Question.... (Processes of Logic)

crashfrog responds to me:

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but I didn't mean to decribe math as a unqiuely human endeavor, but rather an endeavor unique to symbolic, social intelligence. While humans consitute the most advanced example of that I don't believe we're the only ones.

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Please let us know what symbols a hummingbird uses in its mental map.

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If space aliens visit us, I assume they'll have some kind of math. If they're able to communicate with us at all it's likely we'll find they have the same numbers. But only because their minds are similar to ours, not because numbers have some kind of independant phsyical reality.

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But if the numbers are universal, how is that not indicative of a universal existence?

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Um, no. If you look carefully, you will see that in some of these cases, the animals were specifically raised to ensure they did not have any human mental model and yet, they perform the same way.

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I read the exact opposite. Your citations demonstrated animals trained by humans to absorb human-like mental models. I don't know how you think it could be otherwise - what techniques could humans use that would not result in human-like mental models?

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You're forgetting about the ravens.They were raised from hatchlings to make sure they never saw a human doing anything like pulling on a string, holding it down, and then pulling it up more. Did you not see that? Indeed, some of the animals need to be taught human methods such as the grey parrots counting bits of wool balls since the way we are getting them to tell us how many are there is through speech. Thus, we need to teach them the word.But what human taught a hummingbird how to make a mental map? What human taught the nut-burying bird to make a mental map?And what human taught the cat?

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Can you think of another possibility?

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That animals can absorb human-like mental models because intelligence is a social phenomenon. I said that already.

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That would be the second case: Animals invented math, too.

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Hummingbirds aren't exactly social creatures.

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All creatures are social to some degree. Including hummingbirds.

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That pretty much strips the phrase "social animal" of any meaning, then. Obviously, sexually-reproducing species need to find one another otherwise they will never reproduce. That doesn't make them "social creatures."

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My position is that math is simply a mental construct because number is not a physical property of matter but rather a property of imaginary sets of objects, which exist only in our heads and which we communicate to each other via mathematics, language, and other ways of describing relationship. Most animals have some capability to communicate mental models, so it's not surprising to me that animals can be taught - or even learn themselves - other kinds of mental models, such as "number". Especially when humans are communicating to them.

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But you're forgetting about the animals that were deliberately raised to have no human contact.How did they get taught?And what are they reacting to if not something that exists?

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That still doesn't prove that numbers have a unique, self-sufficient physical reality.

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I would say that it does. We start reducing the amount of mental cognition and still mathematics pops up. And when we finally completely remove all mental function and look at things that are purely physical, we still find mathematics all over the place.And that's not surprising considering that physics is nothing more than applied mathematics.

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So I guess I'm wondering what your point was in displaying incredulousness at the idea of a cat who can tell the difference between odd and even.

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Actually, my incredulity stemmed from the fact that your example was all too convenient. But even if it's true it doesn't speak against my position - the cat detects parity because it absorbed a mental model of parity through communication, not because parity is some inherent property of an object.

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Um, who taught the cat?

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You seem to be stuck on the symbology rather than the substance behind the symbol. The number of fingers on your hand is not dependent on if you call it "five" or "cinco" or "5."

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You don't seem to understand what we're arguing.

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Strange...I've been saying the same thing to you for days now.Why do you think I keep suggesting that you let it go?

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And honestly, if you refuse to understand, why should I argue with you?

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What do you think I've been saying to you for days?I seem to recall saying that we were at an impasse. Did you not take it seriously?

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I'm actually getting a little tired of this because you just repeat your assumptions over and over again and ignore any challenge to them. You're not a very good debater.

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Strange...I was going to say the exact same thing to you. You don't respond to points, when asked direct questions you avoid them at all costs, you jump to psychoanalysis, ascribe ulterior motives, have no respect for the people you're debating with, etc., etc. You're not a very good debater at all.

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I don't really see any reason to continue.

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Then why not take the suggestion I made more than a week ago?Let it go.------------------
Rrhain
WWJD? JWRTFM!

Close, crash, but no cigar.Autocatalysis writes:

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but worse still, principal mathematics was shocked when Kurt Gdel demonstrated there is no consistent way of determining mathematical truth. It's an axiom contradiction.

