]
     Full Idea: The function of anything is what it alone can do, or what it can do better than anything else.
     From: Plato (The Republic [c.374 BCE], 353a)
     A reaction: I take this concept to be the lynchpin of Aristotle's virtue ethics. Note that it arises earlier, in Plato. Perhaps he should say what it is 'meant to do'.
If something has a function then it has a state of being good [Plato]
     Full Idea: Anything which has been endowed with a function also has a state of being good.
     From: Plato (The Republic [c.374 BCE], 353b)
     A reaction: 'ought' from 'is'?
22. Metaethics / B. Value / 2. Values / d. Health
Goodness is mental health, badness is mental sickness [Plato]
     Full Idea: Goodness is a state of mental health, bloom and vitality; badness is a state of mental sickness, deformity and infirmity.
     From: Plato (The Republic [c.374 BCE], 444e)
     A reaction: A nice statement of the closeness of goodness to health for the Greeks. The key point is that health is a deeply natural concept, which bridges the fact-value divide.
22. Metaethics / B. Value / 2. Values / i. Self-interest
Clever criminals do well at first, but not in the long run [Plato]
     Full Idea: Clever criminals are exactly like those runners who do well on the way up the track, and then flag on the way back.
     From: Plato (The Republic [c.374 BCE], 613b)
     A reaction: Presumably there is some concept of natural justice lurking behind this comparison. Apart from the money, though, it is hard to imagine any professional criminal leading a flourishing life.
If we were invisible, would the just man become like the unjust? [Plato]
     Full Idea: Glaucon: with a ring of invisibility 'the just man would differ in no way from the unjust'.
     From: Plato (The Republic [c.374 BCE], 360c)
     A reaction: I think a highly altruistic person would behave well with the ring, but I'm sure Glaucon would claim that these habits would wear off after a while. But I doubt that.
22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good
For Plato we abandon honour and pleasure once we see the Good [Plato, by Taylor,C]
     Full Idea: For Plato, once we see the Good, we cease to be fascinated by and absorbed in the search for honour and pleasure as we were before.
     From: report of Plato (The Republic [c.374 BCE], 505d) by Charles Taylor - Sources of the Self §3.2
     A reaction: This is the quasi-religious aspect of the Good - that it is more like a vision than a reason
The main aim is to understand goodness, which gives everything its value and advantage [Plato]
     Full Idea: The most important thing to try to understand is the character of goodness, because this is where anything which is moral (or whatever) gets its value and advantages from.
     From: Plato (The Republic [c.374 BCE], 505a)
     A reaction: I think I'm with Aristotle on this. I understand a good lunch or a good person, but pure goodness just seems to be an empty placeholder. A vote in favour.
Every person, and every activity, aims at the good [Plato]
     Full Idea: The Good is something which everyone is after, and is the goal of all their activities.
     From: Plato (The Republic [c.374 BCE], 505d)
     A reaction: An obvious danger of tautology. If a blood crazed army is 'after' a massacre of some sort, that seems to qualify. What proportion is needed for 'everyone'?
Goodness makes truth and knowledge possible [Plato]
     Full Idea: It is goodness which gives the things we know their truth and makes it possible for people to have knowledge.
     From: Plato (The Republic [c.374 BCE], 508e)
     A reaction: If we take truth to be the hallmark of successful thinking, then I have no idea what this means. I can't see how truth would disappear in an amoral cosmos.
Bad is always destructive, where good preserves and benefits [Plato]
     Full Idea: Badness always manifests in destruction and corruption, while goodness always manifests in preservation and benefit.
     From: Plato (The Republic [c.374 BCE], 608e)
     A reaction: Suspicions of tautology in this one. Can we have any concepts of good or bad which are not linked to desirable or undesirable outcomes?
Good has the same role in the world of knowledge as the sun has in the physical world [Plato]
     Full Idea: As goodness stands in the intelligible realm to intelligence and the things we know, so in the visible realm the sun stands to sight and the things we see.
     From: Plato (The Republic [c.374 BCE], 508c)
     A reaction: The claim seems to be that only goodness makes the world intelligible, but that strikes as closer to mysticism than to objective observation.
The sight of goodness leads to all that is fine and true and right [Plato]
     Full Idea: The sight of goodness shows that it is responsible for everything that is right and fine,…and it is the source and provider of truth and knowledge. It is necessary for intelligent conduct of private and public affairs.
     From: Plato (The Republic [c.374 BCE], 517c)
     A reaction: As so often with Plato, I am baffled by such a claim. I sometimes see things in the world which strike me as right or fine, but I cannot conceive of a separate 'sight of goodness'.
