Kacy's doctrine of the arbitrary propostion


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Okay, so it's not a doctrine as much as a basic sketch, but I'd like to present it for critique.

This stems from the discussion about Peikoff's doctrine of the arbitrary assertion. There has been lengthy discussion of it and as best as i can tell, it has been rightly rejected by the majority of the folks on this forum.

However, the fact that Peikoff's doctrine has fatal flaws doesn't mean that there's no such thing as a truly arbitrary assertion. It doesn't mean that there is no relevant distinction between the false and the arbitrary. And it doesn't mean that distinguishing between the two is not an important cognitive function.

My contention is that:

- Any proposition about the nature of reality will fit into one of two broad categories: Those which have truth value and those which don't.

- Those which do may have a truth value of true or false. (Whether or not that value is as-of-yet determined is irrelevant, so long as it is determinable).

- Those which do not are arbitrary, and the only proper way to handle such statements is to reject them out-of-hand.

Also:

- There are specific features a proposition must possess in order to have truth value. It must be, at a minimum, verifiable, falsifiable, and subject to examination.

- The burden of truth-value-demonstration falls on the person making the proposition. No one is obliged to rack their brains to determine whether a proposition has truth value.

For now, these are the only points I am arguing for. I also contend that an understanding of the principles listed above is a vital component of polemic discourse, as the deliberation of arbitrary propositions only serves to credit them with value and merit that they do not possess.

As examples, I present the following PROPOSITIONS:

1) 1 = 1 ----> True

2) 1 = 2 ----> false

3) 1 = x ----> arbitrary

1) I am a human being = true

2) I am a horse = false

3) I am a deity whose true identity may be known only to the gods = arbitrary

4) I have cancer = Undetermined, but possessing truth value

1) The rapture did not happen yesterday = true

2) The rapture happened yesterday = false

3) The rapture will happen soon, and by "soon", I mean "soon in heavenly terms", because to god a day is as a million years = arbitrary

4) The rapture will happen tomorrow = Undetermined, but possessing truth value.

The propositions numbered 1 and 2 are verifiable, falsifiable, and subject to examination. They therefore have a truth value of either true or false.

The propositions numbered 3 are not. They have no truth value whatever.

The truth value of the propositions numbered 4 are undetermined, but they still has truth value because they meet the criteria I've identified. They are verifiable, falsifiable, and subject to examination.

Sensing that the general tone of the forum seems to be against the idea that there is such a thing as a truly arbitrary proposition, and that the general sentiment stems from an unfortunate, self-serving essay on the arbitrary assertion by Dr. Peikoff, I am interested to hear what everyone thinks about my own formulation, without reference to anything purported by Dr. Peikoff.

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.... well....

1 = x as "arbitrary"

For many years high school algebra accepted problem statements such as

3x - 10 = -2x

solve for x.

Then, as I was entering the 9th grade, and computers were coming, we had to write problems out as

Let 3x - 10 = -2x

solve for x.

My point here is that these are arbitrary assertions for which truth values can be found.

I agree with everything above from Kacy, but his symbology "1 = x ---> arbitrary" is not rigorous.... which would not be a problem in common speech, but Kacy is going for rigor, so it seems appropriate to reply about that.

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Michael,

Thanks for the up-vote, and I do acknowledge that my 1 = x formulation might need some amplifying remarks.

That equation is used to demonstrate, in its rawest and purest form, the arbitrary nature of a proposition which employs undefined or non-specific terms.

In other words - so long as x remains undefined, there is no Truth Value (TV) to the equation. It cannot be called true or false.

Now... could TV be rendered if sufficient information were added to the equation? Certainly - but that applies to all arbitrary assertions. This is logically implied by the formulation I've indicted - that a statement, in order to have TV, must be Verifiable, Falsifiable, and Subject to Examination (VF&SE).

Therefore if you take any arbitrary proposition and insert information that renders the proposition VF&SE, you've provided the TV.

