Philosophical Logic - Riddles and Answers | Puzzles and Solutions - Remarks and Responses
Query: in simple words, what is philosophy?
What philosophy is should be told as "a simple story in words of one syllable", if that be possible. The simplest, I think, is the three parts of philosophy according to the Greek Stoics, although not all philosophers would accept that account, and even that simple account does no more than provide an orientation: This is where on the map of learning philosophy is located.
Is there an essence of Philosophy or of Mathematics? The Afterlife. The Origin of Plato's strange Ideas. [Children's riddles and Philosophy.]
Topics on this page ...
- When a vague metaphor becomes doctrine
- Remarks: The cardinal virtues. Euclid. Flat earth.
- Responses: Reason is Greek Philosophy. The Afterlife.
- Plato's strange Ideas
- Plato did not spring directly from Socrates, nor was Socrates his first teacher in philosophy
- Grammar describes both language's syntax and semantics
When a vague metaphor becomes doctrine
Query: Wittgenstein's metaphor to describe the meaning of words.
The allusion may be to Wittgenstein's tool chest simile, but I shall discuss his "family likeness" metaphor.
Does everything we call 'philosophy' have a defining common nature, something (1) that everything we call 'philosophy' has in common, and (2) that distinguishes philosophy from everything else? I don't know. Suppose we state, as one such general definition, that "Philosophy is the love of wisdom", and that by 'wisdom' we mean the particular types of knowledge sought by the three branches of learning called 'philosophy' -- namely, logic (how to reason), ethics (how to live), metaphysics (what is reality). That "in simple words" is "what philosophy is". And all philosophy can be stated in simple words and "readable sentences" -- but many years of thought and study are needed before anyone begins to understand "what philosophy is".
Earlier I wrote that philosophy is a "basket category". -- However, was that correct? Is it really the case that there is no essence of philosophy, no one thing without which [sine qua non] something cannot be called 'philosophy' (cf. e.g. anything we call a 'simile' must by definition employ the words 'like' or 'as' in a comparison; that is the essence of simile)? Are there instead -- now to use Wittgenstein's metaphor, one which explains nothing and makes nothing clearer in the particular case (where it is just as easy to dogmatically assume this metaphor as the notion of "abstraction", rather than look to see in exactly what way "they differ and are not all alike" if indeed they do differ and are not all alike), but maybe gives a general description (picture) of our language (i.e. of the "grammar" of our words in some or many or most cases) -- but, rather, only "family resemblances" shared among the things we call 'philosophy'? But if there are such resemblances, then we must give an account of them: we must list them as I did with the word 'game' (but have given no other example of) ... or confess that we do not know what we are talking about, and are being dogmatic when we claim that Wittgenstein's metaphor applies to our concept -- i.e. to the rules for using our word -- 'philosophy'.
Note that "family likenesses" or "family resemblances" is not a type or method of definition. You can't say, "This word is defined by family resemblances" e.g., as if those particular resemblances were predictable (as if nature had intended there to be a concept 'game'). Wittgenstein's metaphor is only an after-the-fact characterization of what we may and often do find when we look for an essential [or, one defining feature in common] type of definition. Don't use that expression carelessly.
What is the essence of mathematics? Is it not number? But there are no numbers in axiomatic geometry. Perhaps it is equations, for at least a geometric proof may be likened to an equation. But there are no equations in counting (e.g. from 1 to 10), although there are numbers. Suppose we said that in all mathematics there is greater and lesser. However, there is no greater and lesser in geometry: if we say that line segment AB is shorter (or, lesser) than line segment ABC, we are saying no more than the point B is between points A and C. That is, because the word 'length' is undefined in axiomatic geometry, there is no greater and lesser -- or, in other words, measurement is not the essence of mathematics, because there is no measurement in axiomatic geometry. Nor is there measurement of length in counting, although there is greater and lesser. Is this -- i.e. the concept (or, rules for using the word) 'mathematics', then, an example of "family likenesses"? Likenesses there are, but we should continue our investigation of possible essences of mathematics before we conclude that there is no essence.
Query: why is philosophy undefinable?
