A better way to approach it is to forget about meaning and look to use. Knowing what a number is consists in being able to count, to add, to subtract, to do the things that we do with numbers; not with a definition set out in words. — Banno

I am not sure how you mean it. Human beings, I believe, are capable of classification according to features and of mental homomorphic representations without explicit involvement of applications, just by physical assessment. There is obviously always some action involved, because observation or measurement are usually tied in to some action, but the concept is not always action-oriented. It depends on the concept, and how we mean it.

For example, integers and natural numbers, as most discrete mathematics, are fundamentally tied in with counting. They are procedural by the very essence of their design, because without discrete generating processes, discretisation has no subject matter. There are other ideas involved, such as the equivalence of objects, but counting is the central idea. Real numbers are also inspired by a process, i.e. measurement, a.k.a. geometry. Analysis explains how we bridge the gap between counting and geometry through sequential approximations. In this sense, the intuition for real numbers is also procedurally inspired, but the subject matter of physical relations that we conceptualize through analysis and analytic geometry is not the actual application of a process, but the features exposed through the application of a process. Obviously, geometric intuition, as the name implies, is derived from the need for measurement, and obviously measurement is how we establish the relations in question, but unlike natural numbers where the procedure is the actual concept, geometry describes characteristics independently of the process involved in their determination. Still, I admit that you could argue that at the very fundament of physics, the determination of any geometric feature is connected to the time it takes for bosons to reach from one point to another, so you could argue that all manners of measurement processes are actually fundamentally related. But I would consider this argument belongs to a more fundamental discussion that deals with the static vs dynamic as a distinction in nature.

On the other hand, there are several other ways in which you could mean that actions are relevant here. First, counting specifically (for small quantities) may have preceded conceptualization historically, which may have appeared even before language did. So action may have preceded abstraction, because conceptualization, which apparently was sprung as a faculty linguistically, was not available and rote learned behavior was pertinent. Second, to establish the practicality of concepts, we evaluate their utility, which is usually ascribed to process application, i.e. uses as you put it. Lastly, inference itself is a procedure and usually well exemplified by correspondent real world process.

Edit.

I should have also stated that weighing gravitational mass and measuring time may have also had influence on the development of analysis. Thus, the study may have unified multiple procedurally unrelated subjects. Weighing and geometric measurement could have been seen as a totally separate aspects. However, now we know that inertial and gravitational mass coincide, and we can describe inertial mass, as well as other properties, such as energy, momentum, etc, through the trajectories of motion, and thus geometry. Frequency, albeit a general concept itself, encompassing all sorts of periodic phenomena, usually manifests as mechanical and field waves, either related to momentum and thus to the geometry of motion, or directly to geometric distances between sequential wave peaks and troughs. The measurement of distance itself, originally considered a subject of isometric application of a fixed template object, today is expressed as the rate of travel of electromagnetic signal in a fixed amount of time. Time in turn is measured relative to the period of electromagnetic wave that is emitted by specific energy transition in the electron configuration of an atom. What I mean by all this, is that currently, considering all our knowledge of physics, we can tie most applications of real numbers to the process of electromagnetic radiation.

And that's special pleading.

the concept is not always action-oriented. — simeonz

I disagree. Each concept has a place in a language game. But then, for most of you post I agree with .

@TheMadFool, incidentally, Fool's question was about "2", not 2, so I don't see that emancipate's syntactic answer was improper, nor @Isaac' plonk, but moreover @frank's lawnmower is a semantic example.

The notion that meaning is identical to use is wrong. — frank

That's not what was suggested. Rather, that in this sort of analysis we would do better to look to use rather than to meaning. As your lawnmower example shows.

And I will make the point again that I do not see any relevance to this digression.

"Would you care for another glass of 'Two Barrels'*?" — Isaac


That's a play on words, both meanings are using "two" as a number. — frank

No, because if the whiskey were called 'Three Barrels' and I asked for 'Two Barrels', I would not be given two thirds of a whiskey, I'd just be given the wrong brand. 'Two' in that sentence is not being used to count, it's being used to indicate the type of whiskey wanted (not that it ever would, Two Barrels is awful).

But yes, this is a digression. As you were.

No, because if the whiskey were called 'Three Barrels' and I asked for 'Two Barrels', I would not be given two thirds of a whiskey, I'd just be given the wrong brand. 'Two' in that sentence is not being used to count, it's being used to indicate the type of whiskey wanted (not that it ever would, Two Barrels is awful).

