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Synonyms provoke Philosophical Insight

A slight change of words may cause us to see something new in something old.

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Synonyms I did not See

Query: Wittgenstein, webs of meaning.
Query: Wittgenstein, language, web, net.

A web is also a net: a frame of reference as a spider's web, if, that is, a spider's web is able to catch only certain types of insects, but not all, that pass into it, depending on the size and strength and other characteristics of its mesh. (For this simile's application to the meanings of 'meaning', see Wittgenstein's net.) Although the word 'web' is synonymous to the word 'net' in this context, it nonetheless adds a new image to Wittgenstein's simile: instead of the grid of the fisherman's net, there is the mesh of a spider's web. (What can be done with the new image is another question.)

Query: illustration of Gestalt switch with woman's face.

We say 'shift', but 'switch', although synonymous, makes our meaning clearer, but the instantaneousness of the experience is maybe captured by 'pattern snap'.

Query: language games for family nouns.

Well, why not call (at least some) common nouns instead "family nouns", or, common names "family names"? That would be consistent with Wittgenstein's account of the grammar of common names. But note: (1) some but not all, for some common names do have defining common natures (the word 'simile' e.g. is defined as 'a comparison using the word 'like' or 'as''; Plato cites 'quickness' as another such word), and (2) what meaning is to be given to the word 'family' in Wittgenstein "family resemblances" metaphor is unclear; the metaphor seems stillborn.

Query: what is the word that defines a place where there is no time?

This query especially interests me because of the way it uses the word 'define' -- i.e. to go from a phrase to a word, which is a reversal of the usual [normal, expected] direction. If the query seeks a noun, what is the noun it seeks? For 'timeless' is an adjective, 'timelessness' a noun-form of unclear use -- but neither is a place-name. And there are different pictures of eternity and Heaven and Hell [Hades], not all timeless (e.g. if death is not a dreamless sleep, then after death Socrates hopes to question the shades in Hades to see if any there are wise [Plato, Apology 41b-c]). "What word defines 'a place where there is no change'?" because without change there is no way to measure time and therefore without change there is no time (i.e. the word 'time' is defined by how time is measured).

Query: why does Socrates say the fear of death is unethical?

What is unwise (foolish) is unethical? It is foolish to fear what one does not know whether or not should be feared (here: death), and therefore it is unethical to fear death (Apology 29a)? It is unethical to think you know what you do not know? (The mesh of concepts: we are looking to see the connections among concepts here.) Using 'unethical' as a synonym of 'foolish', and 'ethical' as a synonym of 'wise' -- certainly we can say that Socrates does this in his ethics.

Two aspects to living-goodly

Query: man is free so long as he can master himself. Socrates.

"No man is free who is not master of himself" (Epictetus, Fragment, tr. Crossley) -- but rewritten the idea is shown from a different direction -- that makes its meaning clearer? No, not that. The query's form suggests what the man who would be free must do, whereas the form in fragment is only a description of the human condition.

Note that according to Socrates, virtue is knowledge, which means that a man can only be his own master if he knows what the good is for him, because if he misperceives what that good is, he will be a slave to his ignorance. Thus for Socrates there are two aspects to self-control [mastering oneself], the first being (1) knowledge of what is good; and the second being (2) resistance to base instincts and to bad habits formed in the time of one's ignorance of the good ... but "resisting temptation" -- as if the question here were of resisting choosing what is bad rather than what is good -- is a mistaken notion: rather, Socratic self-control = self-watchfulness. Because man -- (in contrast to the gods, who are fully rational) -- is a "rational animal", i.e. because man is partly irrational, the irrational part of man, namely his beastly impulses and instincts, has to be "resisted" (held in check) if man is to be master of himself.

And, men say, resistance is "an act of willing". But does the nebulous notion "willing" make anything clearer: "Man must will to resist his impulses towards what is evil" versus "Man must resist his impulses towards what is evil"? I think the notion 'willing' is a hiding-place for ignorance, i.e. for pretending we know or understand what we don't know or understand. For it is no clearer to say that the virtuous life requires knowing and "willing" than to simply say that it requires knowledge and self-control.