22. Metaethics / C. The Good / 1. Goodness / e. Good as knowledge
Pleasure is commonly thought to be the good, though the more ingenious prefer knowledge [Plato]
     Full Idea: The usual view of goodness is that it is pleasure, while there's also a more ingenious view that it is knowledge.
     From: Plato (The Republic [c.374 BCE], 505b)
     A reaction: Pleasure clearly has an attraction for everyone (even puritans), and is thus a plausible natural candidate. Is this pure or instrumental knowledge? Hard to justify the former.
22. Metaethics / C. The Good / 1. Goodness / f. Good as pleasure
Even people who think pleasure is the good admit that there are bad pleasures [Plato]
     Full Idea: Those who define good as pleasure are clearly confused, and are compelled to admit that there are bad pleasures, so that the same thing is both good and bad.
     From: Plato (The Republic [c.374 BCE], 505c)
     A reaction: The issue is whether the pleasure can be disentangled from the action. 'It was a hideous murder, but at least the murderer enjoyed it'. Sounds wrong to me.
22. Metaethics / C. The Good / 3. Pleasure / b. Types of pleasure
Nice smells are intensive, have no preceding pain, and no bad after-effect [Plato]
     Full Idea: Nice smells have no preceding feeling of pain, they are very intense, and they leave no distress when they are over.
     From: Plato (The Republic [c.374 BCE], 584b)
     A reaction: A nice example for extreme puritans to contemplate. Objections to enjoying nice smells seem almost inconceivable. Puritans will, I suppose, say 'slippery slope'.
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
Philosophers are concerned with totally non-physical pleasures [Plato]
     Full Idea: A person concerned with learning is concerned with purely mental pleasure, having nothing to do with pleasures reaching the mind through the body - assuming the person is a genuine philosopher.
     From: Plato (The Republic [c.374 BCE], 485d)
     A reaction: It is hard to find any argument which can demonstrate that mental pleasures are superior to physical ones. Mill notably failed to do it.
22. Metaethics / C. The Good / 3. Pleasure / d. Sources of pleasure
There are three types of pleasure, for reason, for spirit and for appetite [Plato]
     Full Idea: Each of the three mental categories (reason, spirit, appetite) has its own particular pleasure, so that there are three kinds of pleasure.
     From: Plato (The Republic [c.374 BCE], 580d)
     A reaction: I'm not sure why the types of pleasure are distinguished by mental faculties, rather than by the variety of sources of the pleasure.
22. Metaethics / C. The Good / 3. Pleasure / f. Dangers of pleasure
Pleasure-seekers desperately seek illusory satisfaction, like filling a leaky vessel [Plato]
     Full Idea: Pleasure-seekers desperately and violently seek satisfaction in unreal things for a part of themselves which is also unreal - a leaky vessel they're trying to fill.
     From: Plato (The Republic [c.374 BCE], 586b)
     A reaction: Plato dreams of some enduring 'satisfaction' which never fades. He should have attended more to Heraclitus, and less to Parmenides.
Excessive pleasure deranges people, making the other virtues impossible [Plato]
     Full Idea: Self-discipline and excessive pleasure cannot go together, because pleasure deranges people just as much as distress. Excessive pleasure cannot partner any of the other virtues.
     From: Plato (The Republic [c.374 BCE], 402e)
     A reaction: This invites an examination of the word 'excessive', which seems too subjective. Aristotle says any good is improved by the addition of pleasure. Pleasure can certainly derange people.
23. Ethics / A. Egoism / 1. Ethical Egoism
We should behave well even if invisible, for the health of the mind [Plato]
     Full Idea: There's nothing better for the mind than morality, and a person ought to behave morally whether or not he owns Gyges' ring.
     From: Plato (The Republic [c.374 BCE], 612b)
23. Ethics / B. Contract Ethics / 1. Contractarianism
Isn't it better to have a reputation for goodness than to actually be good? [Plato]
     Full Idea: Unless I gain a reputation for morality, my actually being moral will do me no good, but an immoral person who has managed to get a reputation for morality is said to have a wonderful life.
     From: Plato (The Republic [c.374 BCE], 365b)
Morality is a compromise, showing restraint, to avoid suffering wrong without compensation [Plato]
     Full Idea: The origin and nature of morality is a compromise between the ideal of doing wrong without paying for it, and the worst situation, which is having wrong done to one while lacking the means of exacting compensation.
     From: Plato (The Republic [c.374 BCE], 359a)
     A reaction: This idea is from Glaucon, and is not endorsed by Socrates. Hobbes thought it was right, though he emphasised safety. Game theory makes this approach to moraliy much more plausible.
