"A priori" in the scientific vs. philosophic case?

[Hal]

double post, sorry

Edited August 9, 2005 by Hal

[Evangelical Capitalist]

A is not the concept. A is A is the concept. The former does not refer to anything at all. The latter refers to everything that exists.

The treatment of A as a variable which ranges over and can take on all the values in the set of everything that exists is absurd. A is not a variable, and does not range over anything, and does not take on values. A is A is another name for the law of identity. It's shorter than saying "it is what it is". That's it. The law of identity does not depend on a knowledge of algebra, set theory, or any other math.

It would be fine to say that 'A is A' is just an informal handle for, say, one of these:

Every entity is itself.

All things are themselves.

Every thing is what it is.

Etc.

But you're expressing that in a language. And so the examples above have pronouns: 'itself', 'themselves', 'it', etc. Those pronouns have referents. Or the referents of the pronouns are left undetermined but the pronoun is understood to stand for different things in some range of things.

'If something is crisp, then Jack likes it' provides that we can refute the sentence if we can plug in something, say a certain crisp apple, as a referent for 'it' and show that Jack in fact doesn't like that apple. One doesn't have to know mathematics to understand that.

But you say that taking 'A' as a variable is absurd. If it were absurd, then you could prove that by showing a contradiction. But you can't. You might show a contradiction with some other premises you hold, but the reasoning you've posted so far shows lack of recognition of certain basic implications of the fact that you are expressing laws with sentences that have words that refer.

Not to reopen this can of worms, but, well... I guess I'm reopening the can of worms...

The concept of identity, as I understand it, is a generalization from experience. Everything we observe possesses the characteristic of self-sameness, or identity. The concept of identity is derived from, and subsumes, all these observations. The statement "A is A" could be reformulated as, "For any existent, A, such existent is identical with itself." Have I changed the meaning at all here? If I haven't, then it seems rather clear to me that A is a placeholder for which any existent may be substituted. To claim otherwise would imply that identity cannot be applied to individual existents, which is clearly absurd. This doesn't require intricate knowledge of set theory or algebra to understand.

Identity acquires its axiomatic status from the fact that any attempt to refute it must implicitly accept it, since refutation implies truth and falsehood, proven and unproven statements, etc. which presuppose existence, identity and so forth.

[Gregory B]

Hal,

Peikoff says that "All truths are a product of the logical identification of the facts of experience" ("Analytic-Synthetic" in the 1990 ed. of IOE, p. 112), and what comes from experience is empirical. Yes, Rand distinguished axiomatic concepts from the rest (otherwise, she would have no concept of "axiomatic concepts"), but it doesn't follow that they are non-empirical concepts. Also, it does not follow from the fact that there are foundational and non-foundational concepts that the former are non-empirical (and those who believe in a priori concepts could make a distinction among foundational and non-foundational a priori concepts). And if any concept were not empirical (a posteriori) it would have to be a priori, and Rand surely does not believe in a priori concepts.

Yes, she and Peikoff would agree with Mill that the truths of arithmetic are derived from experience. But she would not conclude that they are therefore uncertain, as Mill apparently would.

As to Quine, he alternates, sometimes within a sentence, between saying things that Rand and Peikoff would reject and saying thinks that they would agree with. For example, he does agree with them that the analytic-synthetic distinction is nonsense (although for some of the wrong reasons) and that metaphysics should not be rejected.

Greg

[Proverb]

The concept of identity, as I understand it, is a generalization from experience. Everything we observe possesses the characteristic of self-sameness, or identity. The concept of identity is derived from, and subsumes, all these observations.

It is hard to begin to understand what you are saying here. "a generalization from experience." [what do you mean?] This sounds like an attempt at regurgitating things learned by rote.

With anything you say you know and with any words you choose to use you must have a grasp of it's relation to reality within the context of your knowledge.