That is not a philosophical question, for in philosophy the conclusion comes at the end, not at the beginning of an investigation. A philosophical question might be: "Is there an essence [or, common nature, a one thing common to everything called (or, classified in the category) 'philosophy'] of philosophy?" But prior to that is the question: Is there an essence of anything -- i.e. do we "define things" or do we define words? (That would be, in Wittgenstein's jargon, a grammatical investigation.)
Metaphors for Philosophy, Whole versus its Parts
Query: ethics is a sub-branch of philosophy.
But if Philosophy is a branch off any tree you like (e.g. the Humanities, Liberal Arts) and it has sub-branches, then what is this branch that has sub-branches? Philosophy, like a pie, is not a whole as distinct from its parts: even cut up it contains the whole of itself. Logic is present in every part, Metaphysics in every part, Ethics in every part. Now that you cannot say. For how is Ethics (the subject-matter 'ethics') necessarily (if ever in any way) in Logic or Metaphysics?
Can you say that every part, that the whole of Philosophy is contained in each of its parts or in each of its divisions, as one might say that about a pie, that the whole of the pie -- i.e. all its ingredients -- is in every slice? What you can say is that Logic is present in all the parts of Philosophy; and that although an Ethics may (or I imagine it could be) or may not be based on a Metaphysics, you cannot say that Ethics is found either in Logic or in Metaphysics (This is different from the question of whether an ethic of Philosophy is found in each and everyone of its parts). Question: then is the trunk of philosophy -- Logic? But Ethics and Metaphysics are not sub-divisions of Logic; therefore, No. But if they are sub-divisions of something, then what are they subdivisions of? That is, if Logic, Ethics and Metaphysics are sub-divisions of Philosophy, then what is this "some thing" -- i.e. the subject-matter -- named 'Philosophy': what is it that its parts are a division of? This shows that the metaphor of whole and parts is mistaken in the case of Philosophy.
For the whole of Philosophy is nothing more than its parts -- i.e. the whole is not distinguishable from its parts, as a dog can be distinguished from its legs or tail and other parts; because together those parts make up a living organism called 'dog'; and because if you cut a dog up into its parts and collected them in a box, that would not be what we call a 'dog'. But Philosophy -- i.e. the concept 'philosophy', the subject matter called 'philosophy', is not like that: Philosophy is nothing more than its parts collected in a box. (It may be that some philosophies -- i.e. the work of some philosophers -- form "organisms" -- i.e. a fully interlocked system of logic, ethics and metaphysics (I don't know) -- but SOME does not = ALL, if indeed any SOME exist.)
The whole is A + B + C, Logic + Ethics + Metaphysics. But the whole cannot be spoken of because it does not exist -- i.e. 'a whole as distinguished from its parts' is undefined language if applied to Philosophy (I mean the grammar of the word 'philosophy', of course) except as a conjunction and maybe (I don't know) various intersections of its parts. But on the other hand, it seems that is not correct. Because Logic is found in all parts of Philosophy. And if we say that Logic is merely "the tool of philosophy" rather than one of its parts, then what do we call the study of that tool (which is what most of Wittgenstein's work is devoted to)?
There is something common to all Philosophy, namely Logic. But that is only half of a Socratic (according to Aristotle) definition. Because all parts of Philosophy having Logic in common does not "mark them off", does not differentiate Philosophy from all other classes (categories); the subject matter 'Philosophy' is not in that way differentiated from all other subject matters.
So then, I am, apparently I am, searching for a new metaphor.
"Epistemology" (the where in philosophy of "How do you know?")
The question of "How do you know?" or Epistemology is asked everywhere in Philosophy, in each and every one of its parts. But the question makes [has] no sense asked apropos of nothing. The question is always: "How do you know such-and-such?" And, as such, there is no separate part of Philosophy named 'epistemology' that is independent of that question about a particular proposition or about a class of propositions.
The question "What do you know?" must be answered before "How do you know?" just as the question of meaning precedes the question of truth. (This is a connection between Wittgenstein and Socrates.)
As in Plato's Republic 339a-b, I must first ask, What are you saying? and only afterwards ask, How do you know?