Justice is merely the interests of the stronger party [Plato]
     Full Idea: Thrasymachus: Justice or right is simply what is in the interest of the stronger party.
     From: Plato (The Republic [c.374 BCE], 338c)
     A reaction: Not sure whether this is cynicism about the brutal realities of life, or cynicism about the very concept of justice.
23. Ethics / B. Contract Ethics / 3. Promise Keeping
Surely you don't return a borrowed weapon to a mad friend? [Plato]
     Full Idea: If one borrowed a weapon from a friend who subsequently went out of his mind and then asked for it back, surely one ought not to return it?
     From: Plato (The Republic [c.374 BCE], 331c)
     A reaction: Only a Kantian would think of disagreeing with this obvious truth. There is no promise here, but an implicit moral commitment. Such things should always have an all-things-being-equal clause.
23. Ethics / B. Contract Ethics / 4. Value of Authority
Is right just the interests of the powerful? [Plato]
     Full Idea: Thrasymachus: right is the interest of the established government.
     From: Plato (The Republic [c.374 BCE], 339a)
     A reaction: To believe this you would have to believe the powerful control not what is judged to be right, but also the ordinary language which expresses such judgements. Marxism explains that.
23. Ethics / B. Contract Ethics / 5. Free Rider
Sin first, then sacrifice to the gods from the proceeds [Plato]
     Full Idea: The thing to do is to sin first and sacrifice afterwards from the proceeds.
     From: Plato (The Republic [c.374 BCE], 365e)
     A reaction: A bit like Graham Greene's Catholicism. One Greek view of the gods seems to be that they are quite myopic and naïve.
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
For Plato, virtue is its own reward [Lawson-Tancred on Plato]
     Full Idea: The 'Republic' is the first sustained philosophical defence of the idea that virtue is its own reward.
     From: comment on Plato (The Republic [c.374 BCE], Ch.9) by Hugh Lawson-Tancred - Plato's Republic and Greek Enlightenment
     A reaction: Sceptics might say that at the heart of his claim is the idea that the virtuous life is the best means of achieving long-term pleasure (as opposed to short-sighted hedonism). What is it about people which could make virtue attractive to them?
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / j. Unity of virtue
True goodness requires mental unity and harmony [Plato]
     Full Idea: True goodness requires mental unity and harmony.
     From: Plato (The Republic [c.374 BCE], 554e)
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
     Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
     From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
     A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').
A good community necessarily has wisdom, courage, self-discipline and morality [Plato]
     Full Idea: A good community has everything which is good, so it necessarily has wisdom, courage, self-discipline and morality.
     From: Plato (The Republic [c.374 BCE], 427e)
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
Simonides said morality is helping one's friends and harming one's enemies [Plato]
     Full Idea: Simonides claims that morality is doing good to one's friends and harm to one's enemies.
     From: Plato (The Republic [c.374 BCE], 332d)
If the parts of our soul do their correct work, we will be just people, and will act justly [Plato]
     Full Idea: Each one of us in whom each part is doing its own work will himself be just and do his own. …So it is appropriate for the rational part to rule …and for the spirited part to obey.
     From: Plato (The Republic [c.374 BCE], 441d)
     A reaction: 'Do his own' must mean play his own part in society correctly, because his internal faculties are also correctly focused on their role. So balancing the three parts in persons and society is not just an analogy, but one leads to the other. See 443e.
24. Political Theory / A. Basis of a State / 1. A People / b. The natural life
People need society because the individual has too many needs [Plato]
     Full Idea: Society originates because the individual is not self-sufficient, but has many needs which he cannot supply himself.
     From: Plato (The Republic [c.374 BCE], 369b)
     A reaction: Notice that Plato has the liberal individualist approach to problem, of starting with isolated individuals, and asking why they need to gang together. This is despite the dependency of children, and the proximity of extended families.
24. Political Theory / B. Nature of a State / 1. Purpose of a State
All exchanges in a community are for mutual benefit [Plato]
     Full Idea: In the community all mutual exchanges are made on the assumption that the parties to them stand to gain.
     From: Plato (The Republic [c.374 BCE], 369c)
     A reaction: The sole purpose of his society appears to be trading, either of goods or of services. The assumption is that if each individual were self-sufficient there would be no society, which strikes me as unlikely. Aristotle offers a better picture.