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No, that isn't what the Incompleteness Theorems state.Instead, they state that any axiomatic number system sophisticated enough to model arithmetic will be either incomplete or inconsistent. Not everything is such a thing and thus, the Incompleteness Theorems do not apply.Plus, the two concepts of incompleteness and inconsistency are the same thing...the difference is just in how you write things down.------------------
Rrhain
WWJD? JWRTFM!

Autocatalysis responds to me:

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Well I am obviously out of my field I was writing with vague memory of a book by D. Hofstadter godel escher bach sure you no the one .

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Yep...it's one of those books that a lot of people admire but few have actually read all the way through, every word, beginning to end. I've tried and it's tedious (of course, the fact that I don't own a copy and thus have to read it in snatches from other people's copies doesn't help.)

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Hofstadter writes his interpretation all consistent axiomatic formulations of number theory include undecidable propositions is this a good representation of the theory?

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Yes, because it deals with both aspects. The first is that we're dealing with systems that are somewhat sophisticated (number theory) and the second is that he establishes that if you insist upon consistency, then you end up with undecidable. If you don't insist upon consistency, then you can end up with every statement being decidable.

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Plus, the two concepts of incompleteness and inconsistency are the same thing...the difference is just in how you write things down.

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As I read it incompleteness in theory ie. a incomplete set of truths, is different to a set which has inconsistency’s ie untruths and truths?

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Any thoughts?

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An inconsistent set can be turned into an incomplete set simply by changing the way you process the work.That is, you can write things down such that you can prove both A and ~A, or you can write things down such that neither A nor ~A are provable.For example, take the Continuum Hypothesis. Godel proved that if you assume it to be true (c = aleph-one), you don't get a contradiction. Cohen then came along and showed that if you assume it to be false (c != aleph-one), you don't get a contradiction, either.So is this incompleteness or inconsistency? Depends on how you decide to look at it. Since most mathematicians would much rather have an incomplete system rather than an inconsistent system, we tend to look at things as incomplete and thus they're called "incompleteness" theorems rather than "inconsistency" theorems.------------------
Rrhain
WWJD? JWRTFM!

No, John. You've misrepresented my position.------------------
Rrhain
WWJD? JWRTFM!

No, I'm not going to deny that, John.However, you weren't talking about mathematics. You were talking about our representation of mathematics and that, indeed, is invented.------------------
Rrhain
WWJD? JWRTFM!

John responds to me:

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What of mathematics do we have that IS NOT our representation of it?

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The mathematics that exists in reality.Surely you're not saying that an actual apple is dependent upon us calling it an "apple," using those specific letters, pronounced in that specific way, are you? An apple exists regardless of the representation we use to describe it.You confuse the map for the terrain.------------------
Rrhain
WWJD? JWRTFM!

John responds to me:

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The mathematics that exists in reality.

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The question, Rhhain, is which part is the REAL part?

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Oh, you're not about to equivocate on the world "real" are you?

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You cannot answer the question, "Which is the real part?" with "The part that is real." Come on. You can do better than that.

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But what else is there? I've given you plenty of examples. For example, the five fingers on your hand. Or are you saying that if you think about it really hard, you can change it to six?

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An apple exists regardless of the representation we use to describe it.

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Yes, AN apple does exist regardless of what we choose to call it.

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Precisely. AN apple.As in ONE apple.Or are you saying that if you think really, really hard, you can turn AN apple into SOME apples?

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But Apple with a capital 'A' is another story altogether.

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Huh? Didn't we just agree that it didn't matter what you called it? An apple is an apple?

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There is no such animal, no matter what we choose to call it. It is an abstraction.

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Um...last time I checked, my friends all used Apples. They don't like Windows.

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Math is in the later category, not the former.

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You mean you don't have five fingers on your hand?

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You confuse the map for the terrain.

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If this is the case I am sure you can point to a mathematical entity-- a five, for example. Not five things, which is an abstraction.

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No, five things is a concrete example of five.Let me see if I can understand your logic. You want me to show you a real version of an "apple," but you will not accept a piece of fruit because that's an "abstraction"?Are you saying you don't have five fingers?

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Not a character or a word which are mere representations of an idea, but to the real thing--

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I have never been referring to the symbology. That's crash's problem. He seems to think that if we call it "six," it really is six.Are you saying you don't have five fingers on your hand? That if you think really, really hard, you can actually make another finger appear?

