New Discussion of Peikoff's Arbitrary


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(NOTE FROM MSK: This thread is split off from Selective timeline and links of the Kelley-Peikoff schism in the David Kelley Corner.)

*How Peikoff justifies this "Neither/Nor" position with the Law of the Excluded Middle I have no idea.


An arbitrary statement is one to which no truth value can be assigned.

A true statement may be assigned a truth value of 1
A false statement may be assigned a truth value of 0
An arbitrary statement cannot be any truth value at all.

So Peikoff is right on this one. Arbitrary statements are not true. They aren't even false.

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So Peikoff is right on this one. Arbitrary statements are not true. They aren't even false.

This has been extensively discussed on OL here.

Suppose I say, "President Ronald Reagan killed President William McKinley. " Is it not both arbitrary and false?

Anyway, a belated welcome to OL.

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*How Peikoff justifies this "Neither/Nor" position with the Law of the Excluded Middle I have no idea.

An arbitrary statement is one to which no truth value can be assigned.

A true statement may be assigned a truth value of 1

A false statement may be assigned a truth value of 0

An arbitrary statement cannot be any truth value at all.

So Peikoff is right on this one. Arbitrary statements are not true. They aren't even false.

What you are saying is that Peikoff isn't even wrong.

A cruel but true judgment.

Ba'al Chatzaf

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I'd give an arbitrary statement a truth value of 0 and a false one -1.

Frankly, for me an arbitrary statement is merely false. It's a sneaky way to bring in an ad hominem argument with a gloss of reason.

--Brant

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I'd give an arbitrary statement a truth value of 0 and a false one -1.

Frankly, for me an arbitrary statement is merely false. It's a sneaky way to bring in an ad hominem argument with a gloss of reason.

--Brant

I'd caution anyone against failing to distinguish between a false statement and an arbitrary one. It's bad philosophy, and it's just plain wrong.

As analogous to math - 1=1 is true, 1=2 is false, and 1=x is arbitrary. If you said 1=x is false, you'd be wrong in point of fact. Arbitrary and false are not the same.

Arbitrary statements should be treated differently from true/false statements As (I think) Dawkins once pointed out - statements that can be arbitrarily made can safely be arbitrarily dismissed. They are unfalsifiable and unverifiable.

One reason it's important is because it cuts the wheat from the chaff in terms of philosophical argumentation. It distinguishes between those statements which merit examination/consideration and those which don't.

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I'd give an arbitrary statement a truth value of 0 and a false one -1.

Frankly, for me an arbitrary statement is merely false. It's a sneaky way to bring in an ad hominem argument with a gloss of reason.

--Brant

I'd caution anyone against failing to distinguish between a false statement and an arbitrary one. It's bad philosophy, and it's just plain wrong.

As analogous to math - 1=1 is true, 1=2 is false, and 1=x is arbitrary. If you said 1=x is false, you'd be wrong in point of fact. Arbitrary and false are not the same.

Arbitrary statements should be treated differently from true/false statements As (I think) Dawkins once pointed out - statements that can be arbitrarily made can safely be arbitrarily dismissed. They are unfalsifiable and unverifiable.

One reason it's important is because it cuts the wheat from the chaff in terms of philosophical argumentation. It distinguishes between those statements which merit examination/consideration and those which don't.

Sound argumentation (I think) KacyRay. But what Brant is referring to with ad hominem is what

also took me aback: Peikoff was correct up to there, but wouldn't leave it at that - it's the 'from whence it comes' argument he used. That one can and must identify the deliverer of the statement ("a savage") to establish its arbitrariness/truth.

In effect, I think he's saying the statement cannot be assessed separately from assessment of the speaker.

Isn't this what Kelley called "intrinsicist" about Peikoff?

You primarily judge the person by his statements, not the statements by the person, I believe.

(What far-reaching consequences a single, innocuous-looking error can have.)

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Wolfgang Pauli may have tagged the arbitrary assertion correctly. His tart phrase "not even wrong" seems to apply.

Ba'al Chatzaf

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As analogous to math - 1=1 is true, 1=2 is false, and 1=x is arbitrary. If you said 1=x is false, you'd be wrong in point of fact. Arbitrary and false are not the same.

6 + x = 7

therefore 1=x

J

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Okay, obviously if you add information, you may render an arbitrary statement true or false.