The Eternal Questions and Wisdom

Query: what did Socrates mean when he said was wise yet ignorant?

Just by changing 'not wise' to 'ignorant', the meaning is made clearer: Socrates' only wisdom was knowing that he was not wise = Socrates only wisdom was knowing that he was ignorant, i.e. that he did not know what someone who is wise would know (namely the answers to the eternal questions), if anyone were wise, which, if no one is wiser than Socrates (Apology 23b), then no one is. [Socratic wisdom: 'ignorant' = 'unknowing': not to think one knows when one is unknowing.]

Preface. Much wrong-doing requires self-control. But as such then is self-control a virtue? And then are 'self-control' and 'temperance' synonymous, or is by 'temperance' meant 'knowledge of the good plus self-control'? But if virtue is knowledge, then why is self-control required for good-doing, or, good-living (if all living things aim for their perceived good)? And yet it does seem that self-control as such is a human excellence -- although it is not a moral excellence (moral virtue). (The two parts of living wisely: knowledge and resistance.)

"Incontinence is ignorance" (Virtue is knowledge only if man is free to act)

Now we may ask how a man who judges rightly can behave incontinently.... Socrates was entirely opposed to the view [that "when knowledge was in a man something else could master it" [Plato, Protagoras 352b-c] (1145b24)], holding that there is no such thing as incontinence; no one, he said, when he judges acts against what he judges best -- people act so only by reason of ignorance. Now this plainly contradicts the observed facts, and we must inquire about what happens to such a man; if he acts by reason of ignorance, what is the manner of his ignorance? (Aristotle, Nicomachean Ethics 1145b25-30, tr. Ross. Note that according to Guthrie (Aristotle (1981), p. 360, 360n1) "contradicts the observed facts" is a mistranslation: Aristotle's meaning is "contradicts common belief".)

What does the word 'incontinent' mean here? Would that be the same as 'intemperate' = 'lacking self-control' or disobeying the Delphic motto "Nothing too much"? I don't know. But does it simply mean 'yielding to sensuality'? According to Guthrie, the Greek word (akrasia) which is usually translated by the English word 'incontinence' means "lack of [self-]mastery" (ibid., p. 364). But isn't 'self-mastery' simply a synonym for 'self-control'? [The word 'continence' = 'temperance' is another synonym for 'self-control' (cf. self-restraint).]

What must be added to Aristotle's account, if that account is to be useful to ethics, is: when a man is free, he does not act against what he judges best, not if virtue is knowledge he does not. For if a man is thrown from a roof, although he judges that it is best for him not to hit the ground with force, he nonetheless cannot help but hit the ground with force. Similarly, a man overcome by sleep cannot force himself to stay awake, even if falling asleep [and therefore being no longer vigilant] costs him his life. Nor can many men deny themselves water if they are dying of thirst, nor food if they are suffering great hunger, not in the normal case (for a father may choose death so that his children may live in the exceptional case), that is.

Therefore, when a man is free he does not act against what he judges best. For where there is no freedom of choice, there can be no ethics (That is a tautology, but it is not a tautology that "says nothing" -- but instead one the points out interconnections among our concepts). (The notion of "voluntary incontinence" is of no use to ethics ["Now we may ask how a man who judges rightly can behave incontinently" should be "Now we must ask if the man who judges rightly can behave incontinently" -- and, Note, this is a conceptual investigation: the possibility being discussed is logical possibility, if, that is, ethics is practical rather than merely descriptive and indifferent to how man should look at things if his aim is to amend his life], if ethics is practical -- i.e. if it is directed toward helping us become good human beings. It simply lands us back at the unserviceable-to-ethics notion of "weakness of the will".)

Query: is grammar the logic of languages?
Query: isn't grammar the logic of language?