SOCRATES: Now ... I have learned your meaning, but whether it is true or not I have to try to learn.
But what does the question How do you know? ask for in philosophy? It does not ask What is your state of mind?, as if the philosophical question of knowledge were about "states of consciousness". No, philosophy asks What is the justification for what you say? In other words, epistemology in Plato is a branch of logic, not of psychology.
When Kant talks about innate categories that belong to the perceiving subject rather than to the reality the subject perceives, or when Aquinas speaks of naturally known categories, these philosophers are not talking about psychology but about the metaphysical foundations of the axioms of logic.
Query: origin of logic in your own explanation.
If in response to a proposition (assertion or claim), you wonder Is that true?, How do you know that?, you have begun to think about logic or "the art of reasoning", because 'justification' is a logical concept (a concept of logic).
Although Sokratikòs lógos [The earliest Socratic dialogs were records of Socrates' actual conversations (OCD 2e), now lost] these are not, the Greek word logos may signify anything to do with discourse or talk and these remarks and responses (to queries that arrived at the Web site) do concern philosophy. What follow are mostly later ideas or clarifications of earlier discussions (which also weren't discussions).
Remarks: The Cardinal Virtues. Euclid. Flat Earth.
Is it not curious that among the cardinal virtues (courage, justice, piety, self-control [temperance], wisdom), the Greeks did not list: freedom? For freedom surely is an excellence appropriate to man (but so is self-knowledge, which is also not listed), who alone is able to think for himself and in this respect quite unlike a "beast wanting discourse of reason". If the development of the intellect, of man's intelligence -- i.e. of his "wisdom" -- is the good for man, and if freedom of the intellect requires that ... But does that, therefore, make freedom a defining excellence ("virtue" or areté) of man? Yes, because human freedom must be practiced (for the freedom appropriate to wild beasts does not require the beasts to use the reason which they haven't got, but man must force himself to reason if he is to realize [achieve] the freedom that is appropriate to his life form.
It cannot be the case that the Euclidean definition of 'point' ("that without parts") was at the origin [birth] of geometry, for otherwise the project would have been still born, ending in perplexity. It must be a later addition [reflection] after the invention [birth] of geometry. It may be, remembering geometry's straightedge and compass demonstrations [proofs], that the original meaning of 'point' was simply the points the compass made when it was placed in the sand. It may have come later, in answer to an objection like that of Protagoras, that it remarked that the extension of the point made by the compass had no place in the proof, just as the width of the line made by the straightedge had no place in the proof.
"If the earth is round, then why don't we fall off?" That question only has sense in the context of a flat-earth picture: things fall down; they don't fall up. But if the earth is round, then what are 'down' and 'up' to mean, for north is not up nor south down; the globe can [may] be rotated to any position we wish (just as a pie may be cut in many ways). As an object of comparison: "gravity" is a description of what is observed (and can be predicted); the word 'gravity' is not the name of a "force", or a "new entity that has been discovered" (Drury) as if it were a new planet. Isaac Newton did not theorize ["make hypotheses"] about "what gravity is [in itself]"; he simply observed that masses gravitate towards one another, but as to why they do ...? The answer is that the word 'why' is without meaning here (i.e. is an undefined word in this context), just as the words 'extension of a point' and 'width of a line' are without meaning [undefined] in geometry.
Time is a relative or relational concept, N.B. a concept, not a thing that runs or moves more or less quickly ...
Note: this supplements the discussion Is there a science of time, in contrast to a metaphysics of time (a metaphysics invented by physicists)?
Query: describe time without using the word 'time'.
Using the words 'now' and 'then', e.g. "You can talk about time without the word 'time', but not without the concept 'time'." What might that mean? An experiment has been conducted using atomic clocks that have been placed at slightly different altitudes; it was found that the clock at the higher altitude gives a higher pointer reading (to use Eddington's jargon) than the clock at the lower altitude. That is the fact. What is nonsense is to deduce from that fact that "Therefore, time passes more quickly" -- or, to quote the public prints ["Einstein's theory is proved" independent.co.uk - 24 September 2010], "time moves faster" (which form of expression suggests that 'time' is the name of an entity that can move) or that "time itself runs faster" (as if there were such a thing as time in itself that existed independently of language) -- "at higher altitudes than at lower ones", as if 'time' were the name of some thing, some entity, about which a fact had been discovered.
