Friday, February 23, 2007

Basic Fallacies of Objectivist Epistemology: The Mathematical Comparison

Rand's "Introduction to Objectivist Epistemology" is easily the worst thing she ever wrote. Rambling despite its brevity, almost comically incoherent despite its air of supreme intellectual confidence, and shamelessly fact-free despite its high-toned talk about grounding knowledge in observed reality, that she could consider the epistemological theories therein the "solution" upon which "the fate of human societies, of knowledge, of science, of progress and of every human life depends" is a testament to both her alarming overestimation of her abilities and the uncritical groupie-bubble Rand seems to have lived much of her later life in.

While there are boners on pretty much every page of the ITOE, they fortunately boil down to a smaller number of key fallacies. One of the most central is her notion that concepts must be as precisely constructed as mathematical equations. She makes much rhetorical hay over this alleged precision, and the equally alleged "disasters" that will result if anything so horrendous as an approximation creeps into man's automatized conceptualising. She claims that the validity of man's conceptual knowledge "depends on the precision of his concepts, which require as strict a precision of meaning...as the definitions of mathematical terms." (ITOE, 65, emphasis mine).

This supposed precision of concepts leads to the demand for similar exactitude in the symbols that represent them i.e. words.. Words, Rand insists, must be properly treated "as concepts" with "exact meaning...never allowing a break in the chain linking their concepts to the facts of reality." (ITOE, 20-21). Thus the writer or speaker should use words as precisely as a mathematician uses his numbers or algebraic symbols.

But this results in a basic fallacy, for Rand doesn't seem to realise that words and numbers are two very different things. Words cannot have anything like "as strict a precision of meaning...as the definitions of mathematical terms." This is because unlike words, numbers are almost entirely empty of content. This is their great benefit; as a trade-off for this lack of content we gain total precision and the ability to apply them to almost anything. Words, on the other hand, are content-rich, saturated in millenia of cultural development which has left them full of ambiguities, shades, hues, meanings and histories of meanings. The trade-off for this richness, however, is a concomitant loss of precision.

But don't take my word for it - the difference between the two can be easily demonstrated. If I give you a number you've never encountered before - say, 73647789990.871001 - you don't even require a definition to know what it means. It is precise, but empty.

However, should I give you a word you've never encountered before - say, "passalorynchite" - you will need to look it up in a dictionary if you are to have any hope of knowing its meaning. While it certainly refers to something, its meaning is far richer, and thus more layered and complex. As Karl Popper remarks, words are always "necessarily vague" to a greater or lesser degree, and instead of expecting exact precision when using them, we should be careful to remain "within their penumbra."

Thus the belief that words can, in effect, have "as strict a precision of meaning...as the definitions of mathematical terms" is a fundamental error. This error is part and parcel of another fundamental error, Rand's view of definitions, which we will examine in a later post.

9 comments:

Anonymous said...

“Thus the belief that words can, in effect, have "as strict a precision of meaning...as the definitions of mathematical terms" is a fundamental error.”

Not only that, but such an insistence would lead to a starving of knowledge and an aridity in our aesthetic life. The vagueness, I would say, flexibility, of language is probably indispensable to the creation of new knowledge, as well as the power of prose, and most particularly, poetry.

If Objectivists do in fact follow this dictum faithfully, it would explain the lack of any major new knowledge or aesthetic creations emanating from that quarter.

Brendan

gregnyquist said...

Daniel: "Rand claims that the validity of man's conceptual knowledge 'depends on the precision of his concepts, which require as strict a precision of meaning...as the definitions of mathematical terms.'"

Rand is here embracing just the sort of false ideal of knowledge that has led to so much trouble in modern philosophy, but which, fortunately, cognitive science has once and for all refuted. By false ideal I mean this notion, embraced both by simple-minded idealists and naive realists, that knowledge should somehow or other replicate it's object--that in other words, the mind is, or ought to be, a mirror that perfectly reflects reality. When modern philosphers noticed how far the mind was from achieving this ideal, they were scandalized. Hume, contemplating this situation, wrote: "I am confounded with these questions, and begin to fancy myself in the most deplorable condition imaginable, inviron'd with the deepest darkness, and utterly depriv'd of the use of every member and faculty." And all because he found that human knowlege didn't measure up to all to the false ideal and precision (and certainty as well)!