Here the form of the question makes it look as if what you were asking for is a real definition -- i.e. a proposition of fact -- about grammar -- whereas whether or not grammar = logic is a question of how we are going to define the words 'grammar' and 'logic'. In the jargon of the "later" Wittgenstein (Russell's WII, or the "second" as contrasted with the "first" Wittgenstein), the answer to the query is Yes, more or less: 'grammar' = 'rules for using signs', and part of grammar -- namely, 'logic' = 'rules of sense and nonsense' ... although that definition is only useful if meaning is not a matter of form but of use in the language, which Wittgenstein believes he demonstrated it is.

But that is not the only way people have placed or set the limits of the concepts 'grammar' and 'logic'. Words are tools and those two words have been assigned different tasks by different authors and thinkers at different times.

Query: the investigation of the meaning of words is the beginning of education, Antisthenes.

I don't know if Antisthenes said that. He did say that "A proposition says what a thing is" (Diog. L. vi, 3) and to say what a thing is, according to the ancient Greek way of thinking, is to define the meaning of its name. About the query's "education", that is certainly a statement that would characterize Socrates' method in both Xenophon and Plato, if by 'education' is meant 'search for truth'. However, that is not merely the beginning of education, according to the Socratics, but its beginning, middle and end.

Query: the excellent life, Plato, Apology.

Does 'good' = 'excellent'? Those words do have similar grammars, quite similar -- and they both allow many different criteria to be set for their application (e.g. from different points of view). Rough synonyms maybe. Cf. the next example:

Query: Socrates' meaning of what is a worthy life.

I.e. of the [way of] life worth living as opposed to the [way of] life "not worth living" (Plato, Apology 37e-38a). The life worth living for man is the life that is proper to his nature, or in other words, the life that is in accord with the "virtue" or characteristic excellence of his nature, which obeying the command "Know thyself" should by the use of thorough-going reason and the tests of reason and experience tell man.

Query: Socrates' quest from the oracle at Delphi.

It seems that I do not think in synonyms naturally; they have to be pointed out to me. Does 'quest' = 'mission' in this case? What was Socrates' quest? According to Plato (Apology 23b): to demonstrate through the method of question and answer that no man is wise, for if no man is wise, then "no man is wiser" (ibid. Apology 21a) than Socrates: "It seems to me that [the god] is not referring literally to Socrates, but has merely taken my name as an example ..." (Apology 23a-b, tr. Tredennick).

And Socrates' quest in my view? To discover whether his own solution to Apollo's riddle was correct or not. For, note, that the Platonic Socrates' answer could only be a solution, one of many possible solutions. There are many ways this story may be told, and there is no way to know whether or not Plato's Apology is an account of what really happened (or, history, for Plato's work is philosophy, not historiography). (Cf. Socrates' mission according to W.K.C. Guthrie.)

Query: how does Socrates test the oracle's riddle and what does he discover?

The first part of Socrates' quest was to find a meaning for Apollo's riddle that "no man is wiser than Socrates" (because it was clear to Socrates that Socrates himself was without wisdom, for if he had been wise he would have been "able to tell" -- i.e. to give an account of his wisdom to others that could stand to the test of cross-questioning in discussion). The second part of Socrates' quest was to daily test whether this meaning was consistent with what he found when he questioned various men who were reputed to be wise (to discover whether or not any of them was wise).

Query: why does Socrates want people to have wisdom?

So that they will know what the life that is the good for man (the specific excellence proper to man) is, and, therefore, will live that life ("Virtue is wisdom"). That is the aim of Socrates' work in philosophy -- namely, Ethics or How we should live our life (Logic [or, Dialectic] is only a tool toward that aim). But we could also say: because he wants people to be happy (The good man harms no one, but benefits all men, as Plato shows in Republic 335b-335e).

Query: love of thinking, Greek.

I don't know if the Greek word sophia can be rendered into English as 'thinking'. Is philosophy "the love of thinking" (Plato, Phaedrus 278c-d)? Well, if 'thinking' means 'learning' (ibid. 230d), maybe, but it must be, I think, "thinking about logic, ethics and/or metaphysics".

More Ghost-like Objects ("concepts")

Note: this supplements the discussion "all nouns must be names, either of visible or of invisible entities". (Discussed below: 'geometric line' as an abstract concept)

Query: explain why 'point', 'line' and 'plane' are abstract concepts such as 'love'?
Query: why are 'point', 'line', and 'plane' abstract concepts like 'love'?