The meaning of the word 'time' is given when the way time is measured is given [stated]. If on the basis of this experiment you go on to say that "And, therefore, time ...", what you are doing is stating which definition of the word 'time' [i.e. which method of measurement] you are using, not stating "what the real nature of time is". The word 'time' does not name a thing or entity which has a nature in itself. And if you say that this experiment proves Einstein's thought-experiment that he called his Special Theory of Relativity (1905), then you are saying what you mean by the word 'proof' here. (The question remains "Is that the only possible explanation?", which means: is there no other way to conceive the meaning of this event ["event-meaning"]?) Further, the assertion of this experiment is that the atomic clocks used provide an absolute standard, but is there such a thing as an absolute, rather than a freely chosen, standard of measurement (cf. points of reference, the origin of the Cartesian graph)?
"... the way time is measured." Contrast biology's "circadian clocks" both with the atomic clocks of physics and with the mechanical clocks we use (or used to use) in everyday life. (Can you say that each is concerned with defining a unit or interval of measurement and thereby giving a specific meaning to 'time'? or instead giving meaning to the word 'time'?)
Is it true that "Time is a relative concept"? Yes, for it is the meaning of the word 'time' that is relative to how time is measured [Rather than a "relative concept" it might be called a "relational concept", although regardless of the name we assign to it, the meaning of the name of this category will have to be explained]. If that is what you are calling 'the science of time', then it is partly a factual, partly a conceptual ("definitional", or grammatical) investigation. And do I know what I am talking about? See the next query.
[Related topic: Movement is Relative = 'Movement' is a Relational Concept (M. O'C. Drury's philosophy of science)]
Query: what does it mean 'speaking in ignorance'?
Exactly what my remarks above about the science of time per se, if there is such a science, are an example of.
Read Plato's Apology, for it's not too long
The difference between a professional school and a Liberal Arts college is that students at the latter are asked to read a few of the books and to think about the ideas on which Western Civilization is founded. But when teachers do not clearly and forcefully explain to children why they are asked to do this, and further when students are given too many subjects at once and too much to read at one time, that is not an education of any kind. The following are examples of students who are not students and are therefore being cheated by the schools they attend.
Query: Socrates argued that his advantage over others was that he had lived longer and was wiser. (Pittsburg State University, Kansas)
If Socrates had, that would have been an appeal to authority (as if there were such a thing as authority in philosophy, a wisdom that magically came with age, whereas of many men it can be said what the Fool says to King Lear: "You should not have grown old before you grew wise"), rather than to the test of reason (which is the only master in philosophy: anyone's claim to wisdom must "Stand and deliver!", to be agreed to or refuted in discussion). An appeal to authority would not have been Socratic. (The query's proposition looks like a true-false or multiple-choice exam question. As does the next query.)
Query: did Socrates investigate the heavens?
Only in Aristophanes' The Clouds, not in Plato's Apology (which you may have been assigned to read, but seem not to have read). After his youth, Socrates took no interest in physics (or, "metaphysics", as the Physics of the ancient philosophers was called in later times).
Query: in his trial Socrates does not mention the oracle at Delphi, fearing that this would hurt his case.
Philosophy reduced to true-or-false questions. Is it so difficult then to bring students to perceive the importance of philosophy to our life, if philosophy is philosophy as Socrates conceived it (i.e. set the limits of the concept 'philosophy', its subject and aim)?
Responses: Reason is Greek Philosophy. The Afterlife.
Query: questions about life-views.