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
After a taste of mutual harm, men make a legal contract to avoid it [Plato]
     Full Idea: Once people experience committing wrong and suffering it, they see the disadvantages are unavoidable and the benefits unobtainable, ...so they enter into a contract, guaranteeing no permitting or receiving wrong, ...and they then make laws and decrees.
     From: Plato (The Republic [c.374 BCE], 359a)
     A reaction: This seems to be the earliest statement of the social contract idea. Here it both sets up the state and creates morality. This is Glaucon speaking, and is NOT endorsed by Socrates.
24. Political Theory / B. Nature of a State / 4. Citizenship
People doing their jobs properly is the fourth cardinal virtue for a city [Plato]
     Full Idea: The power that consists in everyone's doing his own work rivals wisdom, moderation, and courage in its contribution to the virtue of the city.
     From: Plato (The Republic [c.374 BCE], 433d)
     A reaction: Making conscientious the fourth cardinal virtue. Well said! My maxim for the modern world is that nearly all human misery consists of either bad health or other people not doing their jobs properly. You know I'm right.
24. Political Theory / C. Ruling a State / 2. Leaders / d. Elites
Reluctant rulers make a better and more unified administration [Plato]
     Full Idea: The less keen the would-be rulers of a community are to rule, the better and less divided the administration of that community are bound to be.
     From: Plato (The Republic [c.374 BCE], 520d)
Only rule by philosophers of integrity can keep a community healthy [Plato]
     Full Idea: Unless communities have philosophers as kings, or the people who are currently called kings and rulers practise philosophy with enough integrity, there can be no end to political troubles.
     From: Plato (The Republic [c.374 BCE], 473d)
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
Is there anything better for a community than to produce excellent people? [Plato]
     Full Idea: Is anything better for a community than for it to engender women and men who are exceptionally good?
     From: Plato (The Republic [c.374 BCE], 456e)
25. Social Practice / E. Policies / 5. Education / b. Education principles
Dialectic is the highest and most important part of the curriculum [Plato]
     Full Idea: Dialectic occupies the highest position and forms, as it were, the copestone of the curriculum.
     From: Plato (The Republic [c.374 BCE], 534e)
To gain knowledge, turn away from the world of change, and focus on true goodness [Plato]
     Full Idea: To gain knowledge we must turn the mind away from the world of becoming, until it becomes capable of bearing the sight of real being and reality at its most bright, which we are saying is goodness.
     From: Plato (The Republic [c.374 BCE], 518c)
25. Social Practice / E. Policies / 5. Education / c. Teaching
Compulsory intellectual work never remains in the mind [Plato]
     Full Idea: Compulsory intellectual work never remains in the mind.
     From: Plato (The Republic [c.374 BCE], 536e)
28. God / A. Divine Nature / 4. Divine Contradictions
If Plato's God is immaterial, he will lack consciousness, wisdom, pleasure and movement, which are essential to him [Cicero on Plato]
     Full Idea: Plato holds God to be without a body, immaterial; but this is an incomprehensible idea. Such a god would inevitably lack any consciousness, any wisdom and any pleasure (…or motion), all of which are bound up in our idea of God.
     From: comment on Plato (The Republic [c.374 BCE]) by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') I.30
28. God / C. Attitudes to God / 3. Deism
If the gods are non-existent or indifferent, why bother to deceive them? [Plato]
     Full Idea: If there are no gods or if they care nothing for human affairs, why should we bother to deceive them?
     From: Plato (The Republic [c.374 BCE], 365d)
     A reaction: There is incipient deism here, as well as atheism.
29. Religion / D. Religious Issues / 2. Immortality / b. Soul
Something is unlikely to be immortal if it is imperfectly made from diverse parts [Plato]
     Full Idea: Something is unlikely to be immortal if it's a compound, formed imperfectly from diverse parts.
     From: Plato (The Republic [c.374 BCE], 611b)
29. Religion / D. Religious Issues / 2. Immortality / d. Heaven
Is the supreme reward for virtue to be drunk for eternity? [Plato]
     Full Idea: (the poets think) 'the supreme reward of virtue was to be drunk for eternity'.
     From: Plato (The Republic [c.374 BCE], 363d)
     A reaction: A perceptive thought. Most people consider the best life to contain endless fun and physical pleasure, so a boozy bawdy holiday in the sunshine ticks all the boxes.
29. Religion / D. Religious Issues / 3. Problem of Evil / d. Natural Evil
God is responsible for the good things, but we must look elsewhere for the cause of the bad things [Plato]
     Full Idea: God and God alone must be held responsible for the good things, but responsibility for bad things must be looked for elsewhere, and not attributed to God.
     From: Plato (The Republic [c.374 BCE], 379c)