Question.... (Processes of Logic)

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There is a "culture" that can only count to four. Integers beyond four are known by the phrase "hrair", which generally means many, or thousand. Hence their God is known as El-Ahrairah, or Prince with a thousand enemies.

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Bonus points to the first who can tell me where this culture exists.

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Mark

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Watership Down, baby. I read it for the 3rd or 4th time a few months back. It always made me cry when the prince with a thousand enemies took Hazel to join his Owsla.

Hey, watch it there. I can categorically state that most inhabitants of my newfound home can count to at least eight, if they haven't lost any fingers to farm equipment.

Wow... thats better than it was where I grew up.------------------
No webpage found at provided URL: www.hells-handmaiden.com

Zephyr,A golden star is winging it's way towards you as I write. By coincidence I just reread it too, & I also get, ahem, dust in my eye, when Hazel leaves his body behind because he no longer needs it......I feel no shame at all when I tell you this is my favourite book of all time. Wonderful stuff.Mark------------------
Occam's razor is not for shaving with.

Unbelievable. I seem to have, uhhh, dust in my eye, right here in the office, just thinking about it.Thanks for the star

crashfrog responds to me:

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A simple scale detects number without knowing what numbers are.

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Um, a scale detects mass, not number.

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It does more than detect mass. It detects a relationship between masses: Inequality, which is a mathematical description of number without necessarily requiring a definition of number.Knowing that something is "greater than" another doesn't tell you what the values of the two actually are...just that one is larger than the other.

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That's why if I put one gold coin and one feather, the scale tips towards the coin, despite there being only one of those objects. How is that detecting number if a scale can't detect number?

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Because the mass has a number.

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And yet, all cultures develop mathematics.

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Do they?

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Haven't heard of one that hasn't. Even animals can do mathematics.

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Plenty of cultures create artifacts that have "mathematical" properties (weaving patterns, etc) but that's simply indicative that we apply mathematics as a description to patterns. The culture itself certainly has no knowledge of the processes of math.

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What is recognition of pattern if not a knowledge of the processes of mathematics?You seem to have a very narrow idea of what math is.

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Even animals develop mathematics. My best friend's cat, for example, knows the difference between odd and even.

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Firstly, you have no idea what the cat is reacting to.

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Actually, I do because we've tested him. My friends and I are all a bunch of scientists. We specifically devised a series of tests to see how he reacted, each time repeating the scenario with a different number of treats. The only change in his behaviour happened when the odd/even trait of the number of treats changed. Time of day, when he last ate, who was giving him the treats (even me, whom he rarely sees), flavor of treats, etc., he only begs for more when there is an odd number.

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You have no idea what kind of mental model the cat is operating from.

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I didn't say that I did. I simply said that he can distinguish between odd and even. I'm not saying I know how he conceptualizes this distinction. For all I know, he's obsessive-compulsive and does a left-right thing and must have things "balanced," but that is the same thing: A recognition of the difference between odd and even.

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And likely, the cat was probably trained to do so

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Nope. They've had him since he was a kitten.

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no animals do math unless trained to do so by humans.

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Who do you think I should believe? You who claim that no animal can or the animal in front of me that's actually doing it?You're basically calling me a liar, crashfrog.And now I know there is nothing more to discuss. If you don't have the decency to treat me with the respect of being honest, then we shall have precious little to say to each other of any value.------------------
Rrhain
WWJD? JWRTFM!

Chavalon responds to me:

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I know. I do understand what you are saying. I just don't understand how you can truly hold it. It is as if one were to say, "I see 'red,' but I'm not sensing 'red.'" How can one possibly see red and not actually be sensing it?

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One cannot, of course see red without sensing it. The colour analogy does not hold.

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And that's why I have a hard time comprehending: The color analogy does hold. Color and number are both physical properties of existence. I don't understand how a person can look at something and say that it's red and that the color of the object is not just a mental construct of the person looking at it but then say that the number of objects being looked at is somehow different.

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Why? Are you saying that things don't exist if there is nobody there to pay attention to them?

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Only sentient beings can decide things, a lack of sentient beings must mean a lack of decisions. Do *you* believe that things only exist when sentient beings are around to make decisions about them?

