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All the ideas for 'works (fragments)', 'On Eternal and Immutable Morality' and 'Investigations in the Foundations of Set Theory I'

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49 ideas

1. Philosophy / A. Wisdom / 2. Wise People
A wise man's chief strength is not being tricked; nothing is worse than error, frivolity or rashness [Zeno of Citium, by Cicero]
     Full Idea: Zeno held that the wise man's chief strength is that he is careful not to be tricked, and sees to it that he is not deceived; for nothing is more alien to the conception that we have of the seriousness of the wise man than error, frivolity or rashness.
     From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by M. Tullius Cicero - Academica II.66
     A reaction: I presume that this concerns being deceived by other people, and also being deceived by evidence. I suggest that the greatest ability of the wise person is the accurate assessment of evidence.
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
When shown seven versions of the mowing argument, he paid twice the asking price for them [Zeno of Citium, by Diog. Laertius]
     Full Idea: When shown seven species of dialectic in the mowing argument, he asked the price, and when told 'a hundred drachmas', he gave two hundred, so devoted was he to learning.
     From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.Ze.20
     A reaction: Wonderful. I have a watertight proof that pleasure is not the good, which I will auction on the internet.
1. Philosophy / D. Nature of Philosophy / 4. Divisions of Philosophy
Philosophy has three parts, studying nature, character, and rational discourse [Zeno of Citium, by Diog. Laertius]
     Full Idea: They say that philosophical theory is tripartite. For one part of it concerns nature [i.e. physics], another concerns character [i.e. ethics], and another concerns rational discourse [i.e. logic]
     From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.39
     A reaction: Surely 'nature' included biology, and shouldn't be glossed as 'physics'? And I presume that 'rational discourse' is 'logos', rather than 'logic'. Interesting to see that ethics just is the study of character (and not of good and bad actions).
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine]
     Full Idea: On Zermelo's view, predicative definitions are not only indispensable to mathematics, but they are unobjectionable since they do not create the objects they define, but merely distinguish them from other objects.
     From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Shaughan Lavine - Understanding the Infinite V.1
     A reaction: This seems to have an underlying platonism, that there are hitherto undefined 'objects' lying around awaiting the honour of being defined. Hm.
3. Truth / H. Deflationary Truth / 3. Minimalist Truth
Someone who says 'it is day' proposes it is day, and it is true if it is day [Zeno of Citium, by Diog. Laertius]
     Full Idea: Someone who says 'It is day' seems to propose that it is day; if, then, it is day, the proposition advanced comes out true, but if not, it comes out false.
     From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.65
     A reaction: Those who find Tarski's theory annoyingly vacuous should note that the ancient Stoics thought the same point worth making. They seem to have clearly favoured some minimal account of truth, according to this.
4. Formal Logic / F. Set Theory ST / 1. Set Theory
We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo]
     Full Idea: Starting from set theory as it is historically given ...we must, on the one hand, restrict these principles sufficiently to exclude as contradiction and, on the other, take them sufficiently wide to retain all that is valuable in this theory.
     From: Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908], Intro)
     A reaction: Maddy calls this the one-step-back-from-disaster rule of thumb. Zermelo explicitly mentions the 'Russell antinomy' that blocked Frege's approach to sets.
Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo]
     Full Idea: Set theory is that branch whose task is to investigate mathematically the fundamental notions 'number', 'order', and 'function', taking them in their pristine, simple form, and to develop thereby the logical foundations of all of arithmetic and analysis.
     From: Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908], Intro)
     A reaction: At this point Zermelo seems to be a logicist. Right from the start set theory was meant to be foundational to mathematics, and not just a study of the logic of collections.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg]
     Full Idea: Zermelo-Fraenkel axioms: Existence (at least one set); Extension (same elements, same set); Specification (a condition creates a new set); Pairing (two sets make a set); Unions; Powers (all subsets make a set); Infinity (set of successors); Choice
     From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.15
Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy]
     Full Idea: Zermelo proposed his listed of assumptions (including the controversial Axiom of Choice) in 1908, in order to secure his controversial proof of Cantor's claim that ' we can always bring any well-defined set into the form of a well-ordered set'.
     From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1
     A reaction: This is interesting because it sometimes looks as if axiom systems are just a way of tidying things up. Presumably it is essential to get people to accept the axioms in their own right, the 'old-fashioned' approach that they be self-evident.
Set theory can be reduced to a few definitions and seven independent axioms [Zermelo]
     Full Idea: I intend to show how the entire theory created by Cantor and Dedekind can be reduced to a few definitions and seven principles, or axioms, which appear to be mutually independent.