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Five in its unadulterated glory, in the same sense as you can point to an apple.

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I've been pointing to your hand for months and the fingers that are on it.Or do you have some other number of fingers on your hand? Can you make the number change just by thinking about it?------------------
Rrhain
WWJD? JWRTFM!

John responds to me:

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Or are you saying that if you think about it really hard, you can change it to six?

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This isn't mathematics, Rh.

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Yes, it is. You are saying that mathematics is something that doesn't exist outside of a person's thoughts.If that were the case, then you could think really hard and change the number of something since number is a mathematical property.But if you can't change the number of something simply by thinking about it, then number must necessarily be something that exists outside of a person's mind.

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It is physics.

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Thus showing that number is a property that has physical existence. If number, which is a mathematical property, can only be changed by physical processes, then number must physically exist.And thus, mathematics physically exists.Thank you for finally coming around.------------------
Rrhain
WWJD? JWRTFM!

crashfrog responds to me:

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Or are you saying that if you think about it really hard, you can change it to six?

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You've asked this about a hundred times

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And it's been avoided every single time.I know you don't like it. I know you don't think it's important. But it is, however, the entire point: If you can't change it simply by thinking about it, then it isn't a mental construct but a physical one.

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I can't change the meaning of words just by thinking hard

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Sure you can. That's exactly how meanings of words change: People think they mean something different. That's how new words come into existence: People think them into being. "Spam" didn't exist as a word until the Hormel company came along and then a bunch of computer geeks started using it to mean not a registered trademark referring to canned pork and pork shoulder but to junk email.It all happened with a thought.

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Why should numbers change under the same circumstances?

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Um, you've got it backwards. You can't change number simply by thinking about it. You can change language simply by thinking about it.

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I've been pointing to your hand for months and the fingers that are on it.

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A fruitful (pardon the pun) question might be - would numbers exist if there was nothing to count?

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Of course.The empty set is still a set, you'll recall.

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If so, where would they be?

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In the nothingness.Now you can understand why it took so long for many cultures to come to terms with zero.And you're learning why many people who don't spend a lot of time in cosmological origins have a hard time conceptualizing the "nothingness" out of which the Big Bang happened...to the point that there was no time, no space, no matter, no energy, etc. Absolutely nothing.------------------
Rrhain
WWJD? JWRTFM!

crashfrog responds to me:

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I know you don't like it. I know you don't think it's important. But it is, however, the entire point: If you can't change it simply by thinking about it, then it isn't a mental construct but a physical one.

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Since when?

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Since brains became powerful enough to think abstractly.

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People - emphasis on the plural - can change language, because languages are defined by communities of thinkers, not an individual.

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But numbers aren't. You can't change numbers no matter how many people you get involved.You will notice that human communities, when left to their own devices, will come up with completely separate languages. But they will come up with the same mathematics. Oh, they won't develop the same notation, but the Pythagorean Theorem was developed by the Chinese independently. Newton and Liebniz discovered the calculus independently.If mathematics were just something in your head, then we should have all sorts of mutually exclusive mathematics. But we don't. It's all the same no matter what culture or perspective the person studying the topic comes from. Isn't that what we claim is part of the justification for science? It's consistent and real because you can do the same thing and come up with the same results? That it doesn't matter what your personal opinions are, so long as you follow the method then you wind up with the same result?

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Just as the President is elected by a community, not by an individual. And just as one person can't change the election by voting "harder", no one person can change language by thinking any harder than they usually do.

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Sure they can. Remember The Fifth Element? That weird language Milla Jovovich was speaking? She wasn't just babbling. It was a language she and her brother (if I recall correctly) invented.Klingon is completely artificial. One person invented it.Now you're right that one person can't change other people's words just by sitting in a corner and thinking about it, but one person can change language by his useage and getting others to think about it. And thus, through a process of simple thought, the language shifts.No matter how much you think about it, you won't be able to change number. We can conceivably get all the speakers of a language to use the word "clelf" for the number of fingers on your hand, but that wouldn't change the actual number of fingers there.

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I mean, if what you say is true - that one or even several thinkers could alter the meaning of a word for everybody else - then why would Hormel (and I'm oh-so-glad you brought up the example of spam) have to sue to prevent the use of the word "spam" in reference to junk email? If what you say is true they could change the meaning by thinking hard. They wouldn't have to bother with the lawsuit.

