An argument for relativism

Philosophy Forums Philosophy
1

This isn’t really a defense of relativism overall, but a response to a certain objection to relativism. It goes as follows:

If all truth statements are relative, then any relativistic qualifications that you add into a statement stand in need of further qualifications. For example, in order to make clear the relativity of a statement like “The sun is hot” I have to phrase it as “The sun is hot for me.” But then this too is a statement that stands in need of relativistic qualification. So one may ask “Is the statement ‘The sun is hot for me’ true relative to something, or is it true absolutely?” As a relativist, I have to answer that it is true relative to something. And what is that something? It’s me. I have to say “The sun is hot for me, for me.” As you can see, this will lead to an infinite regress whereby for any statement to be accurate, it needs an infinite number of qualifications tacked onto it.

Now I’m reminded of a debate I got into a while back on whether or not thirds were possible. That is, is it possible or is it not that you can have a third of something, anything. Wonderer and I got into it pretty thick part way into the thread. He insisted that because it takes an eternity to write out all the 3s in 0.333…, you can never really have a third of anything. I argued that of course you can have a third. The problem of writing out all the threes is a problem of notation, not of the quantity 1/3 itself. You would need an infinite amount of paper and ink to write it out, and an eternity of time to say it, but that doesn’t mean that the idea of a third is inherently flawed. And even this problem (of notation) can be overcome by adopting a different notation, such as “1/3” or “a third” or “one out of three”. I don’t think he quite got it:

viewtopic.php?f=4&t=162910&hilit=0.333

Anyway, my point is that the exact same reasoning can be applied to this objection to relativism. What’s being pointed out here is that it would take an eternity to utter, or to write out, a relativistic statement if you want to be perfectly precise. But it doesn’t follow that the relativity of such statements can’t hold in principle. One can very easily conceptualize what it means for a statement to be true relative to me, or you, or some story, or some paradigm of reality, etc. without having to spell out all the qualifications that would be tacked onto the end of such a statement. And even then, we can do the same as what we do with one third–invent a new notation, or a new way of speaking that implicitly connotes the infinite chain of relativistic qualifications. So, for example, if I say “The Sun is hot relative to me,” you can take that to imply that “The sun is hot relative to me, relative to me,” or “The sun is hot relative to me, relative to me, relative to me,” ad infinitum. You can assume the infinite chain is just there. Or I could say “The Sun is hot relativistically”. Maybe “relativistically” is the qualifier we need–it’s the notation that symbolizes the infinite chain. If relativists adopt that convention, the objection above is addressed and we can carry on.

2

In base3, the notation of 1/3 would be .1 I think. Maybe relativists think that people who use base3 can have thirds of things, but not people who use base10…

:laughing:

3

Thanks for your input Flannel, but it seems this thread died a quick death. I suspected it might be one of those topics that’s too particular for anyone to care, but at least I got it out. :smiley:

4

So when you say that just because you don’t have time to write out all the 3s, that this doesn’t mean you can’t have a third, I think about this.

Just because something isn’t possible in the world of engineering, doesn’t mean it’s not possible per se. The entire idea of theorizing, is to determine whether things are possible, impossible, necessary, probable, or improbable. If you can realize that the only limitation to having properly notated thirds is one of engineering, or of time limitations or what have you, then you can in theory determine that it’s possible that thirds exist. Kinda like a higgs boson. If it doesn’t exist, then a lot of shit doesn’t make sense. For what you already hold to be true about mathematics to remain true throughout your experiment with thirds, you’ve gotta determine that the problems of the existence of thirds isn’t an analytic one but instead one of practical limitations.

5 
 No it doesn't have to die, Gib.  In other mathematical examples, for instance the extremely minute number which separates 0 time from the time measured from the occurrence of the so called Big Bang, time becomes relatively stretched, so that those last minute iotas , if conceivably were able to be experienced, would seem like eternity.  Here a .00000000000000000000000000000000 micro second would approach a span of infinity.

From normal course of experience, this does not occur, so we round up, for the sake of convenience.

6

Gib,

“If all truth statements are relative, then any relativistic qualifications that you add into a statement stand in need of further qualifications. For example, in order to make clear the relativity of a statement like “The sun is hot” I have to phrase it as “The sun is hot for me.” But then this too is a statement that stands in need of relativistic qualification.”

Huh?