     From: Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908], Intro)
     A reaction: The number of axioms crept up to nine or ten in subsequent years. The point of axioms is maximum reduction and independence from one another. He says nothing about self-evidence (though Boolos claimed a degree of that).
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy]
     Full Idea: Zermelo's Pairing Axiom superseded (in 1930) his original 1908 Axiom of Elementary Sets. Like Union, its only justification seems to rest on 'limitations of size' and on the 'iterative conception'.
     From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1.3
     A reaction: Maddy says of this and Union, that they seem fairly obvious, but that their justification is of prime importance, if we are to understand what the axioms should be.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy]
     Full Idea: Zermelo used a weak form of the Axiom of Foundation to block Russell's paradox in 1906, but in 1908 felt that the form of his Separation Axiom was enough by itself, and left the earlier axiom off his published list.
     From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1.2
     A reaction: Foundation turns out to be fairly controversial. Barwise actually proposes Anti-Foundation as an axiom. Foundation seems to be the rock upon which the iterative view of sets is built. Foundation blocks infinite descending chains of sets, and circularity.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation
The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy]
     Full Idea: The most characteristic Zermelo axiom is Separation, guided by a new rule of thumb: 'one step back from disaster' - principles of set generation should be as strong as possible short of contradiction.
     From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1.4
     A reaction: Why is there an underlying assumption that we must have as many sets as possible? We are then tempted to abolish axioms like Foundation, so that we can have even more sets!
Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD]
     Full Idea: Zermelo assumes that not every predicate has an extension but rather that given a set we may separate out from it those of its members satisfying the predicate. This is called 'separation' (Aussonderung).
     From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by William D. Hart - The Evolution of Logic 3
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD]
     Full Idea: In Zermelo's set theory, the Burali-Forti Paradox becomes a proof that there is no set of all ordinals (so 'is an ordinal' has no extension).
     From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by William D. Hart - The Evolution of Logic 3
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Zeno achieved the statement of the problems of infinitesimals, infinity and continuity [Russell on Zeno of Citium]
     Full Idea: Zeno was concerned with three increasingly abstract problems of motion: the infinitesimal, the infinite, and continuity; to state the problems is perhaps the hardest part of the philosophical task, and this was done by Zeno.
     From: comment on Zeno (Citium) (fragments/reports [c.294 BCE]) by Bertrand Russell - Mathematics and the Metaphysicians p.81
     A reaction: A very nice tribute, and a beautiful clarification of what Zeno was concerned with.
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy]
     Full Idea: For Zermelo the successor of n is {n} (rather than Von Neumann's successor, which is n U {n}).
     From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Naturalism in Mathematics I.2 n8
     A reaction: I could ask some naive questions about the comparison of these two, but I am too shy about revealing my ignorance.
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy]
     Full Idea: Zermelo was a reductionist, and believed that theorems purportedly about numbers (cardinal or ordinal) are really about sets, and since Von Neumann's definitions of ordinals and cardinals as sets, this has become common doctrine.
     From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1.8
     A reaction: Frege has a more sophisticated take on this approach. It may just be an updating of the Greek idea that arithmetic is about treating many things as a unit. A set bestows an identity on a group, and that is all that is needed.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR]
     Full Idea: In Zermelo's set-theoretic definition of number, 2 is a member of 3, but not a member of 4; in Von Neumann's definition every number is a member of every larger number. This means they have two different structures.
     From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by James Robert Brown - Philosophy of Mathematics Ch. 4
     A reaction: This refers back to the dilemma highlighted by Benacerraf, which was supposed to be the motivation for structuralism. My intuition says that the best answer is that they are both wrong. In a pattern, the nodes aren't 'members' of one another.
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Whatever participates in substance exists [Zeno of Citium, by Stobaeus]
     Full Idea: Zeno says that whatever participates in substance exists.
     From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by John Stobaeus - Anthology 2.05a
     A reaction: This seems Aristotelian, implying that only objects exist. Unformed stuff would not normally qualify as a 'substance'. So does mud exist? See the ideas of Henry Laycock.
11. Knowledge Aims / A. Knowledge / 1. Knowledge
Perception an open hand, a fist is 'grasping', and holding that fist is knowledge [Zeno of Citium, by Long]
     Full Idea: Zeno said perceptions starts like an open hand; then the assent by our governing-principle is partly closing the hand; then full 'grasping' is like making a fist; and finally knowledge is grasping the fist with the other hand.