Then it is no longer arbitrary. But the fact remains, a statement cannot be simultaneously arbitrary and false (or true).

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If this keeps on about Peikoff's hypothesis about arbitrary as a third logical alternative to true and false, I may move these posts to a suitable thread or even open a new one.

Michael

And make room for the excluded middle? About time!

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As analogous to math - 1=1 is true, 1=2 is false, and 1=x is arbitrary. If you said 1=x is false, you'd be wrong in point of fact. Arbitrary and false are not the same.

6 + x = 7

therefore 1=x

J

It is usually written x = 1 because x is what we are looking for.

Ba'al Chatzaf

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As analogous to math - 1=1 is true, 1=2 is false, and 1=x is arbitrary. If you said 1=x is false, you'd be wrong in point of fact. Arbitrary and false are not the same.

6 + x = 7

therefore 1=x

J

It is usually written x = 1 because x is what we are looking for.

Ba'al Chatzaf

Right. I skipped a step in getting in getting back to KacyRay's phrasing of it as "1=x." I assumed that it was logically implied, but here's the entire chain:

6 + x = 7

therefore x = 1

therefore 1 = x

J

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Whether an argument merits examination is purely an individual choice for various reasons. The arbitrary is only one. You can export your explanation of the arbitrary if you want, but not logicaly impose it in the name of reason called "rational" wrapped up in high moral dudgeon. Take out Peikoff's assault on Barbara Branden's Rand biography would we even be discussing this? I don't see how it can be properly used respecting complex statements without twisting your mind through unnecessary labyrinths.

--Brant

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Right. I skipped a step in getting in getting back to KacyRay's phrasing of it as "1=x." I assumed that it was logically implied, but here's the entire chain:

6 + x = 7

therefore x = 1

therefore 1 = x

J

Whether an argument merits examination is purely an individual choice for various reasons. The arbitrary is only one. You can export your explanation of the arbitrary if you want, but not logicaly impose it in the name of reason called "rational" wrapped up in high moral dudgeon. Take out Peikoff's assault on Barbara Branden's Rand biography would we even be discussing this? I don't see how it can be properly used respecting complex statements without twisting your mind through unnecessary labyrinths.

--Brant

Whether an argument merits examination is purely an individual choice for various reasons. The arbitrary is only one. You can export your explanation of the arbitrary if you want, but not logicaly impose it in the name of reason called "rational" wrapped up in high moral dudgeon. Take out Peikoff's assault on Barbara Branden's Rand biography would we even be discussing this? I don't see how it can be properly used respecting complex statements without twisting your mind through unnecessary labyrinths.

--Brant

I disagree, and I'll give you a couple examples...

Consider the following statement, made (hypothetically) in the year 1000 A.D.: "The Earth is flat"

It is a statement that is verifyable, falsifiable, and subject to examination. It makes an important proposition about reality and it objectively worthy of examination (as it would affect our ability to navigate and to understand other sciences better). It is objectively worthy of consideration.

It also happens to be false.

Now consider this statement, made countless times (in various forms) by my beloved uncle:

"God is all-knowing"

Is this statement worthy of consideration? Objectively? I don't think that saying this statement merits no consideration is wrapped up in "high moral dudgeon" or anything like that - I think it's prettty clearly an arbitrary statement that has no truth value whatsoever and merit's no consideration at all.

To be able to distinguish between statements that have truth value and those which don't is a vital polemic tool. In fact, it's all the more important because to elevate an arbitrary statement up to the status of "false" is giving it more credit than it deserves, and implies that the proposition merits serious consideration.

Note: I haven't read the in-depth discussion you linked me to yet, but I will. I recognize that I might be hitting on already-covered territory.

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Brant,

What's worse is that you have to eliminate context and focus solely on one part of an "arbitrary" statement to the exclusion of all else to dismiss the entire statement as having no cognitive content.

The problem is, all knowledge in the Objectivist theory is contextual. Eliminating context is a blank-out, but only one.

Another problem is that concept formation might be hierarchical in general terms, but no concept is formed linearly from a small number of referents. There is a vast number of inputs into the integration from all kinds of referents, both perceptual and conceptual, and at all levels in the different hierarchies (yes there are more hierarchies than one in any given concept, but that is something to elaborate on at another time). This is clear in ITOE, especially when abstractions, and abstractions from abstractions, not just perceptual concretes, are presented as conceptual referents. And this process is even more prominent in broad concepts like justice.