In fact... I'd be quite surprised to hear a mathematician claim that the proposition 1 = x is false. Or true. He would probably say it was undetermined and in need of more information in order to be either true or false.

Such is the nature of arbitrary propositions.

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I don't see anything to argue about. I like the idea of showing truth-falsity value of a proposition falling on the asserter. It stops most nonsense in its tracks. Or, you've made a claim, start to back it up with correct, basic methodology. Thus reason excludes mere asseveration from the start. This I think is the key to the value of arbitrary proposition identifications: first, you show your proposition is not arbitrary. I have to give Kacy a big gold star on this one.

--Brant

now I have to grind this into my own brain

three threads to get me here--should I be proud or appalled? (feeling both)

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Thanks Brant. Good to see I'm not off my rocker on this one.

I think it is just a simple matter of applying basic principles of reason and science methodology to the realm of basic propositions.

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Kacy, I first thought you came here carrying a sword for Leonard's stuff. I didn't know you were offering me the blue pill or the red pill, and I took one.

--Brant

king of the matrix: I am the One

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I am just recently coming to understand the differences and importance of differing views on logic and or formal logic in argument.(Both to argument itself and the 'logical premises' of the participants in an argument eg those who recognise an analytic synthetic dicothomy and those who deny a dicothomy exists).

Is it correct to say that formal logic is a 'type' of logic that is only operative inside a specialised method? Is it best understood as a way to verify mathematic propositions?

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tmj - I think this subject might merit its own thread but...

I personally think the word "logic" is one of the most misused and misunderstood concepts among junior-varsity intellectuals. I am of the firm opinion that Star Trek's Mr. Spock character went a long way in destroying people's understanding of what logic is. He was a cultural icon, and his most frequent catch phrase was "that's illogical" or something to that affect.

He used the word "logical" as a synonym for "sensible" or "reasonable" or "true", and I have heard countless people use it that way as well. It's unfortunate, because as much as I like the original Trek, his misuse of the term "logic" spoiled the ability to understand the word for at least a couple generations.

Logic is, put simply, an "if/then" statement. The IF is the premise and the THEN is the conclusion. I'm no expert on logical theory, but I do know that logic can be applied to math, reason, science, and many other pursuits where non-contradictory identifications are sought.

If x = 1 then 10x = 10. That's a mathematical statement that applies logic.

If the word "atheist" is defined as "one who does not have a belief in a god", and you do not have a belief in a god, then you are an atheist. This is a statement of reason that applies logic.

If all dogs breathe air and this newly discovered animal does not breathe air, then this newly discovered animal is not a dog. A statement of science that applies logic.

Those are logical statements. Whether they are true or not is irrelevant - they are still statements of logic. So I would say that logic is best understood as a process of non-contradictory identification (to borrow a textbook Objectivist formulation).

Like I said... we can start a new thread on this if you like.

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No I like logic as noncontradictory identification.

Given the three sets of examples, is the first group analogous to the others? It seems to me this is where the ASD comes in. Propositions whose terms are abstractions of method(?, ie numerals and symbols) are further removed from the perceptual chain and 'harder' to point to as fact. It seems this is where logicians come in and say that words are the same as the symbols, so how can truth be determined since neither actually points to things 'out there'.

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In the discussion from MSK, "This One Might Surprise You..." the Wason Selection Task came up. (See Wikipedia here.) Only 10% get the right answer. Among the explanations for the high failure rate is the difference between "natural language" and formal logic.

In natural language, we take p -> q in that direction: if p then q. However, we know "naturally" that the existence of q does not imply the existence of p because q could have other causes. This is not so with formal logic.

Similarly, in formal logic "necessary and sufficient" means "equal to" but in natural language that is not so. Regarding the federal response to Hurricane Katrina, President Bush insisted that the response was necessary and sufficient. He did not mean that it was just as bad as the hurricane -- or at least it was not supposed to have been.