     From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by A.A. Long - Hellenistic Philosophy 4.3.1
     A reaction: [In Cicero, Acad 2.145] It sounds as if full knowledge requires meta-cognition - knowing that you know.
11. Knowledge Aims / A. Knowledge / 7. Knowledge First
A grasp by the senses is true, because it leaves nothing out, and so nature endorses it [Zeno of Citium, by Cicero]
     Full Idea: He thought that a grasp made by the senses was true and reliable, …because it left out nothing about the object that could be grasped, and because nature had provided this grasp as a standard of knowledge, and a basis for understanding nature itself.
     From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by M. Tullius Cicero - Academica I.42
     A reaction: Sounds like Williamson's 'knowledge first' claim - that the basic epistemic state is knowledge, which we have when everything is working normally. I like Zeno's idea that a 'grasp' leaves nothing out about the object. Compare nature with Descartes' God.
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / c. Tabula rasa
If the soul were a tabula rasa, with no innate ideas, there could be no moral goodness or justice [Cudworth]
     Full Idea: The soul is not a mere rasa tabula, a naked and passive thing, with no innate furniture of its own, nor any thing in it, but what was impressed upon it without; for then there could not possibly be any such thing as moral good and evil, just and unjust.
     From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Bk IV Ch 6.4)
     A reaction: He goes on to quote Hobbes saying there is no good in objects themselves. I don't see why we must have an innate moral capacity, provided that we have a capacity to make judgements.
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
Senses cannot judge one another, so what judges senses cannot be a sense, but must be superior [Cudworth]
     Full Idea: The sight cannot judge of sounds, nor the hearing of light and colours; wherefore that which judges of all the senses and their several objects, cannot be itself any sense, but something of a superior nature.
     From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Ch.II.VI.1)
     A reaction: How nice to find a seventeenth century English writer rebelling against empiricism!
13. Knowledge Criteria / A. Justification Problems / 1. Justification / c. Defeasibility
If a grasped perception cannot be shaken by argument, it is 'knowledge' [Zeno of Citium, by Cicero]
     Full Idea: What had been grasped by sense-perception, he called this itself a 'sense-perception', and if it was grasped in such a way that it could not be shaken by argument he called it 'knowledge'. And between knowledge and ignorance he placed the 'grasp'.
     From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by M. Tullius Cicero - Academica I.41
     A reaction: This seems to say that a grasped perception is knowledge if there is no defeater.
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / d. Rational foundations
A presentation is true if we judge that no false presentation could appear like it [Zeno of Citium, by Cicero]
     Full Idea: I possess a standard enabling me to judge presentations to be true when they have a character of a sort that false ones could not have.
     From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by M. Tullius Cicero - Academica II.18.58
     A reaction: [This is a spokesman in Cicero for the early Stoic view] No sceptic will accept this, but it is pretty much how I operate. If you see something weird, like a leopard wandering wild in Hampshire, you believe it once you have eliminated possible deceptions.
16. Persons / F. Free Will / 6. Determinism / a. Determinism
When a slave said 'It was fated that I should steal', Zeno replied 'Yes, and that you should be beaten' [Zeno of Citium, by Diog. Laertius]
     Full Idea: When a slave who was being beaten for theft said, 'It was fated that I should steal', Zeno replied, 'Yes, and that you should be beaten.'
     From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.Ze.19
A dog tied to a cart either chooses to follow and is pulled, or it is just pulled [Zeno of Citium, by Hippolytus]
     Full Idea: Zeno and Chrysippus say everything is fated with the following model: when a dog is tied to a cart, if it wants to follow it is pulled and follows, making its spontaneous act coincide with necessity, but if it does not want to follow it will be compelled.
     From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by Hippolytus - Refutation of All Heresies §1.21
     A reaction: A nice example, but it is important to keep the distinction clear between freedom and free will. The dog lacks freedom as it is dragged along, but it is still free to will that it is asleep in its kennel.
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
Incorporeal substances can't do anything, and can't be acted upon either [Zeno of Citium, by Cicero]
     Full Idea: Zeno held that an incorporeal substance was incapable of any activity, whereas anything capable of acting, or being acted upon in any way, could not be incorporeal.
     From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by M. Tullius Cicero - Academica I.11.39
     A reaction: This is substance dualism kicked into the long grass by Zeno, long before Descartes defended dualism, and was swiftly met with exactly the same response. The interaction problem.
17. Mind and Body / E. Mind as Physical / 5. Causal Argument
A body is required for anything to have causal relations [Zeno of Citium, by Cicero]
     Full Idea: Zeno held (contrary to Xenocrates and others) that it was impossible for anything to be effected that lacked a body, and indeed that whatever effected something or was affected by something must be body.