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Um, that's my question to you. It would be nice if you would answer it.No, things exist despite people. If everybody were to die right now, the earth would continue to exist and continue to orbit around the sun which would also continue to exist.I do not ascribe to solipsism.

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I say no. An innumerate socity could easily build a number detecting machine. After all, mathematics predates writing.

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What number detecting machine?

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I already gave an example: A scale. It detects the ratios of things. Ratios are numerical. Thus, we're detecting number even though we're not detecting what specific number or even assigning a metric other than non-equivalency.

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We can make things that detect the mass, temperature, pressure, length, charge, wavelength etc. of some specific bit of matter or energy, but the numbers we assign to these measurements are arbitrary social constructs such as SI units.

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Yes, the specific metric used is arbitrary, but that doesn't mean that there is no number. You don't have to define what units of mass you are using in order to determine that something has "more" mass than another. And "more" is a mathematical trait of number.

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How could a person in a society that counts "one, two, oneandtwo, twoandtwo, many" (and, yes, they did/do exist) deduce the existence of a specific large number from an unevenly loaded balance, in the same way that a blind person could deduce the existence of a specific wavelength/colour from a spectrometer?

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By simply ignoring the specificity of the number and gauging the magnitude. It doesn't matter what the units are. They're arbitrary. Mass is real, "gram" is arbitrary and a construct. So rather than be fixated upon the "gram" aspect, abstract it to the mass and simply recognize that one has "more" than the other.

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If number were like colour, it should be possible to build a machine that, when pointed at 3 apples, returns the answer '3', just as it could return the answer 'red'.

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And we can.

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Note that such a machine might be possible using a camera and a computer, but the fact that it would have to be programmed with algorithms in order to give it something equivalent to an understanding of set theory supports my idea that the set's in the eye of the beholder, not yours that it's in the apples.

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Um, you have to do the same thing when programming the machine to respond with "red." So why are you picking on number as if it is somehow different?

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If such a machine were built, and could detect something intrinsic about 3 apples that caused it to return the answer 3, what would happen if you then - still thinking of the apples as a set of 3 - took one to Trincomalee, one to Vladivostok, and the other to Ouagadougou? How's the machine going to detect the threeness then?

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Same way. By your logic, if we take those three apples to those three place and keep the color-detecting machine here in Omaha, then it isn't going to be able to detect the color of those apples anymore, either, so therefore color isn't real but is nothing more than a mental construct.Since number and color behave identically, why are you picking on number as being somehow different?

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How about the threeness of this set: {A cute little kitten, Al Quaeda, The legacy of World War II}. How about {Alex Ferguson's determination to win the Champion's league again before he retires, Free market capitalism, A neutrino a billion light years from the sun}. Where's the threeness there?

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In the fact that you have only three things, not any other number.

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In what place?

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In their very existence.

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Is it detectable in any way except in people's heads?

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Yes.

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You are way out on a limb here.

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Strange...I was going to say the same thing about you.

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But it doesn't answer the question: Does this mean you don't have five of them on the end of your hand?

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Of course I have. But my fingers just *are*. The fiveness is in my head.

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So if you stop thinking about your fingers, their number changes? If you were to think really, really hard about it, you could actually make your hand have six fingers on it rather than five?

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If a number detecting machine were pointed at my hand would it say 'one', the number of hands; 4, the number of short fingernails; 5, for the fingers; some number in the high dozens, the number of hairs; a very large number, for the creases; an even bigger one, the number of cells; a much, much larger one than that, the number of carbon atoms? Almost any number could be said to inhere in my hand. It depends on your point of view. A mental construct.

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Point of view is a mental construct, yes, but what does that have to do with anything? If that color-detecting machine were to look at the stem of the apple, it would say "brown." If it were to look at the soft spot, it would return with "brown." At the leaf attached to the stem, "green." At the bitten part, "beige" (possibly "white"). Heck, if you look closely at the skin of the apple, it's actually a mottled conglomeration of colors rather than one solid one so if you look really closely at just one part of that red apple, that color-detection machine may just respond with "yellow." It depends upon your point of view.Since color and number are behaving identically, are you now saying that color is just a mental construct?