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Their lawsuit is irrelevant for two reasons. First, their suit is over money. They don't want the brand name diluted so that other manufacturerers of potted meat could call their product "Spam." Of course, I doubt they could even win that claim since the use of "spam" as a reference to email does not dilute the connection of the term "Spam" to potted meat as email and potted meat are not similar. You will notice that there is "Apple" to refer to computers and "Apple" to refer to music and there is no conflict. Why? Because computers and music are not related. If we're talking about music and we refer to "Apple," it is generally understood that we're talking about the music publishers, not the computer company. Similarly, if we're talking computers and we refer to "Apple," it is generally understood that we're talking about the computer company, not the music publishers.Second, they cannot control the popular useage. The lawsuit can come forward, but if it can be shown that the term has become so common and popular then there is nothing to be done about it. Alas, Kleenex and Aspirin and all those other names have entered the vernacular as common words.So Hormel can sue all they want and they might be able to get some money out of it in the process, but they won't be able to stop anything. Google may be worried that their trademark is being diluted, but you can't sue the general population.

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It's obvious (to everyone but you, perhaps) that languages aren't thought into being by an individual, but rather agreed upon by a community.

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Tell that to Dr. Okrand, the inventor of the Klingon language. He's written a few books about the subject: The Klingon Dictionary, Conversational Klingon, and Power Klingon.Esperanto is another artificial language created by people. Since there is no true "community" of speakers of Esperanto, it is still in tight control by the people on the language board. Similarly, Latin, since it is a dead language, is also under the control of the board that oversees the language.

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Sometimes the community agrees that the language won't change, as is the case with "dead" languages. Esperanto has not changed significantly since it's inception, nor LogLang or any other contrived language. That they are more constant than English is not indicative that they represent some kind of independant reality.

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I haven't said they are. However, these languages betray your point. Because they are not actively used by an independent community of speakers, they are subject to the whim of those that monitor the language. Thus, people can directly state what words mean.

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You can change language simply by thinking about it.

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If this is true, then do it.

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Fine:Beetaratagang and clerendipity.Ask me what they mean.How about I describe the opposite direction: The destruction of a word. When I was younger and in the Boy Scouts, I read the Boy Scout Handbook thoroughly in order to prepare for the interviews. In the section on "Do Your Best," the book kept using the word "best" over and over and over. So much so that the word lost its integrity and simply became, for me, a collection of letters. I was directly experiencing the arbitrariness of the system. To this day, I still have a hard time with the word. When I'm reading, words come as complete units and it isn't like I consciously look at every single letter. But with the word "best," there's a bit of a hiccup and I suddenly see each letter individually and I have to reconstruct it.My friends have had similar experiences. We call it "losing a word." When a word gets repeated over and over again, we start to lose it as a word and it becomes just a vocal reverberation or particular visual pattern.

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Change the meaning of a word in a way that would be congruent to how you're asking me to change the number of fingers on my hand just by thinking about it.

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We already have. Notice how "bad" means "good" these days? How if something is "hot," it is "cool" to have it?

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Why don't you make more of my fingers "thumbs"?

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I can. At the beginning, it will only be me who understands this. But if it catches on, soon others will be calling them "thumbs," too.No matter how much I try, I can't manage to get the number of fingers on your hand to change just by thinking about it. Perhaps you can help me. How can I possibly get the square of the hypotenuse of a planar right triangle to be unequal to the sum of the squares of the other two sides?

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While you're at it, change who the President is by voting really hard.

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Um, voting isn't a mental action. It's a physical one.

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In the nothingness.

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Ooh, spooky. Now how about an answer that's not mystical claptrap?

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You're calling cosmology "mystical claptrap"?Tell me: What came before the Big Bang? Doesn't it seem to be the case that there is no "before" in that case, at least as we understand it? Since time came into being at the Big Bang, the concept of "before" is nonsensical.Is that "mystical claptrap"?

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It's becoming obvious that Platonism is an occupational hazard for mathematicians.

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Strange how so many of them seem to do just fine.

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I can only surmise that it's because the idea that everything they've studied and worked on for so many years could be nothing more than ideas in their heads is a hard cheese to swallow.

