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Some Thoughts on The Arbitrary

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2 hours ago, necrovore said:

In all these kinds of cases, there's an X which we say "can be arbitrary" (e.g., pick any particular lighting of a stick of dynamite) but X is only part of the statement under consideration.

That's different from saying that the entire statement is arbitrary.

Is X a statement?

Is X an assumption when/after you pick?

Can "if x then y" also work as "assuming x then y"?

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On 7/27/2021 at 1:59 AM, Boydstun said:

Not every sort of arbitrary claim in the negative sense of 'arbitrary claim' is neither true nor false. "Some tigers are trees" is an arbitrary claim, it has a plain meaning, and under that meaning, it is false.

 

In what sense is this arbitrary? I seems clearly false.

Is it in the sense of purposeless or randomly chosen?

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14 hours ago, necrovore said:

As Boydstun pointed out early in this thread, the word "arbitrary" can be validly used in statements of the form "Take an arbitrary triangle." A lot of our knowledge takes the form "For all X, Y follows." And in the latter case, if Y is true for all X (in a given context), then it doesn't matter which X you choose, Y will be true for it. So the choice of which X is "arbitrary" in the sense that the choice of X does not affect whether or not "For all X, Y follows" is true.

In a proof that starts out with something like "Let x be an arbitrary triangle", we are not so much choosing a triangle as assigning the name x to an indeterminate triangle.  x could be any triangle; all we know about it is that it is a triangle.  If this is enough to prove that x is Y, this proves that all triangles are Y.

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18 hours ago, Easy Truth said:

You hit a fork in the road, you have no idea about where left will go or right will go.

You choose right.

In this case, I maintain that the choice is what Ayn Rand called "optional", not what she called "arbitrary".

It would be arbitrary if you claimed that you could somehow tell which choice was better when you had no clue.

It would be arbitrary if you jumped to the conclusion that there was no clue without putting any thought of any kind into the matter.

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11 hours ago, Easy Truth said:

In what sense is this arbitrary? I seems clearly false.

Is it in the sense of purposeless or randomly chosen?

Yes, false in my view also. The arbitrariness of “Some tigers are trees” would be in its break with cognitive purpose. It is (presumably) asserted without evidence or warrant, which is a requirement insofar as the statement’s purpose is to communicate literally a fact about the living world.

Objecting to the idea that a statement could be both arbitrary (and in at least the vicinity of meaningless) and false, someone could say: “Whoa! In saying ‘Some tigers are trees’ you are saying ‘There exist organisms that are both tigers and trees’ and that is false (and profoundly false, given the different ways of life of animals and plants and the deep difference in constitution of their cells), and I think that in order to be false (or true), a statement has to be purporting a fact, which, furthermore, would be a statement exclusively either true or false. And any such statement is cognitively purposeful." On the other hand, it does seem sensible to me to say that as an assertion of literal fact, the false statement “Some tigers are trees” is not so devoid of the arbitrary as the statement “Some blood is gelatinous matter” and, so, not so fully cognitively purposeful.

Yes, ET, the statement “Some tigers are trees” is also arbitrary in the sense of being generated at random. My process for getting a candidate for the topic used that random generation, and perhaps there is an element of that in all arbitrary statements. That process of random [or loose-associative] generation can also be a way of getting a start on some poem, say, a narrative “Some tigers are trees / fooling the Daphnes. / . . .”)

Edited by Boydstun
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4 hours ago, Doug Morris said:

In a proof that starts out with something like "Let x be an arbitrary triangle", we are not so much choosing a triangle as assigning the name x to an indeterminate triangle.  x could be any triangle; all we know about it is that it is a triangle.  If this is enough to prove that x is Y, this proves that all triangles are Y.

I like it. David Hume got himself into something of a see-saw over the nature of mathematics. On the one hand, he denied one could think of a triangle in general, only a particular triangle with specific lengths of its sides. From which, really, you couldn't have proved anything about triangles in general, though you were proving it of a specific triangle---the 2R characteristic, say---and by the very proofs we usual folks use. That reduces the character of generality in geometry to the character of generality gotten by statistical sampling, which is absurd.

Edited by Boydstun
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4 hours ago, Doug Morris said:

In this case, I maintain that the choice is what Ayn Rand called "optional", not what she called "arbitrary".

It would be arbitrary if you claimed that you could somehow tell which choice was better when you had no clue.

It would be arbitrary if you jumped to the conclusion that there was no clue without putting any thought of any kind into the matter.

Interesting, in the thesaurus, optional comes up as a synonym for arbitrary.

So you think about it. And you see no evidence of going left or right is better, none at all. But you have to move forward, let's say you are pursued by dangerous people.

You toss a coin.

Tails means go right and you do.

Was that an arbitrary choice?

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14 hours ago, Easy Truth said:

In what sense is this arbitrary? I seems clearly false.