In English we have only one "or" so we often confuse exclusive and inclusive disjunctions. In computing we have both OR and XOR, and, in fact, Latin is among the languages that has an exclusive-or, AUT and an inclusive-or VEL.

To me, that reflects the basic problem with philosophers such as the Early Wittgenstein who attempted to make claims about "natural language."

Spock's problem was that English is the official language of Starfleet. Unfortunately, the Vulcan Language Institute is defunct. Also, that was one of two distinct attempts by fans to create a Vulcan language from the few hints in the canonical shows. On the other hand, Klingon is much better developed. I own a Klingon-English dictionary.

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.

To me, that reflects the basic problem with philosophers such as the Early Wittgenstein who attempted to make claims about "natural language."

Spock's problem was that English is the official language of Starfleet. Unfortunately, the Vulcan Language Institute is defunct. Also, that was one of two distinct attempts by fans to create a Vulcan language from the few hints in the canonical shows. On the other hand, Klingon is much better developed. I own a Klingon-English dictionary.

q'Plah!

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Kacy, how would you characterize the following proposition:

"Rush (the band) is good."

(I'm being serious here)

That's not a proposition. It's a statement of opinion.

A proposition is a statement about reality - as in, the metaphysical nature of reality.

An opinion is a statement of value judgment, or simply judgment.

(And before you go asking "Isn't it a reality that Rush is good?", the answer to that is that the only reality contained in that statement is that Rush, in your judgment, is good.)

Instructive question, though. It is important to remember that my formulation applies specifically to propositions, not just any ol' statement.

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Kacy, how would you characterize the following proposition:

"Rush (the band) is good."

(I'm being serious here)

That's not a proposition. It's a statement of opinion.

A proposition is a statement about reality - as in, the metaphysical nature of reality.

An opinion is a statement of value judgment, or simply judgment.

(And before you go asking "Isn't it a reality that Rush is good?", the answer to that is that the only reality contained in that statement is that Rush, in your judgment, is good.)

Instructive question, though. It is important to remember that my formulation applies specifically to propositions, not just any ol' statement.

A proposition is a meaningful declarative sentence (if the proposition is expressed in English) which is either true or false.

The sentence "The assertion "Rush is good" is true. That makes sense, but it might not be a true sentence. It could be false, depending on what the world "good" meant.

Ba'al Chatzaf.

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Kacy, how would you characterize the following proposition:

"Rush (the band) is good."

(I'm being serious here)

That's not a proposition. It's a statement of opinion.

A proposition is a statement about reality - as in, the metaphysical nature of reality.

An opinion is a statement of value judgment, or simply judgment.

I'm afraid your reply raises more questions than it answers.

My first reaction has been anticipated by Bob. I'm not into the whole "logic" thing, but my limited understanding of the subject meshes with Bob's: a proposition, in the most fundamental sense, is simply a declarative sentence which is intelligible. You are free of course to draw a line between propositions which "relate to reality", and propositions which are "a statement of opinion", but isn't that begging the question? Who decides which propositions fall into which category? Do you think value judgements are not rational or objective? To wit: "Independence is a virtue". Is this a statement about reality, or a statement of opinion? Ethics and morality are all about value-judgements. Anyone proposing an "objective" code of morality better believe that value judgements relate to reality.

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No I like logic as noncontradictory identification.

The definition of logic given by most professional logicians is: logic is the discipline of valid inference. Most logical systems deal with the -forms- of inference more than the content. Logic is primarily about inference and consistency.

Ba'al Chatzaf

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Bob, you just said what Rand said, only using different words.

--Brant

I like them both

No I didn't. Identification has an empirical content. Logic is about form, for the most part.

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Bob, you just said what Rand said, only using different words.

--Brant

I like them both

No I didn't. Identification has an empirical content. Logic is about form, for the most part.