This appears to be a variation of 'world-views', although 'life view' is only part of that concept. Compare with "Life-philosophy" versus "Nature-philosophy" -- a 'world-view' integrates (unites and, if need be, reconciles into a consistent whole) the two parts of philosophy (namely, Life-philosophy and Nature-philosophy) ... or, rather, the two parts of philosophy if philosophy is so conceived, for there are many ways to slice a cake. This particular way, which was Albert Schweitzer's way, regards logic as a mere tool rather than as a distinct part of philosophy -- a way which runs the risk of neglecting to think about the logic of language, and drowning in a sea of language (although maybe we drown in any case). Yet it is possible to say many important things despite a muddled picture of how our language works, and Schweitzer did. After all, it is not Socrates' logic, but the questions behind it which matter, is it not? and in many cases, although not in all, worthwhile things can be said about those questions despite the many misunderstandings of logic the investigation may involve. In Plato's words:
Query: we are discussing no small matter but how we ought to live.
Query: Socrates' philosophy, know thyself to be wise.
And how ought we live our life? The 'good' is not the end toward which all life aims, for it is possible for human beings not to know what is the good for man and so not to aim at the good. The good for man is the end towards which the 'wise man' aims, if any man is wise. According to the Greeks, a man can become wise by obeying the precept "Know thyself" (Seek the know what the defining excellence of man is, for the life that seeks to fully live according to that excellence is the good for man). And indeed, that can be called "Socrates' philosophy" (or, better, the method of the Greeks), for it is not the only possibility.
Another way, a non-philosophical way, of seeking to know what the good is for man is the religious way: to know the will of God or gods is to be wise (i.e. again: to be 'wise' means to know what is the good for man) ... although, according to the philosophers, it is either impossible to do this (for what man can understand the thoughts of God), or unnecessary (because reason alone can answer the question of what the good is for man, and because the gods, being themselves good must, as does mankind, love [and command] what is good, not because what is good is whatever is their caprice, but because the good is good in itself).
Query: explain the importance of Euthyphro's question is an action holy because the gods approve it.
Because if the answer to that question is Yes, then "The good is what[ever] the gods commands" (which was Wittgenstein's view of the good), which denies reason the most important role in ethics -- namely, to determine what the good is for man. But to the contrary, "The gods will what is good because it [like them] is good [in itself, quite apart from anyone's will]" is the Greek view (the view Wittgenstein dismisses as "rationalistic"; and indeed it is, for by 'rational' we mean 'based on reason').
Query: Socrates' ethical position in terms of intellectual integrity.
Query: intellectual integrity definition by Socrates.
The rigor of reason is the only path to intellectual integrity. To claim that right and wrong is merely a matter of an arbitrary [inscrutable, irrational] individual conscience (as Russell does in Wood's biography) is to deny ethics ("how we should live our") any fundamental intellectual integrity. It is the Protagorean account of ethics ("The individual man is the measure of all things").
Query: in what manner did man participate in God's creation?
Man did not participate: he alone created God, i.e. the concept 'gods' or 'God'. That is the philosophical answer. However, if anyone asks this question in the context of revealed religion, then the answer is (or, may be): in no manner.
The Philosophical Question of an Afterlife
If I were asked "Do I believe in an afterlife?", I would have to answer [feel forced to answer] "I don't know". But given that this [the various pictures of an afterlife] is not an hypothesis, what would I mean by the word 'know' in this context? I think it means that the picture of an afterlife is not unimportant to me; it's not something I dismiss; it does have a place in my thinking about life and about my life [despite that], but as to whether or not we "find a continuing place" after this life -- as Socrates says is a possibility in Plato's Apology [40c-41c, 29a]: I don't know [my thinking about this picture is characterized neither by firm belief-in nor by disbelief-in]; for to say I know one way or the other would be to imagine that I know what I do not know -- but only because the picture of an afterlife does have a place in my thinking, in my Life-Philosophy; if it had none, then there would be no sense in saying either that I believed or I didn't believe [disbelieved], but only that this picture played no role in my thinking.
There are or seem to be people for whom this picture plays no role in their thinking -- i.e. their Life-Philosophy -- at all, who are just certain that this life is the end of everything. But again, their certainty has nothing to do with an hypothesis; it is, rather, that they simply do not use a particular picture -- i.e. it does not guide their lives. Of course they may say that they deny that there is an afterlife, as if this were a proposition, a question of facts, an hypothesis, but just saying that doesn't make it the case. They may say, "Well, look at biology: the body deteriorates, and 'mind' and 'soul' are not the names of objects; there is therefore nothing to survive the death of the body." [Note that there were "materialists" even in Plato's day (see the Sophist 246a-b), those who assume that "Reality is in principle limited to what can be perceived by the five human senses", many centuries before there was modern natural science.] But I do think that, well, if they are willing to set up the test of that [as if there could be "a material proof for a non-material -- i.e. imperceptible -- reality"] and treat it as an hypothesis, that is not the way I use the picture or the way Socrates used the picture or the place the picture of an afterlife has in our thinking.