'A is A' is a conceptualization of the law of Identity which is a corollary of the primacy of existence.

to explain:

In order to understand any amount of sensory data you must first realize that you are sensing something. In order to grasp the 'something' you are sensing, you have to realize that 'something' exists and is causing you to sense it. (this comes through realizing that some thing exists apart from your capacity to sense it) This is the process (however crudely represented here) through which you are able to eventually 'know' anything. This is the progenerate of 'existence exists' (which is only actually conceptualized at a higher level after you are able to understand what the word "exists" means)

In order to fully understand the nature of 'existence' and to advance to the level of conceptualization, you have to see that that which exists, exists with some attributes which may be directly perceived, or may not, but are present. It is thus that you are able to differentiate existents from one another and to form concepts through selective exclusion of measurements. The fact that existents exist and have measurements (attributes), is the fact through which the Law of Identity is drawn as a corollary.

"You see that 'it' exists as with 'these' attributes. To see this is to understand that 'it' is as 'it' is. A is A"

It is impossible to 'know' anything and to argue anything in this thread or anywhere without first accepting and not evading the fact that existence exists and exist such that 'A is A'

[Evangelical Capitalist]

It is hard to begin to understand what you are saying here.  "a generalization from experience." [what do you mean?] This sounds like an attempt at regurgitating things learned by rote.

I mean that our experience consists of perceptual concretes, and that we form concepts, i.e. generalized principles, by integrating those perceptions. All concepts are formed from experience. Identity is not an exception to this principle. It it were, then it would constitute a form of a priori knowledge, would it not?

With anything you say you know and with any words you choose to use you must have a grasp of it's relation to reality within the context of your knowledge.

This is precisely the point I was making. To understand identity is to realize that it is not merely some nebulous abstraction, but an attribute of everything we perceive, of everything which exists in reality. Thank you for agreeing with me.

'A is A' is a conceptualization of the law of Identity which is a corollary of the primacy of existence.

This sounds like an attempt at regurgitating things learned by rote. (Sorry, I couldn't resist throwing that back at you.)

to explain:

In order to understand any amount of sensory data you must first realize that you are sensing something. In order to grasp the 'something' you are sensing, you have to realize that 'something' exists and is causing you to sense it. (this comes through realizing that some thing exists apart from your capacity to sense it) This is the process (however crudely represented here) through which you are able to eventually 'know' anything. This is the progenerate of 'existence exists' (which is only actually conceptualized at a higher level after you are able to understand what the word "exists" means)

Existence and identity are implicit in any understanding of sensory perception. They are, in essence, the very first things to be grasped. Is this what you're saying? (It's hard to begin to understand what you're saying here. My apologies again.) If so, you have yet to contradict anything I've said. The fact that existence and identity are implicit in any such understanding is what makes them axiomatic. It does not alter their method of formation, i.e. they are still derived from the particulars of experience. They are not a priori.

In order to fully understand the nature of 'existence' and to advance to the level of conceptualization, you have to see that that which exists, exists with some attributes which may be directly perceived, or may not, but are present. It is thus that you are able to differentiate existents from one another and to form concepts through selective exclusion of measurements. The fact that existents exist and have measurements (attributes), is the fact through which the Law of Identity is drawn as a corollary.

"You see that 'it' exists as with 'these' attributes. To see this is to understand that 'it' is as 'it' is. A is A"

It is impossible to 'know' anything and to argue anything in this thread or anywhere without first accepting and not evading the fact that existence exists and exist such that 'A is A'

Have I denied the validity of "Existence exists," or of "A is A"? Your explanation seems to argue only that concepts are formed from the particulars of experience, which is precisely what I was saying in the first place. My apologies if I failed to make that clear, which is evidently the case.

The particular point I was trying to get at, and which has evidently been misunderstood, is this: since the concept of identity is formed from the particulars of experience and applies to any of those particulars, the expression "A is A" may well be viewed as an algebra-like expression, in which the letter 'A' is a placeholder for which any particular existent may be susbtituted to produce a valid statement. In this function, it expresses the concept of identity. This is in opposition to y_feldblum's earlier argument. It is, in fact, difficult to see how "A is A" could have meaning, in relation to reality, without such treatment.

[Proverb]

E.C. My post was not aimed directly at you. I wished to simply better understand your point. (The level of acidity I use is mostly the tool by which I learn best, because if my arguments are ever shot down it's hard to forget it.)