Note: that is not a philosophical question. The philosophical question is: are point, line and plane abstract concepts like love? (The conclusion comes at the end, not at the beginning, of an investigation. Unless a child be a parrot rather than a thinking human being.)

And even prior to that is the question of whether the concepts 'point', 'line', 'plane' and 'love' are "abstract concepts", whatever an abstract concept is when it's at home!

What does the query mean by calling 'love' an abstract concept? That we cannot state what the essence of love is, but must somehow (I don't know how; magically apparently) "abstract" its meaning by being acquainted with the various phenomena we call 'love'?

But if that were how we explained the meaning of (i.e. defined) the word 'love' -- i.e. if it were the case that we knew the meaning of that word but were unable to tell what we knew -- then how would we know whether we or anyone else had abstracted that word's meaning correctly? That does not, therefore, seem to be a true account of how we use the word 'love'.

If the word 'abstract' in the query means anything other than that the word 'love' is a non-name-of-object word -- i.e. a word we do not define ostensively (i.e. by pointing at an object, as we define the word 'cow' e.g.), then what more does it mean? A ghost, a shadow, a notion "in the mind" that just somehow (who knows how) must exist?

In Wittgenstein's work there is a logic of meaning, not a theory of meaning. Logic describes practice, a description of what is public, objective, verifiable about our use of language. In practice, as opposed to in any theory, our common criterion for saying that someone knows the meaning of the word 'love' is whether he calls the various phenomena that everyone normally calls 'love' by that name. Experience offers no reason to suppose that all these various phenomena have any one thing in common, an essence. If we describe what we know, rather than what some theory demands (because "it seems that it just must be that way"), then all we can point to are various resemblances among the phenomena. In logic we say no more than what is public and knowable by anyone. ("Do I know any more about it myself? Or is it just other people I cannot tell?" ... which is very Socratic: for if a man knows anything he can give an account of what he knows to others.) If that describes the practice of how we use the word 'love', then that use of the word is the word's meaning -- or which other meaning of the word 'meaning' should we select in order to make an objective distinction between sense and nonsense?

If it were said that it is "impossible to define" the word 'love' or that the word 'love' is "undefined", that would mean no more than that we do not define the word 'love' by pointing to an object (There is no barer of any kind -- whether visible or invisible -- of the name 'love'), but rather that there are a variety of phenomena we call 'love', but no one defining characteristic of love (i.e. of everything that we call 'love').

That picture of how our language works -- i.e. the theory of abstraction of unstateable essences -- is the preconception the ridding of which is our whole problem in logic: "abstract" (ghost-like), "concept" (notion in the mind, as if the word 'mind' were itself the name of a ghost-like object) -- as if the meaning of the words 'abstract' and 'concept' or the combination of those two words were clear to everyone, clearer even than the meaning of the words 'point', 'line' and 'plane' in geometry! The combination of words 'abstract concept' is at best suggestive of "something" (the notion of a something ghost-like in a ghost-like somewhere), at worst nonsense (i.e. mere sound without sense, what logic means by the word 'nonsense') -- and as such it makes nothing clearer.

"Invisible concepts"

Query: words such as 'dog' and 'horse' name concepts that are invisible.

Common names ("concepts") ... "dog-ness" and "horse-ness"? No one has ever seen either, which makes them rather like "muchness" (as in 'much of a muchness'). Well, are you going to call that a "theory of meaning"? But if you can only define 'dog-ness' by pointing at individual dogs and saying that all dogs have a common nature (essence) although no one can say what it is ... Is that a "logic of language" -- i.e. does it make an objective distinction between sense and nonsense? If a word cannot be defined ("no one can say what it is"), then how is sense to be distinguished from nonsense? -- Is it not the case that "whatever seems correct is going to be correct, but that only means that we cannot speak of correctness here"? -- i.e. there is no objective way to distinguish and therefore there is no distinction.

Query: invisible abstract concept.