Whether or not there is "something" to survive the death of the body, I don't know [How would I know? As if there could be "a material proof for a non-material -- i.e. imperceptible -- reality"!] [because in order to know, I would have to be able to answer the question]: is reality confined to what is in principle perceptible to the senses? But that suggests that the question is a philosophical question, not a question for natural science, which answers that question with Yes, because its very defined-nature is to be a materialist project which sets such questions or "pseudo questions" aside, but I don't think that is an objection to the way Socrates treats the picture of an afterlife, of "removal from this place to another". What I mean is: it is not a question of providing a doubt to this hypothesis, a doubt that seems to lend certainty to their denial that there is an afterlife. I don't wish to dispute any facts with them; I would simply say: I don't know with regard to the picture of an afterlife. It is not an unimportant picture to me, anymore than the picture of the last judgment is unimportant to me. That is not to say that I believe in these things [or even that I don't disbelieve in these things] as some people claim to believe in them with the certainty of faith. So maybe it is a philosophical [rather than a narrowly religious] question then, as far as I am concerned. But it is a question without an answer. Nonetheless I have tried to say, and I think it is true, that these questions without answers are not nonsense; they are not "sound without sense". (This all goes with "the fox has his burrow, but the son of man [not the biblical Son of Man] has no place to lay his head".)
"If all is to be lost, all forgotten, then nothing matters." Yet, although "here we find no continuing place", the picture of "a continuing place", of an afterlife, is very important to us, as is the picture that there is no continuing place, no afterlife. But of course, Socrates would never have said that nothing matters if all is to be forgotten, all lost, because there is still a good for man, and the wise man will seek out that good and live according to it. We do not believe that we shall end our life by wrapping a pretty bow around it -- and then tossing it into the trash; in this sense, we do not live in order to die, but for the good. If only you can keep that bright ideal of the good before you, not falling into bitterness because of all the ugliness in life; if only you can look up to what is higher, not despairing of what is lower.
God was made for man, not man for God (pace Augustine). That is, the concept 'God' -- the "grammatical" rules for using the word 'God' -- was made for man, by man, as a tool for man to use, like any other word of our language. Just as all pictures were made by man for man to use (or to mystify himself with).
Plato's strange Ideas
Asking the wrong questions is a sure way to remain ignorant. What do I mean by 'wrong'? Questions that are based on preconceptions [i.e. notions taken for granted] or pictures that are inapplicable [e.g. "the theory of abstraction"] or false [as in the following example]: misconceptions. For example, the misconception that (1) all nouns are names, and (2) the meaning of a name is the thing the name stands for, and (3) the thing may be anything -- i.e. any entity, of whatever kind, whether perceptible by the senses or presumed to be ghost-like (for a ghost the thing must be if it be not perceptible); and e.g. therefore, so that picture of meaning says, the word 'mind' is the name of a thing, and the thing the name stands for is a ghost.
If you do not break free of that misconception, then you will never understand the logic of our language, the tool of all philosophical thinking (although, in some cases, it is possible to think worthwhile thoughts without that understanding). (Of course it may be impossible to break free of a misconception if one knows of no alternative conception to it.)
Query: can a ghost sound like crumpling-paper noise?
That is, of course, a grammatical question. It asks for a convention, a rule for using a word. It does not ask about "the nature of ghosts". It is in appearance a factual question ("Is it possible -- is it a real possibility?"), but once we understand the logic of our language we see that it is a conceptual question (RPP i § 949) (a question of logical, not factual, possibility).
Query: is logic and wisdom the same thing?