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No, it's because we can see them in real life. Remember the beginning of A Beautiful Mind? John Nash is looking at the refractions of light coming through a glass and he notices the patterns repeating in the fruit and the table cloth and traces them up to a pattern on a colleagues tie at which point he quips, "There has to be a mathematical explanation for how bad that tie is."Are you saying the tie doesn't exist?This is why I keep coming back to the same questions:Are you saying you don't have five fingers on your hand? Your fingers exist. There are five of them. Therefore, five exists, too. It is part and parcel of your fingers.

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But we don't hear you arguing for the independant existence of language. I can only assume this inconsistency is the result of a mental timidness that won't allow you to view mathematics as what it truly is - just another human langauge with very, very strict grammar.

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Well, that's what you get for assuming.I think I had pointed out the difference quite directly:If I think hard enough, I can change the langauge.No matter how hard I think about it, I can't change the number of fingers on your hand.------------------
Rrhain
WWJD? JWRTFM!

John responds to me:

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If that were the case, then you could think really hard and change the number of something since number is a mathematical property.

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Do you really not understand the difference between an objects and a count of the objects?

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Do you really not understand that number is part of existence?

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But if you can't change the number of something simply by thinking about it, then number must necessarily be something that exists outside of a person's mind.

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No, Rh, the THING exists outside the person's mind, not the count of it.

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But the count is outside the person's mind, too.Are you saying that if you stop thinking about it, the number of fingers on your hand changes? That if everybody were to drop dead right now where they are, the number of fingers on your hand would change?

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Number is not a THING. Number is grouping.

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But grouping is a thing.

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You are thinking of number as if it were something like color or texture.

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That's because it is.Does the number of fingers on your hand change when you look away any more than the color or texture of your hand change when you look away?

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There are X identical objects on my desk. I'll ship these objects, one each, to several independant labs. Now here is the question I'll ask each lab, "How many objects were in the original group of objects on my desk?" If number were a real thing, a genuine property of reality, there should be a test these labs could perform to answer this question.

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And there is: Look at all of the objects.You seem to be forgetting that you are taking something apart, looking at only a single part of it, and then trying to determine the properties of the whole.Is an atom a real thing? But if I take it apart, send all the protons, neutrons, and electrons to different people and ask them what kind of atom they came from, they're going to be hard-pressed to make that determination.Why? Because an atom is the collection of protons, neutrons, and electrons.Suppose I take a long chain molecule and break it up into its constituent atoms and send those atoms to different labs. Do you think they'll be able to tell what the original molecule was? Even if we told them what all the other atoms were, they still might not be able to since many times you can get very different molecules from the same set of atoms.Why? Because a molecule is the collection of atoms.So why are you picking on number when you would never do this with other objects?

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Consider this relationship. "Harrap's New College French and English Dictionary is a foot from my left arm." This relationship is the same as the numerical relationships between objects, yet is this also a 'real' thing?

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Yes and no. Your arm exists, the book exists, space exists, and thus the space between your arm and the book exists and can be mathematically described.Now, a "foot" is an arbitrary thing. We can change the definition of a "foot" just by thinking about it. But we can easily determine the number of both arbitrary and concrete objects that can fit between your arm and the book.

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I can't change this relationship by thinking reeeeaaaaalllllly hard.

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And thus, it isn't a mental state.It is real.

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Is it an entity? Nope ( though by your formula for determining a things reality, it must be. )

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Congratulations. You figured it out. It is, indeed, real.Are you saying the space between your arm and your book doesn't exist?

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If you answer otherwise, any such arbitrary relationships become 'real' things. This is a major problem with Platonism, and, well, it was realized as early as Aristotle. So you are a bit behind the curve.

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(*sigh*)Has it occurred to you that "Platonist" doesn't quite mean the same thing in mathematics as it does in philosophy, even though the terms are related?------------------
Rrhain
WWJD? JWRTFM!

crashfrog responds to me:

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Another mental construct that's immune to "change by thinking hard" is ownership.

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Not at all. Ownership is a completely mental process.We can transfer ownership of something simply by thinking about it. If I have something that I think is mine and I want to make it yours, I don't have to do anything to it. I simply think it's yours and that's that.When I buy pizza for my friends, one could claim that they're mine. After all, I paid for them. And yet, my friends are eating the pizza and I don't feel as if they have stolen from me. Nothing about the pizza has changed, but it has suddenly become community property.Simply because we thought it was.