Rand, who took the scandalized qualms of modern philosophy far too seriously, also believed in these false ideals of knowledge, particularly of precision and certainty; the difference is that Rand was convinced that she could succeed where Kant and Hume had failed: i.e., she believed she could defend and, as she liked to put it, "validate" man's conceptual knowledge. That is what IOTE is all about: its her (alleged) prove that concepts perfectly (or "essentially") correspond with reality. But the problem with IOTE is not so much the "boners" on every page (although that is a problem), but that the whole thing is irrelevant: she's defending a false ideal of knowledge. Precision is not necessary. Cognitive science has shown that metaphor plays a huge role in knowledge, so much so that some cognitive scientists have suggested that all knowledge is metaphorical. Example of metaphors in ordinary speech would be propositions like "John is in love with Jane." "Joe is out of his mind." "Sam is on top of the situation." "She picked his face out of crowd." All these statements are utterly absurd if taken literally, but entirely intelligible as metaphors. They do not succeed as precise, literal description (how can a metaphor be precise!), but only as appropriate description. "Therefore any degree of inadequacy ... is tolerable in [knowledge], or even requisite," wrote Santayana, who understood this issue so much better than Rand, "when the constitution of the objects which the animal encounters is out of scale with his images. A sensation or a theory, no matter how arbitrary its terms, will be true of the object, if it expresses some true relation in which the object stands to the self, so that these terms are not misleading as signs, however poetical they may be as sounds or as pictures." In other words, ideas, concepts, even percepts and images, are only misleading if you insist that they can only be valid if they are precise.

David said...

When I read ITOE (I think it was ITOE) I laughed when she declared that there was no such thing as connotation, only denotation. Were she more honest, she would have said, "I find the idea of connotation problematic and irrational since the connotation of a word is imprecise at best and subjective at worst, so for the sake of this discussion, all terms used will be in their denotative sense." (Of course, in one examines two different dictionaries, or two different editions of the same dictionary, you'll find that the definitions vary, so she'd have to further restrict herself to one particular dictionary, inform us what it is, and for multi-definition words, she'd have to specify which definition she was using.)

Rather than do any of that (or just using words with their everyday meaning and qualifying them when necessary), she banished connotation from her universe. And given her tendency to radically redefine words (like "altruism" and "selfishness") to make her case, she pretty much rejected the idea of denotation as well.

(Of course, the some Randians may argue that her definitions are somehow the "objective" denotations and the commonly accepted meanings are actually the subjective ones.)

It's been a while, but I also seem to recall that her theory of languae rejected the idea that language evolved out the communicative calls and cries of our animal ancestors. Rather, she argued that human individuals intentionally created language to enable individual thought and that communication among individuals was a mere by-product.

I'm sure she would have rejected Noam Chomsky's innatist theories of language as deterministic or materialistic or somesuch, had she bothered to read his work, assuming she was aware of it. (Of course for Rand, Chomsky's politics would have invalidated all of his liguistic work out of hand, no matter how well-researched or well-reasoned.)

Any linguists out there able to (and who care to) comment?

Daniel Barnes said...

Greg:
>In other words, ideas, concepts, even percepts and images, are only misleading if you insist that they can only be valid if they are precise.

Yes, exactly. This is an deep error that goes back to Rand's great influence, Aristotle, who talks somewhere about knowledge ultimately "becoming one with its object." There can be no 1 to 1 correspondence. Yet from this imprecision it does not logically follow that, as Rand so often hysterically insists, knowledge is therefore "arbitrary" or "severed from reality" or "corrupted" etc. In a similarly illogical fashion she insists her quest for truth must start from truth, failing to notice the slight problem with this position. In fact we can - and mostly do - start in error and try to move closer to the truth.

So yes, Rand's whole project is hopeless. The final blow to it is dealt by herself in the ITOE, when she at last gives us an example of what she means by "absolute precision" - and it is an approximation!!

Daniel Barnes said...

David:
>Of course, the some Randians may argue that her definitions are somehow the "objective" denotations and the commonly accepted meanings are actually the subjective ones.

This is exactly what Rand argues, with her additional implication that only superior men can know the true definitions of words (ie: the true essences of concepts), and that the common public discourse is fundamentally corrupted as the words of the average people are not based on the correct epistemological principles. Hence Rand's attempt to graft her own "true" definitions onto various common terms such as "selfishness", "altruism" etc. At least one Junior Woodchuck has followed in her footsteps in attempting to rewrite the dictionary according to True Principles - see here for example:

http://www.importanceofphilosophy.
com/Dictionary.html

The late Marxist project of de-bourgeoiseification of language springs to mind. Fortunately, we have logic at hand to help us: for it turns out that we cannot, as Rand seems to think, have "true" or "false" definitions of terms. This is a fundamental, if widespread, fallacy. Greg's book makes this point to excellent effect - I intend to further bolster his basically Popperian critique of this point with a little more detail in an upcoming post.