     From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by M. Tullius Cicero - Academica I.39
     A reaction: This seems to make stoics thoroughgoing physicalists, although they consider the mind to be made of refined fire, rather than of flesh.
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / a. Physicalism critique
Sense is fixed in the material form, and so can't grasp abstract universals [Cudworth]
     Full Idea: Sense which lies flat and grovelling in the individuals, and is stupidly fixed in the material form, is not able to rise up or ascend to an abstract universal notion.
     From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Ch.III.III.2)
     A reaction: This still strikes me as being one of the biggest problems with reductive physicalism, that a lump of meat in your head can grasp abstractions (whatever they are) and universal concepts. Personally I am a physicalist, but it is weird.
19. Language / A. Nature of Meaning / 7. Meaning Holism / a. Sentence meaning
A sentence always has signification, but a word by itself never does [Zeno of Citium, by Diog. Laertius]
     Full Idea: A sentence is always significative of something, but a word by itself has no signification.
     From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.Ze.28
     A reaction: This is the Fregean dogma. Words obviously can signify, but that is said to be parasitic on their use in sentences. It feels like a false dichotomy to me. Much sentence meaning is compositional.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / k. Ethics from nature
Zeno said live in agreement with nature, which accords with virtue [Zeno of Citium, by Diog. Laertius]
     Full Idea: Zeno first (in his book On Human Nature) said that the goal was to live in agreement with nature, which is to live according to virtue.
     From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.87
     A reaction: The main idea seems to be Aristotelian - that the study of human nature reveals what our virtues are, and following them is what nature requires. Nature is taken to be profoundly rational.
Since we are essentially rational animals, living according to reason is living according to nature [Zeno of Citium, by Diog. Laertius]
     Full Idea: As reason is given to rational animals according to a more perfect principle, it follows that to live correctly according to reason, is properly predicated of those who live according to nature.
     From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.Ze.52
     A reaction: This is the key idea for understanding what the stoics meant by 'live according to nature'. The modern idea of rationality doesn't extend to 'perfect principles', however.
22. Metaethics / B. Value / 1. Nature of Value / c. Objective value
Keeping promises and contracts is an obligation of natural justice [Cudworth]
     Full Idea: To keep faith and perform covenants is that which natural justice obligeth to absolutely.
     From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Ch.II.4)
     A reaction: A nice example of an absolute moral intuition, but one which can clearly be challenged. Covenants (contracts) wouldn't work unless everyone showed intense commitment to keeping them, even beyond the grave, and we all benefit from good contracts.
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
The goal is to 'live in agreement', according to one rational consistent principle [Zeno of Citium, by Stobaeus]
     Full Idea: Zeno says the goal of life is 'living in agreement', which means living according to a single and consonant rational principle, since those who live in conflict are unhappy.
     From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by John Stobaeus - Anthology 2.06a
     A reaction: If there is a 'single' principle, is it possible to state it? To live by consistent principles sets the bar incredibly high, as any professional philosopher can tell you.
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
Zeno saw virtue as a splendid state, not just a source of splendid action [Zeno of Citium, by Cicero]
     Full Idea: Zeno held that not merely the exercise of virtue, as his predecessors held, but the mere state of virtue is in itself a splendid thing, although nobody possesses virtue without continuously exercising it.
     From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by M. Tullius Cicero - Academica I.10.38
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
One of Zeno's books was 'That Which is Appropriate' [Zeno of Citium, by Long]
     Full Idea: Zeno of Citium wrote a (lost) book entitled 'That Which is Appropriate'.
     From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by A.A. Long - Hellenistic Philosophy 4.1
     A reaction: I cite this because I take it to be about what in Aristotle called 'the mean' - to emphasise that the mean is not what is average, or midway between the extremes, but what is a balanced response to each situation
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
Zeno says there are four main virtues, which are inseparable but distinct [Zeno of Citium, by Plutarch]
     Full Idea: Zeno (like Plato) admits a plurality of specifically different virtues, namely prudence, courage, sobriety, justice, which he takes to be inseparable but yet distinct and different from one another.
     From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by Plutarch - 70: Stoic Self-contradictions 1034c
     A reaction: In fact, the virtues are 'supervenient' on one another, which is the doctrine of the unity of virtue. Zeno is not a pluralist in the way Aristotle is - who says there are other goods apart from the virtues.