But yes, this is a digression. As you were. — Isaac

Not to put too fine a point on it, but branding doesn't obliterate the original meanings of the words involved. "Dos Equis", a so-so beer, has a name that should be understood to refer to two x's. Number used as name.

but branding doesn't obliterate the original meanings of the words — frank

:rofl:

I disagree. Each concept has a place in a language game. — Banno

The syntactical or neurological processing is undeniably an action. Symbolic inference using a deduction system is an action. Thinking is an action. In that sense, mathematics is alive, not stationary. And formal models are sound with respect to the matching between those evaluations made using rules and the facts of the real world. I got the impression that you consider the subject matter of a model, i.e. its interpretation, to be some action in itself. In other words, I thought that you might suggest that before we formalize stationary physical relations around us, we first discover them in terms of applications, uses, and activities. That without some active involvement on our part, it is insufficient to simply observe physical features in order to derive conceptualization. I was trying to clear out in what precisely sense you meant your remark.

TheMadFool, incidentally, Fool's question was about "2", not 2, so I don't see that emancipate's syntactic answer was improper, nor Isaac' plonk, but moreover @frank's lawnmower is a semantic example. — Banno

When TheMadFool quoted the numeral, I assume that they meant to emphasize the syntactical nature of the symbolic constant. Not to prompt interpretations that do not conform to the algebraic requirements posed by the axioms of arithmetic.

You do seem to have been attributing to me a whole lot of stuff that I didn't say.

If you subscribe to total moral and intellectual relativism, then of course there is no such thing as a correct intuition.

Fool's question was about "2", not 2 — Banno

I don't see how it could be otherwise.

If you subscribe to total moral and intellectual relativism, then of course there is no such thing as a correct intuition. — Acyutananda

Perhaps Wittgenstein is the go to person here. Moral intuitions, their variety and seeming incompatibility, is probably due to the fluidity of the concepts good and bad as they participate in distinct language games. Moral relativism assumes, contrary to Wittgensteinian thought, that good and bad refer to the same things, hence the relativism; without that assumption, moral relativism would break up into separate entities which have nothing to do with each other. Right?

good and bad refer to the same things, — TheMadFool

Do you mean "good and bad refer to the same thing [singular]," which would mean "good and bad refer to good-bad," or do you really mean "thingS," in which case the things would be something apart from good and bad? If you mean the latter, what would be examples of the things?

Well, yes. I was unable to follow @simeonz's account. For instance:

The syntactical or neurological processing is undeniably an action. — simeonz

The syntactical or neurological processing of what? An action on someone's part would seem to require some fiat on their part... as if my feeling a surface somehow required my consent.

Do you mean "good and bad refer to the same thing [singular]," which would mean "good and bad refer to good-bad," or do you really mean "thingS," in which case the things would be something apart from good and bad? If you mean the latter, what would be examples of the things? — Acyutananda

What I mean to convey is that it's possible that "good" and "bad" may refer to different concepts in different cultures i.e. morality may not be amenable to generalization across cultures. This is Wittgensteinian in character as you might've figured out by now.

Why bring Wittgenstein in at this juncture?

Well, moral relativism, to my knowledge, claims that moral values vary with culture with all of them being as equally right. However, for that to be true, the notion of morality has to be universal in scope i.e. every culture must mean the same thing when they use the words, "morality", "good", and "bad". If not then moral relativism doesn't make sense for then different cultures would be talking about different things when they use these words.

moral values vary with culture with all of them being as equally right. However, for that to be true, the notion of morality has to be universal in scope i.e. every culture must mean the same thing when they use the words, "morality", — TheMadFool

So you are saying that –

moral values vary with culture

– and –

every culture must mean the same thing when they use the words, "morality" . . .

– can both be true at the same time (and must be in order for W to be correct). In order for both to be true at the same time, your "moral values" must mean something different from your "'morality', 'good', and 'bad'."

Does your "'morality', 'good', and 'bad'" refer to CONCEPTS, while "moral values" refers to SPECIFIC ISSUES?

Would you say, for instance, "In Mexico they consider bull-fighting good and abortion bad, and in NYC they consider abortion good and bull-fighting bad, but in both cultures, when people hear 'bad' their minds become clouded and there's a yucky feeling in the stomach, and when people hear 'good' their minds become expanded and radiant" – ?

All I'm saying is for moral relativism to be true, the word "morality" in America must mean the same thing as the word "morality" in Iran for instance. Only then can we say morality is relative to culture - the same thing (morality) is culturally determined (in America homosexuality is ok but in Iran it's immoral). If, on the other hand, the word "morality" means different things e.g. in America it might have a meaning associated with equality and in Iran the word maybe associated with the Quran then Americans and Iranians aren't talking about the same thing are they?