This sounds like an attempt at regurgitating things learned by rote. (Sorry, I couldn't resist throwing that back at you.)

Did you say that because you have not validated the statement: "'A is A' is a conceptualization of the law of Identity which is a corollary of the primacy of existence." I have, and if the clarity leads you to believe that I have learned it like a voice recorder how can you even address the situations of my learning it in the first place?

We are in agreement for the most part E.C. and I apologize of you were taken aback by my language. Because of what this forum is, I use a little bit of rock throwing to weed out the people that think it is of importance. Those who respond to me in clear and without throwing back the same rocks are the one's I respect the most. I have something from nearly every regular in this forum, including you.

The fact that existence and identity are implicit in any such understanding is what makes them axiomatic. It does not alter their method of formation, i.e. they are still derived from the particulars of experience. They are not a priori.

"...formed from the particulars of experience," This is not what I was saying.

I think that it is impossible to advance past the stage of perception without first recognizing, in the first feat of cognition, the primacy of existence and the concept that A is A. To say that they are derived from the particulars of experience I think is incorrect because you could not have the understanding of what 'experience' is or about the 'particulars' as such without this primary cognitive feat. (of course the 'primacy of existence' and 'A is A' are conceptualizations that are arrived at at a later time after one has a grasp of the language in which to use them) Is this the process by which they are 'derived' as you say?

To say that you may use A is A as some algebraic formula and not change the specific meaning is incorrect. Yes it is true that if you use some other concept in place of 'A' it is still a statement of the Law of Identity (it is important that you understand that I do not disagree with that) however you are more specifically defining the concept with referents. A is A (this is with the assumption that you are not referring to the letter 'A') is the aesthetic way in which one can state directly, the Law of Identity as an abstract concept without a direct referent. (I say aesthetic because it could have very well been B is B )

[mightyTeuton]

The concept of a priori knowledge, that we know some things without having to integrate them ourselves from perception, seems to be false. However, when we are discussing things in science, we distinguish between "a priori" and "empirical" formulae. The former is preferred over the latter, since it is derived deductively from a general principle instead of tweaking parameters (for mostly no good reason) until you get a match with reality. It also allows one to demonstrate the validity of that general concept.

My question is, does a priori in the scientific sense represent a different concept than a priori in the epistemological sense? My thought is that it does, but I'm confused by the similar terminology.

[dougclayton]

The concept of a priori knowledge, that we know some things without having to integrate them ourselves from perception, seems to be false. However, when we are discussing things in science, we distinguish between "a priori" and "empirical" formulae. The former is preferred over the latter, since it is derived deductively from a general principle instead of tweaking parameters (for mostly no good reason) until you get a match with reality. It also allows one to demonstrate the validity of that general concept.

My question is, does a priori in the scientific sense represent a different concept than a priori in the epistemological sense? My thought is that it does, but I'm confused by the similar terminology.

I suspect, without being an expert in this area, that the terminology is the same because those who called some formulas "a priori" and others "empirical" accepted the a priori/a posteriori dichotomy and thought this was a case of it. In fact, as you suggest, they are not the same at all. Both types of formulas come from reality; the difference is that empirical formulas rely on some attribute that simply has to be observed on its own, rather than being computed from more fundamental elements. For instance, sliding frictional force is the coefficient of friction multiplied by the force perpendicular to the surface. Why is that number required? Where does it come from? No one knows--but that linearity approximates reality very well. So we determine coefficients for various materials by actually measuring the force required to move an object as well as its weight, computing the ratio and documenting it in a table for future reference.

All such equations with "coefficients of x" in them have the same characteristics. It is a perfectly legitimate practice--even if we don't know why friction depends on this coefficient, we know that it does. So "empirical" is an acceptable usage as long as it doesn't reinforce the a priori/a posteriori dichotomy.

I'd be interested in hearing from scientists who have thoughts on this.