Why are we human beings so gullible? credulous, naive -- vulnerable to word magic, like children swallowing "ghost stories" about "intangible objects" such as justice and love ... Well, don't justice and love exist? we ask ourselves.

Is there a darkness too profound for one to grope one's way out of? There are wells too deep to climb out of without a ladder (philosophers construct their own, but philosophers are the rarest of creatures), or without a rescue rope someone has extended down to one (as a philosopher does, if one can grasp it, although one still has to climb up the rope by oneself: "what a philosopher has seen is difficult to see, and whatever it has cost him it will cost you too" (cf. CV p. 10, 13)). That apropos of misconceptions. For who has ten years to give to philosophy, as I needed those years to learn to see language as I think Wittgenstein later saw it -- or, rather, as I think Wittgenstein looked at language and as I think it should be looked at, namely that, in many cases, the 'meaning of a word' is most serviceably defined in logic -- because our aim is to distinguish between sense from nonsense, not leaving that to whatever "seems to make sense" to someone or other -- as 'its use in the language' (PI § 43).

Both the words 'dog' and 'horse' are the common names of objects, but they themselves do not name objects, neither visible or invisible (tangible or ghostly), but have a different use in our language. They are the names of classes, we say, but the meaning of a class name is not the membership of that class (Otherwise the common name 'dodo' would be meaningless, because that species of bird is extinct), nor is it what all members of that class have in common (for the members of most classes do not have a defining thing in common). And what is that use? That is all we know and --

Logic is not speculation -- it is, rather, distinguished from speculation. The picture that the meaning of the word 'dog' is the invisible concept 'dog-ness' or 'dog-hood' belongs to Plato's metaphysical theory of Forms, Plato's solution to the perplexing question of the meaning of common names, not to the facts of our language use in plain view. And those facts are what concern the logic of language.

Seeming correctness

... in the present case I have no criterion of correctness. One would like to say: whatever is going to seem right to me is right. And that only means that here we can't talk about 'right'. (PI § 258)

It is precisely a "criterion of correctness" that makes a proposition true or false, and that includes statements about the meaning of words. And if that is the case, then what service does the word 'dog-ness' perform? (It gives ignorance sanctuary: it makes it appear as if we knew what we don't know.) Curious that the word 'dog-ness' or 'dog-hood' is not found in the dictionary, because e.g. the word 'abstraction' is.

Sometimes the word 'abstract' is used to contrast with the word 'tangible' (or, 'touchable'). Consider the statement: 'You can't touch love'. Is it clear what anyone might mean by that combination of words? (What would it be like if you could.) "You can't touch love." -- "Can't you?" You can see a line drawn on a piece of paper, just as you can see the piece of paper itself -- aren't they both "tangible"? See the next query. (If 'love' is defined ostensively, it is not by pointing to an independent thing named 'love' but to things that illustrate love. "You cannot touch love" (how a child acquires the concept 'love').)

Concepts are selections and deselections. To invent or revise a concept is to make a selection.

Query: why 'point', 'line', and plane are abstract concepts

We might think to answer: because the words 'point', 'line' and 'plane' are not defined ostensively (that is, by pointing at an object); indeed, nothing in axiomatic geometry is. And yet that won't do, because explanations of meaning for those words -- explanations that involve ostensive definition -- are needed. We could say that those concepts are "abstractions" -- i.e. that they abstract -- i.e. select -- some qualities of ostensively defined words and deselect others -- at least in the case of 'line' and 'plane' we can say that; to say that about 'point' in geometry (wherein the word 'point' is simply used to mean 'a unique address in the plane') would however be not merely misleading -- but wrong.

What does the query mean by 'abstract'? We use only those features of actual lines and planes -- i.e. shapes we can draw on paper or illustrate with a flat piece of paper -- which interest us: that is, we select and deselect features (e.g. we select the extension of a line, but deselect its width or height, because any line we draw or any sheet of paper has the features of width and height) to include in our concepts -- i.e. our rules for using the words -- 'line' and 'plane' in our geometry.