I guess I now understand what you're saying, but – perhaps changing the subject – wouldn't you say that in order for the terms "good" and "bad" to be most useful, to be truly normative (using your examples), "good" in Iran would have be associated not only with the Quran, but also with a positive quasi-emotional feeling, and "good" in America would have be associated not only with equality, but also with a positive quasi-emotional feeling?

I guess I now understand what you're saying, but – perhaps changing the subject – wouldn't you say that in order for the terms "good" and "bad" to be most useful, to be truly normative (using your examples), "good" in Iran would have be associated not only with the Quran, but also with a positive quasi-emotional feeling, and "good" in America would have be associated not only with equality, but also with a positive quasi-emotional feeling? — Acyutananda

We would all converge to a point (a set of ideas) but the cost of that is we'd be losing out on the richness of human thought.

We can all agree on word definitions, for the sake of communication, without agreeing on anything else. People of all cultures can agree that "good" should be associated with a positive quasi-emotional feeling, even if in some people that feeling is elicited when they hear "marry whomever you love," and in others when they hear "throw homosexuals off rooftops." I wouldn't see any value in lack of agreement that "good" should be associated with a positive quasi-emotional feeling, and thus people talking past each other.

I.e., I wouldn't call people talking past each other, due to lack of agreement about defs., "richness," because to me "richness" has a positive meaning.

We can all agree on word definitions, for the sake of communication, without agreeing on anything else. People of all cultures can agree that "good" should be associated with a positive quasi-emotional feeling, even if in some people that feeling is elicited when they hear "marry whomever you love," and in others when they hear "throw homosexuals off rooftops." I wouldn't see any value in lack of agreement that "good" should be associated with a positive quasi-emotional feeling, and thus people talking past each other. — Acyutananda

Aah! You mean to say that "positive feelings" are not a good yardstick for morality. I agree for the reasons that you put forth. Americans may feel good when they see homosexuals marrying each other but an Iranian may experience the exact same "positive" emotions when they see homosexuals taken to the gallows.

Yet, there seems to be something generic about morality in re "positive feelings" - we feel good, barring some exceptions, for the same things - a partner, a family, friends, food, health, helping others, shelter, clothing, amenities, etc. Should we ignore the many instances where "positive feelings" are aligned to our ideas of morality and focus only on the cases where the two don't concur?

You mean to say that "positive feelings" are not a good yardstick for morality. — TheMadFool

I mean that they ARE a good yardstick for the meaning of the word "morality," but not a good yardstick for which actions are genuinely moral. I think that some actions are genuinely moral and some are genuinely immoral – in other words, I believe that an objective morality exists. (This discussion all goes back to my saying "Intuitions can become more and more correct. . . . I think that we all, to different degrees, possess deep in our minds a capacity for more and more accurate feelings of knowing," and your feeling that that statement of mine did not jibe with something else I had said.)

Let me illustrate. Suppose there are a dozen Americans and a dozen Iranians who agree with me that "good" should be applied to actions that elicit in the speaker a positive feeling – not an emotion exactly, but definitely a feeling, not part of any rational process, a unique feeling often called a moral intuition – and "bad" should refer to actions that elicit in the speaker a unique negative feeling. If the action is one's own, the mechanism that causes the positive moral intuition or the negative moral intuition to arise is known as the person's conscience. So all these people will completely understand what the others mean when they use the words "good" and "bad".

Nevertheless, those particular dozen Americans will say, "I did something good today. I feel good about it, moral about it. I helped a couple in some fundamentalist country have a same-sex wedding." And those particular dozen Iranians will say, "I did something good today. I feel good about it, moral about it. I helped get a couple hanged for having a same-sex wedding."

Yet I would not say that all those people's moral intuitions are equally valid (moral relativism).

Let's find the most uncontroversial example we can. If someone experiences the negative feeling, the "This is bad" moral intuition, when they see someone torturing puppies for fun, I think that is an objectively correct moral intuition. If the torturer and his friends have a different moral intuition about it, I think their intuition is simply incorrect, and should not be framed as "their truth" or "all right from their point of view."

And I think that any person's moral intuitions can become more and more correct. When asked me how they could become more correct, I replied, "I think that the most basic answer is meditation, but I would like to say a little more." Then other participants sidetracked me from that discussion.

Epistemology is the science of knowing, and knowing is possible only in the mind. The mind plays thousands of tricks, but still, knowing is possible only in the mind. Meditation is designed to cast sunlight on the tricks as they originate in the mind, so that the tricks shrivel up and fall away. So to me, it seems that meditation is indispensable for epistemology.