[WHYMASTER]

The concept of a priori knowledge, that we know some things without having to integrate them ourselves from perception, seems to be false. However, when we are discussing things in science, we distinguish between "a priori" and "empirical" formulae. The former is preferred over the latter, since it is derived deductively from a general principle instead of tweaking parameters (for mostly no good reason) until you get a match with reality. It also allows one to demonstrate the validity of that general concept.

My question is, does a priori in the scientific sense represent a different concept than a priori in the epistemological sense? My thought is that it does, but I'm confused by the similar terminology.

*******************************************************************************

Justin,

(FWIS) (From Where I Stand,) There is a ever widening divide between the two. Priori Knowledge is just that , Knowledge is ledgered info. It is a recorded, and then reported Form of data, It is a fact of the past. In manipulating a fact, by a comparison to the self or in reference to another known fact, "Shows" it to no longer in the State of Observation, "epistemological" which is in a "present" State of Change. Any Priori knowledge may no longer be the Present State of Reality. In the Present, the colors of light found may be seen, as the end of the rainbow, falls on our location, but to go to examine, the location where that rainbow was reported will not be sufficient, to the experience itself. [email protected]

[progressiveman1]

A priori knowledge is knowledge you acquire without applying any actual means of acquiring knowledge. The use of the concept implies that knowledge, to be acquired, does not have to actually be acquired.

How do you know thats the correct meaning of a priori?

Edited July 18, 2007 by progressiveman1

[softwareNerd]

How do you know thats the correct meaning of a priori?

How do you use the term?

[DavidOdden]

How do you know thats the correct meaning of a priori?

The way you acquire any knowledge: a posteriori.

[progressiveman1]

Some people use the term a priori as: "A priori describes truths justified by Reason. In other words, knowledge is a priori if its justification condition is independent of experience."

How do you know this isnt the correct meaning of the word?

[DavidOdden]

How do you know this isnt the correct meaning of the word?

How would you know that is the correct meaning of the term, if it were? A posteriori. Compare your supposed definition "truths justified by reason" with Y. Feldblum's characterization "knowledge you acquire without applying any actual means of acquiring knowledge." The only difference is that his definition is more explicit, but they refer to the same thing. The former definition, the one you found (where? gotta source??) is dishonest because it deliberately omits the word "exclusively", and thus tries to gain credibility by only mentioning half of the actual source of knowledge. In light of the Cartesian rationalists, we know that you must say something more than "by reason" to refer to how man acquires knowledge.

The correct definition, given how the "a priori" is actually used, is to say "conclusions justified only by mental gymnatics, with no prior experience". Such a term has no referents (see Peikoff's ASD paper).

[progressiveman1]

It seems like a lot of people mean a priori to be how its explained on wikipedia: http://en.wikipedia.org/wiki/A_priori_and_...ri_(philosophy)

Why is that meaning wrong?

[softwareNerd]

In what way do you find Feldman's definition different from the one you pointed to on the wiki? They're pretty much the same.

Rough and oversimplified explanations are as follows: a priori knowledge is independent of experience, while a posteriori knowledge is dependent on experience. In other words, statements that are a priori true are tautologies.

Edited July 18, 2007 by softwareNerd

[progressiveman1]

In what way do you find Feldman's definition different from the one you pointed to on the wiki? They're pretty much the same.

The examples they used as a priori: "All bachelors are unmarried. All triangles have three sides." How is that a priori? Also, the example under "Intuitive Distinction" on wiki.

[softwareNerd]

The examples they used as a priori: "All bachelors are unmarried. All triangles have three sides." How is that a priori? Also, the example under "Intuitive Distinction" on wiki.

A person who claims that "All triangles have three sides" is a priori is basically saying that one doesn't need to learn anything about triangles or experience anything about triangles before concluding that they have three sides, because that's what triangles are by definition.

Do you have or have you read "Introduction to Objectivist Epistemology"?

Edited July 18, 2007 by softwareNerd

[y_feldblum]

Some people use the term a priori as: "A priori describes truths justified by Reason. In other words, knowledge is a priori if its justification condition is independent of experience."

How do you know this isnt the correct meaning of the word?

That is indeed the correct meaning of the word as well -- if and only if one takes into account certain facts.