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Rrhain owns his computer, but that's not a physical property of the computer. There's no way to determine ownership unless Rrhain's left his name and address in it.

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But that doesn't make it mine. If I break into your home and put my name and address on your computer, that doesn't make it mine.Ownership is a mental construct. Things belong to people simply because we think they do. As a society, we have developed methods of arbitrating differences in opinion, but they are opinions, nonetheless.

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But I can't make his computer mine just by "thinking really hard".

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Sure you can.And I'll try to stop you from making good on that thought because I seem to think that it's mine. Fortunately, everybody else seems to think that it's mine, too, and thus if I complain to them about what you did, they'll generally side with me.Not because anything in the object has changed. Simply because they think it. The only way they'll come to agree with your thought that it's yours is if it can be shown that I, too, think it's yours.

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Clearly the "thinking really hard" argument is a straw man.

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Nope. It's the actual argument. If you can change it simply by thinking about it, then it's a mental construct.But if you can't change it simply by thinking about it, then it isn't.------------------
Rrhain
WWJD? JWRTFM!

crashfrog responds to me:

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That if everybody were to drop dead right now where they are, the number of fingers on your hand would change?

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Another question that you keep asking, and the answer is "no". If the fingers cease to exist then the number of them ceases to exist as well. What's hard to understand about that?

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Nothing.It's my point, however.If the number of them ceases to exist when the fingers cease to exist, then the number must be part and parcel of the fingers. And if the fingers exist, then the number exists, too.The color of the fingers and the texture and such are all part and parcel of the fingers. If the fingers go away, so does their color and texture.And their number.Since number behaves identically to color and texture, then if color and texture exist as a real thing, then number does, too.------------------
Rrhain
WWJD? JWRTFM!

crashfrog responds to me:

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But if you can't change it simply by thinking about it, then it isn't.

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Whether or not you can change it with your mind has nothing to do with whether or not it's a mental construct.

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Incorrect. That's the point behind a mental construct: It exists simply because you think it does.

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There are mental constructs that cannot be changed.

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No, there aren't. Mental constructs, by definition, exist only in your mind. Therefore, all you need to do is change your mind.------------------
Rrhain
WWJD? JWRTFM!

crashfrog responds to me:

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When I read your responses, it's like you're responding to a totally different post and then putting my quotes in to make it look like a reply.

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Hey, I can't control what you write. If you don't like your own words, then change what you're saying.

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Since brains became powerful enough to think abstractly.

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This doesn't even begin to address my point. Try actually reading my posts.

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Ah, but I did. Notice how I keep including your words.If you don't like what you said, then change what you're saying. Remember how you said that you didn't think I was the most honest of debators?Did you ever stop to think that perhaps I have the same opinion of you?

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Mental malleability is not inherent in every mental construct.

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Incorrect. Mental constructs by definition exist only in your mind. Thus, they can be changed simply by changing your mind.

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Math could simply be (and my position is, it is) a language with a very strict grammar.

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So you're saying the number of fingers on your hand does change when you stop thinking about them?

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You will notice that human communities, when left to their own devices, will come up with completely separate languages.

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You're quite wrong about this.

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No, I'm quite right about this. That's why English in the US is different from English in the UK and both are different from English in Australia. They became isolated and changed. They evolved.

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All languages obey basic deep grammars (which first began to be outlined by Chomsky). No human has ever invented a language that runs counter to those deep grammars. They're so universal that it has been proposed that they're actually hardwired into our brains. But their universality doesn't mean they have independant existence outside of our minds.

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Logical error: Changing the subject. Language is not grammar, though languages have grammar.And if humans are hard wired to have a huge preference for a single type of grammar, that just means we have an intense bias, not that there cannot be any other grammar.By the way, Chomsky's concept of "deep grammar" isn't exactly universally accepted.

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If mathematics were just something in your head, then we should have all sorts of mutually exclusive mathematics.

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Why?

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Because mental constructs are by definition all in your head.

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Deep grammars are just a mental concept, and we don't find all sorts of mutually exclusive grammars. Instead we find just one deep grammar.