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You mean if you think about it hard enough, you can wind up with six fingers on your hand? Here...think really hard and make my hand have six fingers. So far, I can only see five. Can you show me how to make it six?

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Again, this is not to the point - at least not to yours.

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On the contrary. It is precisely my point. If number is just a mental construct, then you can change the number of things just by thinking about it hard enough.If you can't do it, and by "can't" I mean a universal "can't" rather than a personal inability, then number isn't a mental construct but it something that exists on its own.

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I can visualise my hand with 6 fingers, but it's in my head, and changes nothing about my actual hand, which, as we agree, does not change according to, or depend upon, my or any conceptualisation of it.

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Then you agree that number is not a mental construct but is a property of existence.If you can't change the number of fingers on your hand without actually physically manipulating them, then number is a physical property.This isn't surprising since physics is simply applied mathematics.------------------
Rrhain
WWJD? JWRTFM!

But that's not what you claimed it would do. You claimed to have a machine that would detect the number of objects, since that's what we were talking about. All you have is something that determines between "heavier" and "lighter". As narrow as your idea of math is broad enough to encompass all human endeavor, it seems. Not unusual for a mathemetician. Honestly I have been finding it a little suspicious that you have so many positive counterexamples from your own experience. Apparently you live in a community of people whose animals count, use the word "niggardly" regularly, have little to no difficulty thinking of people as ungendered persons, use pronouns in ways that exist only in dictionaries, and a host of other conviniently unusual traits that counter all the negative universal statements a bunch of us have made.Wouldn't you find that just a little suspicious? If you want me to accept your cat counterexample you'll have to do a bit more than complain about being called on the carpet. That's simply too unbelieveable for me to take your word for it.

Normally I wouldn't nest quotes this deeply, but just this once -You'll excuse me bolding your reply. If you can't detect specific numbers, you don't have a number detecting machine. A spectrometer can detect specific colours, after all, and could scarcely be worthy of the name otherwise. A small part of it. Not enough to persuade me. You really don't have a number detecting machine, do you? But spectrometers don't need software that models set theory. But a colour detector in any of those wonderfully named places will detect the redness, wheras a number detector won't see threeness, even if I'm standing next to it thinking as hard as I can 'this apple is one of 3'. Unsupported assertions with no supporting argument at all. This is about the properties of sets, rather than those of the objects they contain, right? The threeness of those sets is in our heads and nowhere else, isn't it? If not, to what physical location am I to go to find their very existence? Of what substance are those sets made? The sets, mind, not the objects they contain.Obviously I think that the objects in the set {Alex Ferguson's determination to win the Champion's league again before he retires, Free market capitalism, A neutrino a billion light years from the sun} have real existence, independent of me or anyone else (apart from Fergie, of course). But I see the set itself as a decision to consider these things as a group, whether in my head or written as {...} - a construct with no existence independent of sentient beings.Which experiment would you perform in order to falsify the theory that the set - rather than the objects it contains - doesn't exist outside people's heads? Ah, well, the thing is I don't agree. I see a thumb, an index finger, a middle finger, a ring finger and a little finger. The set {thumb, index finger, middle finger, ring finger, little finger} and the fiveness inherent in it is in my head. There are no curly brackets around my fingers .Since that's the only other way I can think of to put my view, I might leave you to your Platonism, and you can - if you like - leave me to my conceptualism. That's what proper philosophers call my position, so I'm told. But I would like to know the answer to my last, bolded, question.[This message has been edited by Chavalon, 06-06-2003]