>I also seem to recall that her theory of languae rejected the idea that language evolved out the communicative calls and cries of our animal ancestors.

Yes you are right, but she never puts it as clearly as that. She says that language is essentially cognitive; the communicative aspect is incidental. Her approach is quite bizarre - while she talks a lot about how important words are to concept formation, she barely mentions that words are taught to us by others. Reading the ITOE, one could easily get the impression that the correct term springs to mind in the superior individual sui generis as the final step in a correctly formed conceptual chain - as if all language was essentially private. Which of course is nothing like the case. However I would agree with her that language certainly does have an important cognitive side - think of a diary, for example, or of "telling yourself" to do something.

gregnyquist said...

David: "The vagueness, I would say, flexibility, of language is probably indispensable to the creation of new knowledge, as well as the power of prose, and most particularly, poetry."

Rand didn't have much use for poetry, and liked very little of it. She wanted everything to be clear, precise, unambiguous, and unproblematic. Peikoff, her intellectual heir, once complained on his radio show (now long defunct) about people reality was complex. Such people Peikoff clearly suspected of having vicious motives. They were out to undermine man's mind with complexity. But this presupposition that all of reality must be simple in order to be comprehensible commits two serious errors: (1) First, it underestimates the minds extraordinary ability to grapple with complexity; and (2) it goes against Rand's alleged realism, since it assumes reality must conform to human convenience. But no consistent realist can possibly believe that reality exists for the convenience of human cognition. He must accept reality as he finds it; and if parts of reality are complicated, he must do his best to grapple with those complexities, rather than accusing those who point them out of undermining man's cognitive faculty!

Anonymous said...

If numbers are empty, then if your check book balance is $500, you won't mind if your wife charges $1000 to the account, will you? Or is the bank just being arbitrary when they call your account overdrawn?

Ayn Rand said that valid concepts are precise in that they refer to actual specific things in reality. They are open-ended in that they encompass all past, present, and future instances of it. Lack of precision is not knowing what your concept refers to in reality, such as the concepts in your objection to Rand.

But then you're not actually saying she is wrong, are you, since both the concepts in your objection and her concepts would have to be precise in order for you to pin her down like that, and you won't allow that concepts are precise. Thanks for pointing out the self-contradictions in your meaningless rants yet again, loon.

Anonymous said...

I am glad that someone (emphasis on "one") presented some reasonable dissent in this discussion. The passages of the original post are quite telling. Number one: This person must know that the "average" internet surfer is soooo far transported from--sooo unfamiliar, in every way, to the work, the ideas, the philosophy of such a glorious philosophical behemoth as Ayn Rand.
With this being said, I am particularly sensitive to any unfounded criticism (yes, this is very crudely unfounded) of a woman who devoted her life to ensuring that you and I do not revert to the intellectual abyss of the Middle Ages.

Also, the author denounces her adherence to, and demand for, precise definitions as if it is something detrimental to human progress--as if we could not all benefit from DIRECTion in our lives. He heeds not the fact that, in forming his lame exposé, he had necessarily to utilize words, which are representations of concepts, which did and DO have precise meanings, whether they change with the weather or change every 450 years. What seems to have taken place in the subsequent posts is whining. They said, essentially: "Damn that Ayn Rand for revealing such a high standard to which I should live my life. It's too high! It can't be done!"
And as the previous commenter proclaimed: How in the world does anyone propose to pin-down anyone by intellectual contention without a "strict precision of meaning" in his terms? ? ? Perhaps the author was just kidding; Perhaps every sentence of his analysis was simply "metaphorical".
Allen, Columbus, Ga

Ian Pulsford said...

Anonymous:
"If numbers are empty, then if your check book balance is $500, you won't mind if your wife charges $1000 to the account, will you?"

Ummm by tacking on a dollar sign, naming them as a "check book balance" and a "charge", and making a comparison between the two numbers you've given them information. Take away the context and they are just two numbers with no more information than their numerical values. Your analogy is flawed to begin with.