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Relativism causes infinite regress.

8

No it doesn’t. That’s like saying cause and effect causes infinite regress.

9

I suppose that’s true. And it’s even a subtly different point that the one I was making–about requiring an infinite amount of paper and ink to write out. I mean, if you tried to cut a pie into three equal pieces, I highly doubt any piece would be exactly 1/3 of the entire pie–a problem of engineering as you say. But I have a further suspicion that, whatever the exact quantity of the piece of pie, it wouldn’t be a rational number (I had a thread on this one time explaining why–ask me if you want me to dig it up). So even then, you would still have a quantity requiring an infinite decimal expansion.

Really, obe? How do you figure?

Sorry for the convoluted jargon. All I mean to say that anything you utter is a statement, and that if all statements are relative, it would seem you would have to tack on a “relativistic qualifier” (like “for me,” or “relative to your views,” or “according to such-and-such text,” etc.) to those statements. But then that becomes a statement. Ergo, it too needs a relativistic qualifier. If this goes on long enough, you get statements like “X is true for me, for me, for me, for me, for me…”

Um… the whole point of the OP is to show that it doesn’t. Uttering relativistic statements does.

10

But why for me for me for me? That makes no sense. You could add to the statement hot for me compared to others because I’m an Eskimo or because I live on earth, not mars, and it’s the height of summer. For me for me for me is just gibberish.

11 
 Gib: relativity theory changes the preception of time. At the moment of the Big Bang, there was absolutely no appreciable time. There was no time 0.
12

It’s not gibberish, it’s just not very English-language-friendly.
Kinda like that term I just made up…

Basically “it’s hot” needs a “for me” to make it relative, because everything is relative… for me.
But then “hot for me” now sounds like an absolute. To make it relative we need “(hot for me) for me” in order to be more correct.
But then “(hot for me) for me” now sounds like an absolute. To make it relative we need “((hot for me) for me) for me”.
And so on…
Then we refer to this “infinite regress” attribute as “that which qualifies relativistically”, to escape being caught up in it forever.

But I don’t think this really solves anything since “it’s hot relativistically” is in the form of an absolute…

I prefer the solution “everything is relative except absolute statements such as this one”. But that’s not really news to anyone.
To expand on this and make it more informative, I would say that “statements directly about reality are all relative”.
This remains true by experience, and the statement does not apply to itself, contradicting itself, because it is a statement about statements about reality (it’s indirect).
Only statements indirectly about reality can be absolute. These absolute statements can be about either other absolute statements or relative statements. But any absolute statements about absolute statements etc. are eventually about relative statements directly about reality.
Therefore all statements are ultimately relative, and I can say that without being self-contradictory.

I think that’s a better argument for relativism.

13

Hot for me sounds like an absolute? What have you guys been drinking?

14

Would be .111 recurring actually. Since it cannot be expressed finitely as such except as a fraction rather than a decimal. Oh yes I am a pedant. :stuck_out_tongue:

15

How do you reckon that?

In base 10, moving the decimal place one number to the left is the same as dividing by 10.
E.g. 01.0 divided by 10 is 0.10

Likewise, in base 3, moving the decimal place one number to the left is the same as dividing by 3.
So 1.0 divided by 3 is 0.1 FJ was right.

This is maybe more obvious when you consider that in “base 3”, 3 would be denoted as 10. 1 divided by 3 is written as 1/10, which we know as 0.1 from decimal (and any other base).
Having said all this, in base 3, “base 3” would be written as “base 10”… but maybe that’s getting confusing now (for some).

0.1(recurring) in trinary would be 1/2.

In fact, working this out has caused me to stumble on something rather interesting…
In decimal, 1/9 equals 0.1(recurring).
In trinary, 1/2 equals 0.1(recurring).
In nonary, 1/8 equals 0.1(recurring).
etc.
So in base n, 1/(n-1) equals 0.1(recurring)… except in binary, where since n=2, 1/(2-1) = 1/1 = 1. 0.1(recurring) actually equals 1.
So if the number “zero point n-1, n-1, n-1, recurring” equals 1 in binary, would it not follow that 0.9(recurring) equals 1 in decimal?
I’m aware that I’ve taken a specific pattern, true in binary, and made a general pattern out of it in order to apply it to decimal (and all other number systems with different bases), but it still somehow seems plausible… maybe not.