That is also a grammatical question. "Do these two words, 'logic' and 'wisdom', name the same ghost, ghost-like something floating around somewhere, but somewhere not too far away?" [More examples of Ghost-like Objects ("concepts"), and meaning versus sense (a possible distinction, but one that may mask a misconception).]
Another example of a misconception or false picture [of the logic of our language] springs from a requirement [preconception] Plato brought to his investigation, for it was not the result of an investigation (cf. PI § 107):
Plato did not spring directly from Socrates, nor was Socrates his first teacher in philosophy
In his youth Plato had been familiar with Cratylus and the Heraclitean doctrines, according to which all things perceived by the senses are in incessant flux, and there is no such thing as scientific knowledge [Comment: for by 'scientific' is meant what is universal and unchanging (as e.g. the general laws of physics are thought to be)] of them, and to this part of the doctrine he remained true through life.
Socrates, however, though confining his examination to questions of moral conduct, and giving no study to the nature of the universe as a whole, sought within the moral sphere for the universal, and was the first to concentrate his attention on definitions.
[Socrates, however, was busying himself about ethical matters and neglecting the world of nature as a whole but seeking the universal in these ethical matters, and fixed thought for the first time on definitions; Plato accepted his teaching, but held that the problem applied not to sensible things but to entities of another kind -- for this reason, that the common definition could not be a definition of any sensible thing, as they [sensible things] were always changing. (987b1-7, tr. W.D. Ross)]
Hence Plato, who succeeded him, conceived ... that the objects thus defined cannot be any sensible things, but are of some different kind, since it is impossible that there should be a general definition of a sensible thing, as such things are incessantly changing [are in incessant flux]. Hence he called this kind of things "Ideas", and held that all sensible things exist by the side of them and are named after them; for the multiplicity of things called by the same names as the Ideas exist, he holds in consequence of their "participation" in them.
In this theory of participation the only innovation lay in the name, for the Pythagoreans say that things exist by "imitation" of the numbers, and Plato by "participation" [a mere change of a word]. But what this "participation in" or "imitation of" the Ideas may be, they left for their successors to inquire. (Aristotle, Metaphysics 987a-b, tr. A.E. Taylor)
The example of Plato's Rationalism (Phaedo 99d-100a): "all things perceived by the senses are in incessant flux ... and to this part of the doctrine he remained true through life" (987a); in other words, the doctrine was a picture -- a precondition, a fixed criterion -- that guided Plato's thinking, and his acceptance of any new proposition was decided by whether or not he could fit that proposition into his picture.
Query: Socrates, quantifiable versus unquantifiable.
In the Euthyphro, Plato makes that distinction -- almost; rather, he distinguishes concepts that are quantified from concepts that are not quantified. But Plato's notion is that all concept-words, if they name Forms, must be quantifiable (All the Forms are quantified -- for otherwise they could not be objects of knowledge, and were that the case then we could not recognize anything that participates in them because we could never have known the Forms themselves). And thus the Forms of ethics -- i.e. piety, courage, wisdom, justice, self-control -- must also quantifiable, although we have not as yet discovered in which way they are quantified. And that discovery is what Plato's Socrates wants to make in his discussion with Euthyphro. (Plato's notion is, of course, a requirement brought to the dialog, not the result [conclusion] of the dialog's investigation.)
Grammar describes both language's syntax and semantics
Query: in your own words, define logic.
That is, by the word 'grammar' we mean such a description (rules of use). What you can say is that "a noun is the name of a person, place or thing" [or, "of something", or, "of some object"] serves as a model, semantically misleading, but syntactically useful. It says (as if it were a rule): Take the place and role of a name-of-object word (whether a proper name or a common name) in a sentence as your syntactic model. Something like this. Wittgenstein's "grammar" focuses on sense (semantics), because we already know the syntax of our language: we are already fluent in that aspect of our language; it is the semantic aspect of grammar that we are not fluent in (and out of which, therefore, philosophical muddles may arise).
I cannot put anything "in your own words" for you -- i.e. I cannot do your thinking for you. I have written a few historical notes about the word 'logic', but those are "in my own words" (my own thoughts). Dare to think (The worse that might happen is that you become a philosopher).
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