Both Rand's definition encompasses empirical content and so does the "professional logicians." As for the ratio between content and "forms" in a logical system the amount of content must overwhelm any amount ascribed to forms to the extent the logic is valid and used. Think of a machine stamping out a panel that will go into a car body. One machine, say a million panels. The machine is the forms and the result is the content.

--Brant

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Bob, you just said what Rand said, only using different words.

--Brant

I like them both

No I didn't. Identification has an empirical content. Logic is about form, for the most part.

Both Rand's definition encompasses empirical content and so does the "professional logicians." As for the ratio between content and "forms" in a logical system the amount of content must overwhelm any amount ascribed to forms to the extent the logic is valid and used. Think of a machine stamping out a panel that will go into a car body. One machine, say a million panels. The machine is the forms and the result is the content.

--Brant

See here's my conodrum, are there recognized differences between logic and logic with the f word? Does one need to establish which one the person they may be having a conversation with is using?

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I'm afraid your reply raises more questions than it answers.

My first reaction has been anticipated by Bob. I'm not into the whole "logic" thing, but my limited understanding of the subject meshes with Bob's: a proposition, in the most fundamental sense, is simply a declarative sentence which is intelligible. You are free of course to draw a line between propositions which "relate to reality", and propositions which are "a statement of opinion", but isn't that begging the question? Who decides which propositions fall into which category? Do you think value judgements are not rational or objective? To wit: "Independence is a virtue". Is this a statement about reality, or a statement of opinion? Ethics and morality are all about value-judgements. Anyone proposing an "objective" code of morality better believe that value judgements relate to reality.

For situations like these, I find it useful to draw principles using clear examples, and then use those principles to sort out the not-so-clear examples.

The fundamental difference between a proposed fact-statement and a statement of opinion is that, when it comes down to it, the former provides information about the *object* being discussed, whereas the latter provides information about the *subject* who is discussing the object.

For the sake of discussion, I propose that:

1) You are a human being = A statement about the metaphysical nature of reality

2) Red is the most beautiful color = A statement of opinion.

In example one, the sentence uttered tells the listener something about the object I'm discussing (you), and nothing about the subject discussing it (me).

In example two, the sentence uttered tells the listener nothing about the object I'm discussing (red), and something about the subject discussing it (me).

To reel it back to your original question, when you say "Rush is good", that really tells me nothing about Rush per se. Rather, it only tells me something about you (the fact that you value Rush).

If you doubt this, ask yourself if you've ever been told that a movie was really good, only to watch it and then wish you could have those two hours of your life back again. (Goddamn "Transformers"... I'll never forget the sonofabitch who recommended that to me).

So, no... it's not begging the question at all. The line between a proposition and an opinion statement is neither unclear nor arbitrary. There is a specific delineation to be made, and a principle to be drawn from it.

If this does not satisfy your curiosity let me know, and I'll start peeling back the onion on statements such as "independence is a virtue". But given the information I've provided, I think you should be able to start Figuring It Out Ray.

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For situations like these, I find it useful to draw principles using clear examples, and then use those principles to sort out the not-so-clear examples.

The fundamental difference between a proposed fact-statement and a statement of opinion is that, when it comes down to it, the former provides information about the *object* being discussed, whereas the latter provides information about the *subject* who is discussing the object.

For the sake of discussion, I propose that:

1) You are a human being = A statement about the metaphysical nature of reality

2) Red is the most beautiful color = A statement of opinion.

In example one, the sentence uttered tells the listener something about the object I'm discussing (you), and nothing about the subject discussing it (me).

In example two, the sentence uttered tells the listener nothing about the object I'm discussing (red), and something about the subject discussing it (me).

That's generally a good tack to take, but the specific example that you chose will not work with certain Objectivists. They would see the second proposition as false only because it identifies the wrong color as being the most beautiful. Their argument would be that it is an objective fact of reality, and not a mere "statement of opinion," that blue-green, rather than red, is the most beautiful color.

J

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