Is it helpful to define 'abstract concept' that way -- e.g. what type of concept are we contrasting with it -- for all concepts involve selection? Or, in other words, all concepts are abstract.

"All concepts involve selection." But do they? Is there a concept 'cow'? We define the word 'cow' by pointing at cows, or at photographs of cows, things like this. And what concerns us is the whole beast; we do not select e.g. only its ears or hind legs. But on the other hand we do deselect certain features of cows, e.g. their color: a cow is still a cow if its color is black with white patches or light brown or blue (as in fairy tales).

Concepts are selections and deselections of data: Concept-making is selection. To invent or revise a concept is to make a selection. Compare Goethe's "All fact is already theory", replacing 'theory' with 'concept': all fact is already conceived-fact.

Query: metaphysics is the investigation of the reality behind the appearance of things.

And what is the reality behind metaphysics -- what is it [metaphysics] really?

If we look back to the pre-Socratics and to Plato, that is indeed their intent. But it is not, according to Wittgenstein, the reality of metaphysics, for metaphysics is not an investigation of facts (and it is facts, of course, that are the reality) of any kind (whether visible or invisible). Rather, metaphysics chases after a ghost it calls 'reality', which it imagines to exist "behind the appearances" (i.e. behind what we normally call 'the facts'), a reality that cannot be seen, but which must, according to the way of thinking of the metaphysicians, exist. Indeed, the reality posited by metaphysicians, a "reality" which we do not in any way perceive, is claimed by them to be more real than the "appearances" we do perceive. Metaphysics thus consists in substituting a picture of our own creation for the facts in plain view. That is the reality of metaphysics, according to Wittgenstein in any case.

Query: unanswerable questions in life are those that we cannot find answers to using science, our senses, or logic alone.
Query: is there any question that has not been answered?

The statement of the first query is an example of "a real definition of unanswerable questions"; it is utterly oblivious to the possibility that a question may be unanswerable because it is nonsense -- i.e. an undefined combination of words, because no criterion has been set for a correct answer to it). It is thus an example of philosophy pre-Wittgenstein ii (Russell's jargon for the post-TLP or "later" Wittgenstein). And what has science to do with the ethics of how we should live (our life)? (Superstitious -- or naive -- belief in the power of the scientist as one who knows all things, whether in physics, psychology, or even right and wrong; cf. the second query.)

Similes I do not See

Query: undefined terms of geometry and faith.

They are different in this respect: that it is not logically impossible to define the so-called undefined terms of geometry.

But are the so-called mysteries of faith only examples of self-mystification by means of language, a mere anthropological curiosity (about the human species, human culture, the enculturation of children)? When Jesus tells us to call God our father, do we understand this? But is it not nonetheless important to countless human beings. Thus it makes nothing clearer to compare language as it is used in religion to our everyday language, except to show that language as it is used in religion is for a blunder, too big -- i.e. it are not a blunder, but something else is being done with language there (And what is that something? I don't know). But is not calling God our father, the loving father who forgives his child's wrong-doing, also an instance of anthropomorphism? Everything we say about God is anthropomorphism -- except the contradicting rule which says that nothing anthropomorphic can be said about God. Which is to say that, unlike geometry's "undefined terms", it is not logically possible to define 'God'.

Query: seeing aspects, Wittgenstein, religion.

The Gestalt shift is in this case a metaphor, like 'concept-blindness' (Wittgenstein and blindness to the concept 'God'). But how is that like the duck-rabbit? Suppose it were the case that some people could (as perhaps some really can) only see one or the other aspect. But how is being unable to see the rabbit-aspect (e.g.) to be compared with not being able to understand how any reasonable human being could seriously use the word 'God' (how the concept 'God' may have an important place in a reasonable man's thinking), how he can use the concept 'God'? Can someone be blind to the religious aspect of life? But what is the difference here between blindness -- and seeing but dismissing as of no importance, nonsense or a delusion? Can someone also be blind to that dismissal? In sum, is the metaphor apt, for is this a question of not seeing an aspect of human life? That is what I don't know.