Agree or disagree, this is the Objectivist theory (at least as I understand it). So saying that an "arbitrary" premise negates the validity of these inputs in a statement (however indirectly by insinuation) is a literal blank-out of such vast proportions it is breathtaking.

This creates a rich field for one contradiction after another, and an impression of outright silliness, leading to general discredit of the Objectivist theory of knowledge.

That "arbitrary" thing is a nasty little critter once you dig into the wormhole where it lives.

Michael

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Right. I skipped a step in getting in getting back to KacyRay's phrasing of it as "1=x." I assumed that it was logically implied, but here's the entire chain:

6 + x = 7

therefore x = 1

therefore 1 = x

J

Obviously if you add more substance to an arbitrary statement you can render it true of false.

I was deliberate with my x=1 formulation. We aren't solving for x, we are making an entirely arbitrary statement

If I say x=1, the truth of that equation is not only unknown, it is *unknowable* (unless x is assigned a value). A statement that has no truth value is arbitrary.

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Right. I skipped a step in getting in getting back to KacyRay's phrasing of it as "1=x." I assumed that it was logically implied, but here's the entire chain:

6 + x = 7

therefore x = 1

therefore 1 = x

J

Obviously if you add more substance to an arbitrary statement you can render it true of false.

I was deliberate with my x=1 formulation. We aren't solving for x, we are making an entirely arbitrary statement

If I say x=1, the truth of that equation is not only unknown, it is *unknowable* (unless x is assigned a value). A statement that has no truth value is arbitrary.

But it's not unknowable. In saying "x=1" you are identifying x as 1. And then when you say that x + 6 = y, we know that y = 7.

J

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Kacy, your use of two simple examples merely supports my point. Then you give the game away by interjecting "vital polemic tool" into the discussion plus a heap of implied morality. Keep going and you'll end up in the reductio ad absurdum of Peikoff declaring The Passion of Ayn Rand is arbitrary considering THE SOURCE--i.e., the author.

--Brant

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But it's not unknowable. In saying "x=1" you are identifying x as 1. And then when you say that x + 6 = y, we know that y = 7.

J

Negative. In the context of this discussion, you are PROPOSING that 1 = x.

Remember, this is a discussion of propositions. Not identifications.

Substitute anything for x. Cat. Space. Laughter. 4 to the 4th power. Who knows what x equals? It's not defined.

(For the sake of clarity - when an equation such as "x=1" is made in a mathematical context, it's generally understood that the truth of that equation is *given*, not *proposed* However, this is a discussion about propositions. My apologies for not having been more clear about that.)

Again, take my hypothetical - God is all-knowing. God is all powerful. Those statement are ostensibly arbitrary, since they don't meet any criteria that would give them truth-value (when you drill down into it).

Brant - I categorically reject any rationale that would lead one to reject a statement as arbitrary based on who spoke it, and I'd be interested to see you demonstrate some sort of logical progression from "1=x is arbitrary" to some sort of "implied morality".

Keep going... how, exactly? How do you keep going from there?

When someone says "God is all-knowing", how do you "keep going" from there? It's a conversation-stopper. There's nothing to be said about such a statement... at least not to anyone who understands it's arbitrary nature. It would be as useful as deliberating Russel's teapot. THAT is why it's a valuable polemic tool - it cuts the wheat from the chafe and prevents you from being sucked into rabbit holes or arbitrary assertions.

Would you, Brant, ever spend time and energy discussing something such as what god does and does not know? Would you spend time and effort discussing whether there is a teapot orbiting the sun? If not, ask yourself why.

And then ask yourself if there's a principle to be found in your answer.

My contention is that the *principle* you would arrive at is: Arbitrary assertions merit arbitrary rejection.

- Kacy

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Kacy, but I'm not disputing your examples. I'm just saying--as I originally said--that arbitrary statements work for simple propositions and they can be misused for complicated ones which has been done. I also said you ended up in your statement with implied morality as did someone else a while ago only he to strike out at another person he didn't like and a biography he didn't want to deal with in any way or fashion except out of hand dismissal. I'm pointing out what I think is there, not the logic. I'm also stating now if not already that the arbitrary is frankly a trivial epistemological matter save for those who want to use it as a "vital polemic tool."

--Brant

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