Question.... (Processes of Logic)

Hi Rrhain -Yes, I do see 5 fingers when I look at my hand, but I don't accept this as evidence that 'fiveness' exists anywhere except in people's minds.Evidence of colour exists even in a world of colour blind people - assuming they can make things like spectrometers. But how can evidence of 'pure fiveness' exist independent of our conception of it?

Well, if nobody were around to count, there would be no concept of number, and therefore - it seems to me - impossible to know whether there were such thing as number.
I am quite happy with the idea that sets exist as objects in people's heads, but when you say that numbers or sets exist as objects, I get the impression that you mean that they have an existence independent of people. How? Where?
Of course, I'm in no position to prove that there isn't, for example, an empty set of five elephants on my computer table, and I am well aware that the view that there can be is a widely held and impeccably respectable philosophical position, but it puzzles me. It seems to be a view that is useful for mathematical purposes but unsupported by any (any possible?) empirical proof. I regard that as a serious objection. What do you think?

You are perfectly welcome to think of me as a set of objects, NosyNed . Perhaps perceptions of people can only exist in each other's minds in that format. But can you find any way to demonstrate which, if either, of these 2 views is correct --The thing we can call the "set of me" really is inherent in me, whatever my opinion.-The things that are me just exist. The idea that they are a set is a useful construct that has no necessary existence in its own right.Plainly both views exist. Discussions of this sort usually seem to end in deadlock - "You're a set" "No I'm not". But if you think I am a set, what grounds do you have for treating that as a fact rather than a belief? If it is an undecidable question, in the sense that it is not publically verifiable, it looks more like a belief to me.[This message has been edited by Chavalon, 05-24-2003]

OK, replace the words 'object' and 'thing' in my previous post with 'pattern' or 'arrangement'.
Can you show that there are sets inhering in those patterns, rather than just in your view of them?[This message has been edited by Chavalon, 05-24-2003]

Hi again Rrhain. Having read your subsequent replies to John and Crashfrog, I think I understand your position now, although it appears you don’t understand mine. After all, the first thing I said to you after saying was , and yet you found yourself able to reply It seems that we must be using the word ‘five’ in different ways!
Plainly the point of difference is that you consider the fiveness inherent to the hand, wheras I regard it as a mental construct.
A couple of points in support of my position. You wrote - If nobody were around, there would be nobody to decide anything, so of course nothing would be decidable.
A blind society could - if they thought of it - make a spectrometer with audio or braille output. It could detect photons and allow them to infer the existence of light with different wavelengths.
An innumerate society could not build a number detecting machine. Number is qualitatively different to colour.And now, it’s show and tell time. There exists a clay pot (or existed, it was in a museum in Baghdad ) with cuneform writing on the lid, which said 16 ewes and 7 lambs, the property of(name)to be looked after by(name)and returned(date). Inside the pot were 23 little clay balls, 16 of one size, 7 smaller. Archaeologists think it was a reciept, recording a deal between a literate town dweller and an innumerate shepherd. The owner kept the lid, the shepherd the pot. It didn’t matter that he couldn’t count, all he had to do was to take the balls from the pot, drive the sheep through a narrow place, put a ball back in every time a sheep went past, and see if any balls or sheep were left over at the end.The point, of course, is that the concept of number is not innate, it is learned. By contrast, a person who had never interacted with other humans would know perfectly well what red is without being taught.
OK, so colour is not a useful analogy. Still, you can perfectly well say that the shepherd had a certain number of fingers, probably five, whether or not he knew it. I can reply that fingers are just fingers, sufficient unto themselves and needing no definition or conceptualisation, and that the fiveness could only be in someones head.So why bother with this (rather long) post? Because I’m interested in knowing why you are so sure that sets can inhere in objects - is there any possible publically verifiable proof that sets inhere in objects rather than being confined to people’s heads? You answered this before with but of course this is not to the point, as looking and recognising happen in my head, not my hand.

One cannot, of course see red without sensing it. The colour analogy does not hold. 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? What number detecting machine? 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. 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?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'. 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.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?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? In what place? Is it detectable in any way except in people's heads?You are way out on a limb here. Of course I have. But my fingers just *are*. The fiveness is in my head.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. Again, this is not to the point - at least not to yours. 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.

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]