Does it matter if it is clearly false? What I mean is that while a conclusion may be false, if you cannot completely evaluate the claim with purported evidence, there is no way to determine if what the person is saying is actually false. The claim cannot be evaluated. In this case, the only thing obvious is the conclusion being false. If you look at the claim, you need to judge it based on the claim itself, not based on what you know to be the case and your own evidence. 

Edited by Eiuol
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41 minutes ago, Eiuol said:

Does it matter if it is clearly false? What I mean is that while a conclusion may be false, if you cannot completely evaluate the claim with purported evidence, there is no way to determine if what the person is saying is actually false. The claim cannot be evaluated. In this case, the only thing obvious is the conclusion being false. If you look at the claim, you need to judge it based on the claim itself, not based on what you know to be the case and your own evidence. 

There are several ways to interpret this

1. If it is context-less, it is arbitrary

2.If you don't have enough information it is arbitrary

3.If you have not been given enough information it is arbitrary

it all hinges on "complete evaluation" as you put it.

Since there is no omniscient knowledge, we must be talking "complete contextual evaluation".

Without enough of a context, it can't be evaluated. If it is in fact false (from an omniscient view), from a personal view it could still be neither true or false i.e. to be determined. Kind of a limbo state of knowledge.

I would agree that that it is one of the two species of arbitrary. The other being the one where you know it can NEVER be evaluated completely.

As far as does it matter:

It would help to know if it will NEVER be evaluated completely or not. You won't go down that rabbit hole.

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4 hours ago, Easy Truth said:

So you think about it. And you see no evidence of going left or right is better, none at all. But you have to move forward, let's say you are pursued by dangerous people.

You toss a coin.

Tails means go right and you do.

Was that an arbitrary choice?

Tossing a coin is as good a way as any of choosing when it is optional which you choose.

If you are pursued by dangerous people, tossing a coin may be a good way to make it hard for them to tell what you choose.

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4 hours ago, Easy Truth said:

Interesting, in the thesaurus, optional comes up as a synonym for arbitrary.

From the Ayn Rand lexicon:

It is important to note that while the choice of a given standard is optional, the mathematical rules of using it are not. It makes no difference whether one measures length in terms of feet or meters; the standard provides only the form of notation, not the substance nor the result of the process of measuring. The facts established by measurement will be the same, regardless of the particular standard used; the standard can neither alter nor affect them. The requirements of a standard of measurement are: that it represent the appropriate attribute, that it be easily perceivable by man and that, once chosen, it remain immutable and absolute whenever used.

“Cognition and Measurement,”
Introduction to Objectivist Epistemology, 7–8

 

The capacity to procreate is merely a potential which man is not obligated to actualize. The choice to have children or not is morally optional.

“Of Living Death,”
The Voice of Reason, 55

 

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23 minutes ago, Doug Morris said:

Tossing a coin is as good a way as any of choosing when it is optional which you choose.

If you are pursued by dangerous people, tossing a coin may be a good way to make it hard for them to tell what you choose.

I think you are saying it does NOT qualify as an arbitrary choice.

It maybe the best way to move forward, but I am arguing that it is arbitrary to go to the right.

As in, if there was no evidence to it's benefit or loss or any comparative advantage and you chose it, shouldn't it be considered arbitrary?

Or perhaps you are making the point that it is rare to make an arbitrary choice?

Could you give an example of an arbitrary choice?

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1 hour ago, Easy Truth said:

1. If it is context-less, it is arbitrary

Not if the claim is at least logically coherent, as I mentioned before.

1 hour ago, Easy Truth said:

2.If you don't have enough information it is arbitrary

I literally said in the paragraph you quoted that you can't judge it in terms of what you know. You don't judge something as arbitrary based on what you know. It is whether or not the claim can be evaluated at all.

1 hour ago, Easy Truth said:

3.If you have not been given enough information it is arbitrary

Same as the above.

2 hours ago, Easy Truth said:

It would help to know if it will NEVER be evaluated completely or not. You won't go down that rabbit hole.

That's what it means for a claim to be arbitrary. It cannot be evaluated true or false. 

I see your newer responses, but I have nothing new to add. I just wanted to point out here that these things were talked about already. Necrovore did as well in his previous post, his point about the entire claim rather than just a part of a claim.

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11 hours ago, Easy Truth said:

As in, if there was no evidence to it's benefit or loss or any comparative advantage and you chose it, shouldn't it be considered arbitrary?

An arbitrary choice is one divorced from one's understanding of reality.  If one's understanding of reality provides no basis for picking one choice over another, the choice becomes optional, not arbitrary.

12 hours ago, Easy Truth said:

Could you give an example of an arbitrary choice?

 

21 hours ago, Doug Morris said:

It would be arbitrary if you claimed that you could somehow tell which choice was better when you had no clue.

It would be arbitrary if you jumped to the conclusion that there was no clue without putting any thought of any kind into the matter.

It would be arbitrary if your understanding of reality indicated you should go left, but you went right on a whim.

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