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So sayeth Chomsky.Others think he's full of it and that his "deep grammar" doesn't even exist.

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Second, they cannot control the popular useage.

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Ah, but you made the claim that they would be able to - by "thinking hard" as you put it.

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And they can. To them, "spam" will never mean junk email but will always be a brand name.But since I can't actively and completely control your thoughts by my thoughts, then we have multiple people thinking different things, all of which are active.And yet strangely, we all seem to come up with the same mathematics. Everybody seems to understand that 1 + 1 = 2.

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You said that by "thinking hard" they could change the meaning of words. So, can they change the meaning, or can't they? You don't seem too sure about this.

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No, I'm quite sure. You're simply changing the goalposts again. You're confusing one person's thoughts with anothers. You seem to want what one person thinks to be the same as what other people think.

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We already have.

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Sorry, I was talking about you, not us. Change my fingers into thumbs.

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Fine: They're thumbs. If you want me to call the digits on your hand "thumbs," then I'll call them "thumbs."Just to be certain, you do understand that by calling the digits on your hand "thumbs," we haven't actually changed anything about them in reality.

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Um, voting isn't a mental action. It's a physical one.

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Not quite right - technically, it's an "locutionary act".

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And that isn't physical?

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You're calling cosmology "mystical claptrap"?

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We weren't talking about cosmology.

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We certainly were. We were talking about nothingness. That's a big subject in the question of cosmological origins because it concerns with how we can get all this something out of nothing.

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You certainly made no cosmological statements.

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I thought I said "nothingness."

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I just asked you where the numbers are if there's nothing to count.

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Same place. With the objects. When space and time and all that disappear, you've got nothing. And in math, that's the empty set.

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I mean, there's zero, obviously, but where are the rest of them?

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Irrelevant. If you take away the light, where does the color go? If you take away the object, where does the texture go?The numbers are part and parcel of the object. You're making my point for me. If numbers were all in your head, then they'd still be there even if there were nothing there. But since they aren't there, since they come and go with the objects, then they're part and parcel of the objects and are just as real as the color and the texture of the object.

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They can't be "in the nothingness", because if they were, there wouldn't be nothing, would there?

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Nope.There'd still be nothing. A set composed of the empty set is not empty, but the empty set is empty.

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Or do you think numbers are nothing?

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Logical error: Equivocation.

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Are you saying you don't have five fingers on your hand? Your fingers exist. There are five of them. Therefore, five exists, too. It is part and parcel of your fingers.

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This is what I mean about asking the same questions over and over again.

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That's because the conversation keeps hinging on the answer to it. When you're not avoiding it outright, you're saying one thing and then immediately contradicting yourself. Thus, I go back to the original question because your later statements seem to be indicative that you have changed your mind.F'rinstance, if I were to ask you what 1 + 1 equals and you were to answer 2, and if you were then to say that if I bring my apple and you bring your apple, we'd have enough apples to give one to Jane and John and Jill, you'd understand why I'd go back to the original question of what you thought 1 + 1 was equal to. That's because your secondary statement seems to be that 1 + 1 = 3 and yet just before you said it was equal to 2.

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Remember when I answered this with a "no"? Guess not.

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No, I do remember. But then you went on to say that since you do have five fingers on your hand and that you can't change that number just by thinking about them and how about there'd still be five of them even if nobody were to count them (such as because everybody dropped dead) and such, that doesn't mean that the number of fingers is a real property but actually it is a mental property.Since those two statements contradict each other, I attempt to find out which one you really ascribe to. Thus, I go back to the beginning and try to find out how you can get to the latter statement given that you advocated the former.

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Just because we all agree that I have five fingers on my hand doesn't mean that five has an independant existence.

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In and of itself, no. We might all be deluded, after all.But if the number of fingers on your hand doesn't change even if nobody counts them, then that does mean five has an independent existence and it is manifesting itself at the end of your hand.Just like the color of the fingers has an independent existence and is manifesting itself at the end of your hand.

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Everyone who develops language agrees on certain deep grammars - universally. That doesn't mean that they have an existence outside of our heads.

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Many people think there is no such thing as "deep grammar."

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If I think hard enough, I can change the langauge.

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Go ahead and do so. Change the deep grammars.

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Can't change what doesn't exist.------------------
Rrhain
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