I have little formal background in Western philosophy, but I'm under the impression that in Western philosophy, propositions such as "'2 + 2 = 4' cannot be proved, but rather rests on intuition" and "'A square must be rectangular' cannot be proved, but rather rests on intuition" are rejected, or considered true but trivial. If my impression is correct, I would like to know why such propositions are rejected, or considered true but trivial. — Acyutananda

To see this, you have to try to conceive of something as being irreducible, which is what an intuition is supposed to be, a non discursive disclosure, a "knowing" that issues straight out of the belly of the world, unmediated by anything else. If something like this actually existed, it would be monumentally important, as if God had written it on tablets, but with out the God or other weird metaphysics. As if Being "spoke" its nature.

Of course, logic and math are intuitive, you might say, but is it true that these are simple, irreducible things? Just because thought cannot get "behind" logic, because doing so would require logic, doesn't mean logic is IT. It is not accessible, but only shown, but, as Wittgenstein tells us, even to talk like this is nonsense. A true expression of intuition cannot be made sense of at all, for the language one is using to express it cannot stand apart from itself. even if it could, a third perspective would then arise to validate this, a third medium that is NOT logic, and this is not conceivable.

Thanks. I need a few clarifications, but let me start with the easy part, which is also a necessary part. Do you mean that correct intuitions (which I believe exist), would be monumentally important, as if God had written them on tablets?

I believe that correct intuitions exist and are monumentally important. But I don't see why for every correct intuition that exists (there is a maximum of one correct intuition per issue), I should consider all the many incorrect intuitions that might exist on the same issue to be monumentally important.

I would not call any intuition, correct or incorrect, important or not, irreducible. My intuitions are by definition feelings (of a certain sort) whose origin is presently unknown to me. An intuition comes out of my unconscious in some way that I cannot understand. But I think it must originate in some way that I cannot presently understand – must be reducible to something that I cannot presently understand – but that I may (or may not) later be able to understand.

If I understand correctly, Wittgenstein's main works were the Tractatus and Philosophical Investigations. Can anyone tell me what writing of his in those books or elsewhere best addresses my concerns?

On the matter of numbers, it looks like Wittgenstein is N/A. The meaning of numbers is confined to mathematics i.e. for a number, say 2, there are no other contexts in which 2 has a meaning. In short, the meaning of 2 isn't a use thing. — TheMadFool

“The concern with grammatical propositions was central to Wittgenstein's philosophy of mathematics because he wanted to show that the 'inexorability' of mathematics does not consist in certain knowledge of mathematical truths, but rather in the fact that mathematical propositions are grammatical. The certainty of'2 + 2 = 4' consists in the fact that we do not use it as a description but as a rule.” Ray Monk

I believe that correct intuitions exist and are monumentally important. But I don't see why for every correct intuition that exists (there is a maximum of one correct intuition per issue), I should consider all the many incorrect intuitions that might exist on the same issue to be monumentally important. — Acyutananda

But it is the very notion of intuition itself that is at issue. Does the concept make sense at all, apart from the casual talk about premonitions and feelings? If you try to give an example of an intuition, can it be defended as truly irreducible? How about my favorite intuition, causality? Try to imagine a spontaneous effect, ex nihilo. Can't be done; I mean knock down, drag out, impossible, a causeless event. Why? Just the way it is. Then there is logic, geometry, math and pretty much that's it. These amount to the same thing, it has been argued, but note, there is no answer to the question, why? Why does the leg opposite the largest angle of a triangle have to be the longest leg?
This is about as close to a genuine intuition that I can imagine. I don't deny that such things are intuitively apprehended. It gets difficult, here, frankly. 1) Is Kant right, and our intuitions are just representations? This would place it in Kant's world, where we are "shown" things through intuition, but intuition is not that which is shown. Its foundation is unknowable. Therefore, intuitions are constructs, and therefore contingent. 2) Enter Derrida's world. I don't know this that well, but as I see it, all thought is part of a web of contingency, no one idea stands alone. I say modus ponens, but these term get there meanings, their sense, from their play against what they are not. Up makes no sense unless down is there to be posited. There IS no stand alone proposition, for all ideas are like this. Thus an intuitively apprehended truth is really an embedded truth, for each part of the utterance is utterly senseless in and of itself. This makes all truth contingent.

"But it is the very notion of intuition itself that is at issue. Does the concept make sense at all . . ."

Thanks. Your later lines make it clear that you do not deny the existence of intuitions. Since you think they exist, you must think that they make sense IN SOME WAY – at least as "premonitions and feelings" that don't necessarily amount to anything, as you say.

We seem to agree that intuitions are feelings that exist. We differ in that I think some intuitions are correct, that is, objectively true, and that such intuitions don't just occur randomly, at least not always randomly.