Chav,
I am not sure that I am prepared to say that I can flow logically from the first question to that wichever is better in this thread but I noticed something in your last post that I hoped I could continue to comment in that vein on. You were quoting about the "detection" of a specific 'number'and then in the name of Opticks you assert that a *spectrometer* "detects" color. Well, that is a question...Without A BELIEF in Boscovich's THEORY OF NATURAL HISTORY written in the generation succeeding Newton I would have said ABSOLUTELY that it does not. Simply reading Wittgenstein can confuse one about how one is to TALK subjectively about what Gothe thought so seriously if one DOES NOT have any idea of what a fit of easy transmission or reflection is (and I do not COUNT the modern attempts to claim that quantum mechancis had this insight but if you wish to call me on this account of history it IS something I can or could research) then it only MEASURES the colour provided one interprets the gauge pointer such just as a caliper really doesnt measure the Snout-Vent length LENGTH of a salamander unless one assumes that the critter could care less for what is moving in a striaght line continues to do so (which is also a part of Boscovich's "theory").As a clear headed undergraduate I could constanly be found asking profeesors at Cornell HOW DO YOU COUNT an organism, because if one does not know how to do this than one can not reliably be certain that the forms attributed to bio-change speciation that were divided in the ledger of not finding transitional forms really contributed to any chi square signifianctly or were obsfuscated by the process of statistical testing itself. I was never answered. I went on to try to do this myself and got the boot. So there was never any even bold ability to "detect" the count in the database nor was there concern about the means I proposed to do it and yet it was known that how one "encodes" polymorphic characters WAS an issue. But THIS is a different question and already implied a usable BASE for doing the association with the numbers and was really the reason that I was seen as a hostile pain in the neck. I was not.Boscovich based his theory on a rest with Newton's conspiring motions and decidee that he would accept (without a cusp) infinite componenability but not infintie divisibility but if one had gone to any math dept and wanted to know what kinds of accounting practices were available for the evolutionist to count on the kinds of organisms in any natural history collection (regardless of if one wanted to use the database to DO catastrophe theory or not...)then one would be aware that there were at least on that black board finite as well as inifinte numbers available. I find NO theoretical difficulty though I would not know how to be a detection machine other than so far yours or my mind to find these attachments in setting the manifold of continuity that the better question bends to assert that Boscovich's breach IS a Cantor actual infinite and enable population genetics in nature to detect this but to DO this I would NOT be able to say as that the spectrometer detects colour. It did not. It dected something we call color and something we accept in the process of naming the same but I did not have to name the organism do to similarliry in theory with an answer evolutionists have been faced with but prefered to even ingore the organic background to the asking of the same question. I hope this helps and yet I have NOt said anything about but those few bold strokes you made in one place.

crashfrog responds to me:

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It does more than detect mass. It detects a relationship between masses: Inequality, which is a mathematical description of number without necessarily requiring a definition of number.

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But that's not what you claimed it would do. You claimed to have a machine that would detect the number of objects, since that's what we were talking about. All you have is something that determines between "heavier" and "lighter".

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But that's number. "More" is a description of number.

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You seem to have a very narrow idea of what math is.

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As narrow as your idea of math is broad enough to encompass all human endeavor, it seems. Not unusual for a mathemetician.

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Ah, but I don't think that math can do that.Why do you think I keep harping on people for misusing the Incompleteness Theorems? Because they don't apply to things that aren't axiomatic number systems. Last time I checked, human endeavors are not all axiomatic number systems.

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And now I know there is nothing more to discuss. If you don't have the decency to treat me with the respect of being honest, then we shall have precious little to say to each other of any value.

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Honestly I have been finding it a little suspicious that you have so many positive counterexamples from your own experience.

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If you don't have the decency to treat me with the respect of being honest, then we have precious little to say to each other.

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Wouldn't you find that just a little suspicious?

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No."There are more things in heaven and earth, Horatio, than a dreamt of in your philosophy."

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If you want me to accept your cat counterexample you'll have to do a bit more than complain about being called on the carpet.

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But you didn't call me on the carpet. You just asserted that it can't be true.

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That's simply too unbelieveable for me to take your word for it.

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Only because you've already made up your mind that it is impossible.I'd be happy to show you the cat, but he won't fit through the cable modem.Have you considered the possibility that your preconceived notion just might be wrong?------------------
Rrhain
WWJD? JWRTFM!

But "more" is not itself a number, which is what you said your machine could detect. You're just shifting the goalposts. I don't find it in the least bit insulting to ask someone making repeated, unusual claims to cite evidence. if you do perhaps you should retreat from scientific or logical discussions. This is simply feigned protestation to conceal a lack of evidence for your more outlandish and unsupported claims. Your personal credulity is hardly a major point in favor of your arguments. And in this case, it's pretty obvious that there are more things in your philosophy, Hamlet, than are found in heaven and earth. No, I simply questioned your conclusion, expressed that I found it highly difficult to believe, and asked for corraborating evidence. If you find that insulting, I find you rather thin-skinned. That's hardly my problem. You brought up the cat; it's your responsibility to demonstrate evidence of this incredible claim. Certainly. Show me evidence that my pre-conciveved notions are wrong and I'll consider it. If I find my notions incompatible with the data I'll change them. So far, though, you haven't offered data - just a story that very well could be made up. I don't find that very compelling.