First, the type of "Reason" meant here is propositions or deductions therefrom, where, of course, all propositions are themselves deductions from still further propositions, off either to infinity (which is of course absurd and no-one believes) or to some arbitrary starting point (which, while also absurd, many people especially religionists believe). "Reason" is then taken to be nothing more than an arbitrary first premise, plus the rule of deduction (one must wonder from what premise was the rule of deduction deduced).

Second, no justification of any knowledge whatsoever is independent of experience.

So: the a priori are the propositions justified by nothing at all, which is all that "Reason" turns out to be, but also not justified by anything at all, since justification inherently depends on experience.

[progressiveman1]

Second, no justification of any knowledge whatsoever is independent of experience.

If you use intelligence for justification instead of observation, wouldnt that be considered a priori? For example, you know basic addition from observation, but justify more complex problems by using your mind independent of observation. Only the genesis of your knowledge would be based on observation(a posteriori), but after that it would be based on no observations(a priori).

Do you have or have you read "Introduction to Objectivist Epistemology"?

I just started it yesterday. Its kind of confusing, but I'll keep at it.

[y_feldblum]

If you use intelligence for justification instead of observation, wouldnt that be considered a priori? For example, you know basic addition from observation, but justify more complex problems by using your mind independent of observation. Only the genesis of your knowledge would be based on observation(a posteriori), but after that it would be based on no observations(a priori).I just started it yesterday. Its kind of confusing, but I'll keep at it.

Justification based on an abstraction based on the facts of reality is no less than justification based more directly on the facts of reality. Only, it is more abstract and more indirect. It is different in degree, but not in kind.

[progressiveman1]

Justification based on an abstraction based on the facts of reality is no less than justification based more directly on the facts of reality. Only, it is more abstract and more indirect. It is different in degree, but not in kind.

So you're saying no knowledge is independent of experience because you need experience with lesser abstractions in order to justify more complex abstractions?

[softwareNerd]

So you're saying no knowledge is independent of experience because you need experience with lesser abstractions in order to justify more complex abstractions?

Yes, but not merely to justify them; even to arrive at them.

[progressiveman1]

The correct definition, given how the "a priori" is actually used, is to say "conclusions justified only by mental gymnatics, with no prior experience". Such a term has no referents (see Peikoff's ASD paper).

Yeah, that is how most people use the term. However, mostly none of those people believe that a person can gain or justify knowledge automatically without the use of their mind. So they ultimately agree with the same things as the person who thinks a posteriori is the only way for humans to justify knowledge, except for the use of the concept. Why did Peikoff think it was so important to write a 30 page essay on the issue? People misuse terms all the time, why make such a big deal out of this one?

[DavidOdden]

Why did Peikoff think it was so important to write a 30 page essay on the issue? People misuse terms all the time, why make such a big deal out of this one?

Because it is widely assumed in philosophical circles that there is a distinction between "analytic" truths and "synthetic" ones. In this case, it is not a misuse of terms, since "analytic" and "synthetic", at least in the context of kinds of truths, are both technical terms of art. (In other words, "synthetic" doesn't mean e.g. "made from petrochemicals"). I am not familiar enough with the literature on the topic to know whether a similar refutation has been published, but it is widely assumed that "analytic" and "synthetic" refers to something meaningful (which, Peikoff shows, is actually not the case). I think it's typical that big deals are made out of how terms are used, in philosophy, and it is necessary to correct these errors. I myself didn't understand why the ASD distinction was invalid until I read P's paper, and I've been professionally acquainted with the distinction for a number of decades; thus the paper is quite valuable, in exposing the nature of the logical error that is made in presuming that there is such a difference.

However, mostly none of those people believe that a person can gain or justify knowledge automatically without the use of their mind. So they ultimately agree with the same things as the person who thinks a posteriori is the only way for humans to justify knowledge, except for the use of the concept.

I disagree, first in that "without the use of the mind" is almost the opposite of what "analytic" refers to (a better characterization would be "with only the use of the mind"), and second, the philosophers who don't think the distinction is erroneous do indeed believe that you can justify a conclusion without reference to fact, using just symbol-manipulative deductive logic.