"If you try to give an example of an intuition, can it be defended as truly irreducible?"

I, at least, do not try to defend it as irreducible. As I said, "I think it must originate in some way that I cannot presently understand – must be reducible to something that I cannot presently understand . . ."

Just to show that this thinking is not incoherent, let me give an example that a Christian might give. I think a Christian might say, "Jesus's moral intuitions, the feelings he would immediately have when any moral issue was brought to him, were invariably correct. There is a reason why they were invariably correct, and the reason is that God intentionally created/fathered Jesus so as to have correct moral intutions. Jesus's moral intuitions were not irreducible – they were reducible at least to an act of creation/fathering by God."

I am not a Christian, but I think that while people may start out with all kinds of bizarre moral intuitions, we can all develop ourselves so that our moral intuitions, the feelings we immediately have when facing any moral issue, are increasingly correct.

there is no answer to the question, why? Why does the leg opposite the largest angle of a triangle have to be the longest leg?
This is about as close to a genuine intuition that I can imagine. I don't deny that such things are intuitively apprehended. — Constance

This much of your post seems to be in almost complete agreement with me. The only difference between us seems to be your "as close . . . that I can imagine." Why not just say "This is a genuine/correct intuition," as I do?

Could not your "there is no answer. . . . apprehended" be paraphrased “The correctness of this geometric principle/proposition cannot ultimately be proved by any discursive argument. Its correctness ultimately rests on intuition, Such intuitions are intuitions that almost everyone has, and they are correct intuitions" – ?

"we are 'shown' things through intuition, but intuition is not that which is shown."

Can you refer me to where Kant says this? Anyway, I agree.

"[Intuition's] foundation is unknowable."

I gave my opinion earlier: "An intuition comes out of my unconscious in some way that I cannot understand. But I think it must originate in some way that I cannot presently understand – must be reducible to something that I cannot presently understand – but that I may (or may not) later be able to understand."

I wouldn't give up on eventually understanding.

"Therefore, intuitions are constructs, and therefore contingent."

Are you still representing Kant here? I don’t see why this should necessarily follow from "[Intuition's] foundation is unknowable." Let’s take my Jesus example above (which I don’t believe in, but which I think is a coherent story – not empirically true, but not a story that violates logic). Jesus may not know where his intuitions came from, and may never know (in which case they are unknowable to him or perhaps to any human being); nevertheless, God put those intuitions in him; so they are not just a construct, and not contingent.

"[Intuition's] foundation is unknowable. Therefore, intuitions are constructs, and therefore contingent."

Would this be your answer to my "Why not just say ‘This is a genuine/correct intuition,’ as I do?"

I don’t see how any uncertainty in knowing the foundation of truth necessarily makes truth contingent. Again, my Jesus example. The Jesus in my story may not know where his intuitions came from, and may never know (in which case they are unknowable to him or perhaps to any human being); nevertheless, God put those intuitions in him; so they are not just a construct, and not contingent.

“2) Enter Derrida's world. . . . This makes all truth contingent.

Can't we distinguish between truth and knowing truth? Derrida must have had some answer to this, but was it a convincing answer?


If I understand correctly, Wittgenstein's main works were the Tractatus and Philosophical Investigations. Can you tell me what writing of his in those books or elsewhere best addresses my concerns?

The syntactical or neurological processing of what? An action on someone's part would seem to require some fiat on their part... as if my feeling a surface somehow required my consent. — Banno

A computer can produce mathematical proofs through syntactical processing and it does not need any fiat at all. I meant action in the sense we talk about in mechanics - some process. But the point was that only the representation needs to be manipulated in accordance to the logic and algebraic rules of the abstraction, in syntactic or neurological terms, and that we don't need to test soundness through its application and involvement in an actual situation. We can derive and confirm soundness through observation that has no relation to any sense of utility. We don't need to be practically involved. We can be observers from a remote perspective. For example, by watching the stars in outer space.

The conceptualization of mathematical abstractions from experience may appear similar to any other form of cognition, but in specific detail, the involuntary subconscious impulses to sensory information become subject to contemplated analytical effort by the observer. Yes, it is still basically neural networks firing, signaling through synapses, cascading neuron activations, but the part of the subject that we would call reflex gives way to the part that we would call intent. At least in contemporary mathematics and sciences. Some primitive mathematical practices may have appeared so early, that it may have been a reflex for a wile.

And I do agree that fundamentals in logic, mathematics and sciences may be situated cognition, i.e. proper behavioral alignment with the environment. But this applies to few ideas - logic, induction, probability, etc. The rest, I conjecture, can and are derived by model extraction without first hand practical experience.