“It is hot relative to my perception of heat” is relative.
This could be re-written as “It is absolutely (hot relative to my perception of heat)”.

Relative vs. absolute seems to me to be a distinction between forms of presentation, or of one’s approach. One can consider something as a particular finite thing, or one can consider something as a universal infinite thing. Considering the universe as either “one” or “many ones”, for example. It’s the same universe considered differently. It isn’t inherently relative or absolute, but then my very point suggests a relativism - and yet to sum it up suggests an absolute truth.

Get it? Or do you need a few swigs of what we’re drinking first?

16

This is going to be hard for me to explain. I’m going to try it in this form:

Relativist: The day is hot.

Absolutist: Is that statement true relativistically or absolutely?

Relativist: Relativistically.

Absolutist: Then who (or what) is it true relative to?

Relativist: To me.

Absolutist: Then the statement “The day is hot.” is true relative to you.

Relativist: Yes.

Absolutist: Now, is that statement true? The one I just made?

Relativist: What? The statement “The statement ‘The day is hot.’ is true relative to you [Relativist].”?

Absolutist: Yes, that statement.

Relativist: Yes, it is true.

Absolutist: And is it true relativistically or absolutely?

Relativist: Relativistically. All statements are relative.

Absolutist: Then who (or what) is it true relative to?

Relativist: To me.

Absolutist: Then the statement “The statement ‘The day is hot.’ is true relative to you.” is true relative to you.

Relativist: yes.

Here’s another way to think about it: If I tell you “The day is hot” but I tell Silhouette “The day is cold,” then it stands to question whether the statement “The day is hot relative to Gib” is true or false. It is true relative to you (because I told you that and you believe me), but false relative to Silhouette (because I told him the opposite and he believed me). So we’d have to say “The day is hot relative to Gib relative to anon,” but “The day is cold relative to Gib relative to Silhouette.” ← in this case, we have two levels of relativistic qualification but with different people on each level (Gib on the first level, anon and Silhouette on the second). The series of qualifiers “for me, for me, for me…” is simply the same person on multiple (infinite) levels.

It looks that way, but looks are deceiving.

Saying that it has an absolute form is like saying that 0.333[bar] takes a finite form because we don’t actually see an infinite series of 3’s. The “relativistically” is a term that stands in for the infinite series of “for me, for me, for me…” Statements only really take absolute forms if there is a final “for me” or no “for me” at all.

Thanks for offering yet another proof that 0.999[bar] = 1. If you haven’t clicked on the link in the OP, I recommend doing so.

17

You’re right actually it was a lazy post, but I think you have stumbled on something interesting.

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I’ve read and contributed to threads exactly the same as the one you’ve linked to in the OP. My conclusion is that 0.9(recurring) does equal 1. That is, one is a representation involving infinites, the other is a finite representation - but they are both representations of the same thing. (The 9s NEVER stop in 0.9(recurring) so there is never any increment between it and 1).

I wouldn’t call what I just posted about “a proof” though. As I said,

This is a significant flaw, don’t you think? To get around it one would need to do something like prove that binary is somehow superior to other number systems with different bases. Perhaps binary is the only representation that can show what is true for all representations?

19

Perhaps, but you can see why it works:

Take trinary: 1/2 = 0.1(recurring) /= 1. It does not equal 1 only because the number it is approaching is not 1. In trinary, there is one more numeral that has to appear in the notation before you go from 0.1(recurring) to 1.0, and that’s “2” (as in 0.111…1112 ← where this “2” appears at the end of some finite series of 1s). In other words, there’s a whole bunch of numbers between 0.1(recurring) and 1.0 that consist of a finite decimal expansion of 1’s terminated by a 2 (0.12, 0.112, 0.1111112, 0.111…1112, etc.). So 0.1(recurring) cannot be approaching 1.0. But in binary, it must be approaching 1.0. There is no other numerals besides 0 and 1 in binary and so there is no such number as 0.111…111x where is x is some numeral other than 0 or 1. Thus, in binary, 0.111(recurring) approaches 1.0, thus, it is 1.0.

20

To make a general rule out of my first post:

All repeating decimals are representable as fractions – they are all rational numbers. All fractions are representable as a non-repeating finite decimal in at least one base – namely the base of the denominator. Therefore, for every infinitely repeating decimal in base10, there is a mathematically equal non-repeating finite decimal in another base.