Chavalon responds to me:

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I already gave an example: A scale. It detects the ratios of things. Ratios are numerical. Thus, we're detecting number even though we're not detecting what specific number or even assigning a metric other than non-equivalency.

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You'll excuse me bolding your reply. If you can't detect specific numbers, you don't have a number detecting machine.

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Yes, you do. You're just stuck on the word "five" being associated with the concept of "five." Crashfrog made the same mistake above. He said that if we all agreed that it were "six," then it actually would be "six"...and then immediately backpedalled saying that "six" would be the same as what we call "five."But if it's the same thing, then there is no difference. Simply having us all call it "six" doesn't make it six. It's still five...we're just using a different vocal reverberation to refer to the concept.

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A spectrometer can detect specific colours, after all, and could scarcely be worthy of the name otherwise.

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But the spectrometer doesn't spit out the word "red." It simply detects the specific type of light and reacts according to the propeties of that light. A spectrometer has no idea what "red" is. It is completely arbitrary that we have divided the visual spectrum up the way we have.But that doesn't mean that color is a mental construct.So why are you picking on number?

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And "more" is a mathematical trait of number.

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A small part of it. Not enough to persuade me.

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What more do you need?You're not expecting a spectrometer to spit out "red," so why are you picking on a scale for not spitting out "five grams"?

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By simply ignoring the specificity of the number and gauging the magnitude

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You really don't have a number detecting machine, do you?

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Yes, I do. A scale.In fact, your spectrometer is also a number-detecting machine. The trait of color in light is distinguished by its frequency, which is a numerical trait.

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Um, you have to do the same thing when programming the machine to respond with "red." So why are you picking on number as if it is somehow different?

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But spectrometers don't need software that models set theory.

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Neither does math. There is more to math than set theory.And you're neglecting that spectrometers need light. Seems you need to get into foundational physics in order to do spectroscopy...and physics is simply applied mathematics.

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Same way. By your logic, if we take those three apples to those three place and keep the color-detecting machine here in Omaha, then it isn't going to be able to detect the color of those apples anymore, either, so therefore color isn't real but is nothing more than a mental construct.

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But a colour detector in any of those wonderfully named places will detect the redness, wheras a number detector won't see threeness, even if I'm standing next to it thinking as hard as I can 'this apple is one of 3'.

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Incorrect. Your color detector won't detect the redness of the apple when it isn't there. It only works when the apple is there to be seen. My number detector won't detect the number of the apple when it isn't there, either. It only works when the apple is there.To use your own words:What would happen if you then - still looking through the spectrometer - took one to Trincomalee, one to Vladivostok, and the other to Ouagadougou? How's the machine going to detect the redness then?The spectrometer can't see the apples, so how can it detect the color of them?

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Unsupported assertions with no supporting argument at all.

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Incorrect. This entire thread has been me giving the supporting arguments. I apologize for not repeating it yet again.

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This is about the properties of sets, rather than those of the objects they contain, right? The threeness of those sets is in our heads and nowhere else, isn't it?

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No, it is in the very existence of the set. Are you saying that you don't have five fingers on your hand? That if you were to stop thinking about your hand, you'd have some different number?

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If not, to what physical location am I to go to find their very existence?

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The same place you'd go to find their color. The same place you'd go to find their gravitational force. The same place you'd go to find everything else about them physically.

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Of what substance are those sets made? The sets, mind, not the objects they contain.

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Their existence.

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Which experiment would you perform in order to falsify the theory that the set - rather than the objects it contains - doesn't exist outside people's heads?

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I've told you over and over:Think really, really had and make your hand have six fingers. Better yet, think really, really hard and make my hand have six fingers.If number is just a mental construct, then all you would need to do is change your mental attitude and the number would change. No, not the arbitrary word we ascribe to the number...the actual number, itself.Come on...why do I still have only five fingers on my hand?