25. Social Practice / D. Justice / 2. The Law / c. Natural law
Obligation to obey all positive laws is older than all laws [Cudworth]
     Full Idea: Obligation to obey all positive laws is older than all laws.
     From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Ch.II.3)
     A reaction: Clearly villains can pass wicked laws, so there can't be an obligation to obey all laws (even if they are 'positive', which seems to beg the question). Nevertheless this is a good reason why laws cannot be the grounding of morality.
27. Natural Reality / C. Space / 1. Void
There is no void in the cosmos, but indefinite void outside it [Zeno of Citium, by Ps-Plutarch]
     Full Idea: Zeno and his followers say that there is no void within the cosmos but an indefinite void outside it.
     From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by Pseudo-Plutarch - On the Doctrine of the Philosophers 884a
     A reaction: Only atomists (such as Epicureans) need void within the cosmos, as space within which atoms can move. What would they make of modern 'fields'? Posidonius later said there was sufficient, but not infinite, void.
27. Natural Reality / E. Cosmology / 1. Cosmology
Things are more perfect if they have reason; nothing is more perfect than the universe, so it must have reason [Zeno of Citium]
     Full Idea: That which has reason is more perfect than that which has not. But there is nothing more perfect than the universe; therefore the universe is a rational being.
     From: Zeno (Citium) (fragments/reports [c.294 BCE]), quoted by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') II.20
Since the cosmos produces what is alive and rational, it too must be alive and rational [Zeno of Citium]
     Full Idea: Nothing which lacks life and reason can produce from itself something which is alive and rational; but the cosmos can produce from itself things which are alive and rational; therefore the cosmos is alive and rational.
     From: Zeno (Citium) (fragments/reports [c.294 BCE]), quoted by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') 2.22
     A reaction: Eggs and sperm don't seem to be rational, but I don't suppose they count. I note that this is presented as a formal proof, when actually it is just an evaluation of evidence. Logic as rhetoric, I would say.
28. God / A. Divine Nature / 4. Divine Contradictions
An omnipotent will cannot make two things equal or alike if they aren't [Cudworth]
     Full Idea: Omnipotent will cannot make things like or equal one to another, without the natures of likeness and equality.
     From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Ch.II.I)
     A reaction: This is one of the many classic 'paradoxes of omnipotence'. The best strategy is to define omnipotence as 'being able to do everything which it is possible to do'. Anything beyond that is inviting paradoxical disaster.
28. God / A. Divine Nature / 6. Divine Morality / d. God decrees morality
If the will and pleasure of God controls justice, then anything wicked or unjust would become good if God commanded it [Cudworth]
     Full Idea: If the arbitrary will and pleasure of God is the first and only rule of good and justice, it follows that nothing can be so grossly wicked or unjust but if it were commanded by this omnipotent Deity, it must forthwith become holy, just and righteous.
     From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Ch.I.I.5)
     A reaction: This is the strong (Platonic) answer to the Euthyphro Question (Idea 336). One answer is that God would not command in such a way - but why not? We may say that God and goodness merge into one, but we are interested in ultimate authority.
The requirement that God must be obeyed must precede any authority of God's commands [Cudworth]
     Full Idea: If it were not morally good and just in its own nature before any positive command of God, that God should be obeyed by his creatures, the bare will of God himself could not beget any obligation upon anyone.
     From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Ch.II.3)
     A reaction: This strikes me as a self-evident truth, and a big problem for anyone who wants to make God the source of morality. You don't have to accept anyone's authority just because they are powerful or clever (though they do bestow a certain natural authority!).
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
Rational is better than non-rational; the cosmos is supreme, so it is rational [Zeno of Citium]
     Full Idea: That which is rational is better than that which is not rational; but there is nothing better than the cosmos; therefore, the cosmos is rational.
     From: Zeno (Citium) (fragments/reports [c.294 BCE]), quoted by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') 2.21
     A reaction: This looks awfully like Anselm's ontological argument to me. The cosmos was the greatest thing that Zeno could conceive.
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
If tuneful flutes grew on olive trees, you would assume the olive had some knowledge of the flute [Zeno of Citium]
     Full Idea: If flutes playing tunes were to grow on olive trees, would you not infer that the olive must have some knowledge of the flute?
     From: Zeno (Citium) (fragments/reports [c.294 BCE]), quoted by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') II.22
28. God / C. Attitudes to God / 2. Pantheism
The cosmos and heavens are the substance of god [Zeno of Citium, by Diog. Laertius]
     Full Idea: Zeno says that the entire cosmos and the heaven are the substance of god.
     From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.148