Abstract Emptiness

As a theory, "the theory of abstraction" -- what does it explain? It is a metaphysical picture, not an hypothesis, because it is consistent with any and all data and therefore cannot be put to the test. What would an anomalous case look like -- i.e. what would be an example of an anomaly, something which would disprove the theory of abstraction? What can come into conflict with it? But further, does it account for all the data? What are we calling the data here -- is it that human beings are able to use words they cannot furnish a general definition [or, state the common nature or the essence] of? How can we account for the fact that they are able to do this? (The presumption is, of course, that it is necessary for human beings to do this, as if that presumed necessity could not be simply a false account of the grammar of our language.)

Surely we cannot call abstractionism a scientific theory ... but then after all, why not -- for are we not willing to call evolution (Darwinism) a scientific theory and that picture cannot come into conflict with reality either?

There is an image of tracing light back through a prism which has separated the particular uses of a word from one another (and thus obscured their common nature) to the light's essence, which would be the separated particulars rejoined (and thus displaying their common nature). But this picture it idle because no way has been defined to apply it: it is a metaphysical picture, a picture of "the really, but unknown, real".

Maybe: abstraction emptiness.

Are numbers abstract?

Query: sample questions to define the meaning of a word or quality.

We might teach [or learn] the meanings [uses] of words this way, with a game that begins: "I'm thinking of something. What is it, then?" But the classification scheme of "Is it animal, vegetable, or mineral?" already points in the wrong direction: for not all words are names of things, and it is not the case that to "think something [think of something]" must be to think about things named by words that name things -- and that all things are objects of some kind, either visible (i.e. perceptible to the senses, whether naked or aided by instruments such as the microscope) or "abstract" -- i.e. essentially imperceptible. If you begin with that classification scheme (its only categories being 'perceptible' and 'abstract'), then if I am thinking of time, then the word 'time' must be the name of an object of some kind (an invisible object which does all kinds of marvelous things, one of which is to flow like a river).

The unclarity fostered by the word 'thing' -- is that it names a category so large as to include anything at all; the word 'name' can also be applied to any word at all, e.g. the word 'the' is 'the name of the definite article in English'. (etymology of the word 'synonym': same + name.)

Query: numbers are abstract.

Numbers are not names of objects; that is not their part of speech [or, grammar], but the word 'abstract' suggests something ghost-like, as if the number 2 were the name of a ghost. But that idle picture tells us nothing about how we actually use the word '2'; it is a false account of that word's grammar, and an instance of self-mystification.

"Numbers are abstract." -- Are you asking (which is Philosophy) or telling (which is Ideology looking for confirmation of a thesis)? Does saying that numbers are abstract make anything clearer? Does it not instead contribute more obscurity (darkness) than light (insight)? It is a mysterious statement about a mysterious something (and the mystery of it is all self-mystification). (What are numbers?)

Query: why do mathematicians use symbols instead of words?

But are not words "symbols" and is not '+' a word; it's not normally a sign we classify in the category 'words'. Similarities and differences. The sign '+' does not belong to a phonetic symbolism [or, notation] (but neither do the Chinese characters used as Japanese Kanji -- so then are Kanji not "words"?). Is a conventional (i.e. well-defined in meaning, as are Kanji and the ancient Egyptian hieroglyphs) pictograph that does not tell you how to pronounce itself a word? We read '2 + 2' as 'Two plus two' ("just as" Kanji can be pronounced and indeed rewritten in the phonetic alphabets of the Japanese language). Why use '2' rather than 'two' -- is it not because it is easier for the human eye to survey? To a machine [computer] which notion is used does not matter in the least. The classical Greeks used ordinary words to write their mathematics.

Is mathematics a language? Isn't a system of symbols a language, then? The proposition 'One water drop plus one water drop equals one [big] water drop' is a proposition of physics (natural science) or simply of everyday experience, but '1 + 1 = 1' is not a proposition of mathematics. (But then why not make just this rule, that 1 + 1 = 1? But mathematics is not simply a collection of rules; it is an interlocking system of rules: it is like a mechanical clock in which all gears must be engaged if the clock is to work.)

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