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Ah, well, the thing is I don't agree. I see a thumb, an index finger, a middle finger, a ring finger and a little finger. The set {thumb, index finger, middle finger, ring finger, little finger} and the fiveness inherent in it is in my head. There are no curly brackets around my fingers.

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You're stuck in the symbology and ignoring the substance.If it's just a mental construct, then make it six fingers. Just change your mental attitude and find a sixth finger in there. Why is that so hard to do?

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Since that's the only other way I can think of to put my view, I might leave you to your Platonism, and you can - if you like - leave me to my conceptualism. That's what proper philosophers call my position, so I'm told. But I would like to know the answer to my last, bolded, question.

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How many times do I need to answer your question before you remember it?Are you saying you can simply think really, really hard and change the number of fingers on your hand?That's how you can prove that it isn't a mental construct. A mental construct would be amenable to mental shifts. If the number of fingers on your hand doesn't change no matter how you think about it, then number isn't a mental construct.------------------
Rrhain
WWJD? JWRTFM!

crashfrog responds to me:

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But that's number. "More" is a description of number.

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But "more" is not itself a number,

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So? Your spectrometer isn't going to kick out "red" because "red" is an arbitrary distinction. It's just going to react to the specific traits of the light that came through.The scale isn't going to spit out "five grams" because "grams" is an arbitrary distinction. It's just going to react to the specific traits of the objects that are being examined.

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which is what you said your machine could detect. You're just shifting the goalposts.

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Strange...I seem to have been saying the same thing to you.You have one standard for color but shift the goalposts for number.

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If you don't have the decency to treat me with the respect of being honest, then we have precious little to say to each other.

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I don't find it in the least bit insulting to ask someone making repeated, unusual claims to cite evidence.

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You're missing the point. It isn't that I am taking offense at being asked to show evidence. It's that this forum is not exactly the place where I can give you the information you want. Come with me to my friend's house and I will show you the cat, you can talk to my friends, and we can show you how he behaves.That isn't exactly something you can do over the internet, wouldn't you think?Speaking of "niggardly," it came up in conversation I had with a friend just last night. No, I wasn't the one saying it, either. That conversation no longer exists. You weren't there. I can't make you hear it.That isn't exactly something I can show you over the internet.The problem is not that the evidence doesn't exist. It's that this medium is not conducive to presenting it. This is not my fault and it is rude to accuse someone of lying simply because I can't fit a cat through a cable modem.

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"There are more things in heaven and earth, Horatio, than a dreamt of in your philosophy."

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Your personal credulity is hardly a major point in favor of your arguments.

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And your incredulity doesn't help you, either.We do know that the argument from incredulousness is a logical fallacy, yes?

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And in this case, it's pretty obvious that there are more things in your philosophy, Hamlet, than are found in heaven and earth.

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So why do I still have only five fingers on my hand. I've asked you to change it to six...it should be easy if number is just a mental construct.

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I'd be happy to show you the cat, but he won't fit through the cable modem.

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That's hardly my problem.

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It is when you are claiming that it can't be. I have the cat. I know where it is. If you don't believe me, all you have to do is ask and get yourself down here and I'll show him to you. Burden of proof is on the claimant, yes, but I can't make you look.

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You brought up the cat; it's your responsibility to demonstrate evidence of this incredible claim.

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So come on down and take a look. Since it is not possible for me to send you the cat, you're going to have to put some effort into it.

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Have you considered the possibility that your preconceived notion just might be wrong?

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Certainly. Show me evidence that my pre-conciveved notions are wrong and I'll consider it.

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I've got a cat here who can count. Why won't you come down and look at him?I'm still waiting for you to think really, really hard and change the number of fingers I have on my hand to something other than five.

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If I find my notions incompatible with the data I'll change them. So far, though, you haven't offered data - just a story that very well could be made up. I don't find that very compelling.

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So let it go. If you don't have the ethical standard of treating people with respect, simply let it go. Nobody is forcing you to respond. If you find my claims incredulous and you are not in a position, for whatever reason, to put in the effort required to verify your incredulousness, then simply let it go.------------------
Rrhain
WWJD? JWRTFM!

Fine, I have six fingers. Wasn't that hard, actually.