Why logic is not certain knowledge (Quine)
September 6th 2006 13:37
His most (in)famous paper is "Two dogmas of empiricism" (Philosophical Review (January 1951), 60(1): 20-43), where he questions two dogmas of empiricism.
The juiciest part of the paper occurs in the last few pages. Among other things, he denies that logic is certain knowledge.
I'll jump ahead to that part, and then, for the few people that might be interested, I'll give some direct quotes from Quine, and go into more detail about the argument of the paper.
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So it's like this. Imagine that every belief you hold is a piece of an interconnected circle. This circle is constantly shifting, because you change your beliefs in the hard light of the facts of experience.
The beliefs at the edge of the circle are more open to change than the beliefs in the centre. But, when any belief is put into question, it's not clear which part of the circle to change. Any belief can be held to be true come what may as long as you make drastic enough changes to the rest of the circle.
Logical truths are simply beliefs that lie at or close to the centre.
Russell makes a similar claim in Problems of philosophy: the so-called "laws of logic" are in fact regularities of experience.
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Quotable Quinean quotes:
"The totality of our so-called knowledge or beliefs… is a man-made fabric which impinges on experiences only along the edges… A conflict with experience at the periphery occasions readjustments over some of our statements. Reevaluations of some statements entails reevaluation of others, because of their logical interconnections -- the logical laws being in turn simply certain further statements of the system, certain further elements of the field… But the total field is so underdetermined by its boundary conditions, experience, that there is much latitude of choice as to what statements to reevaluate in the light of any single contrary experience."
"If this view is right, it is misleading to speak of the empirical content of an individual statement… Furthermore it becomes folly to seek a boundary between synthetic statements, which hold contingently on experience, and analytic statements, which hold come what may. Any statement can be held true come what may, if we make drastic enough adjustments elsewhere in the system. Even a statement very close to the periphery can be held true in the face of recalcitrant experience by pleading hallucination or by amending certain statements of the kind called logical laws. Conversely, by the same token, no statement is immune to revision. Revision even of the logical law of the excluded middle has been proposed as a means of simplifying quantum mechanics".
"For my part I do… believe in physical objects and not in Homer's gods… But in point of epistemological footing the physical objects and the gods differ only in degree and not in kind. Both sorts of entities enter our conception only as cultural posits. The myth of physical objects is epistemologically superior to most in that it has proved more efficacious than other myths as a device for working a manageable structure into the flux of experience." (Other examples of "posits" include forces, energy, matter, subatomic particles, irrational numbers.)
"The edge of the system must be kept squared with experience; the rest, with all its elaborate myths or fictions, has as its objective the simplicity of laws… Ontological questions, under this view, are on a par with questions of natural science."
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So, nice image, but where's the argument?
Quine, in fact, has been accused of merely trading in metaphors.
Well, the suggestion in the paper is that this image is unavoidable, or very attractive, once you abandon two dogmas.
First dogma: that Kant was correct that there is a difference between "analytic" and "synthetic" truths. An analytic truth is something like an unquestionable truth, a truth that's true by virtue of its form and not its empirical content. More exactly, it's something like "A bachelor is an unmarried man", which is supposed to be true because the concept of the subject ("A bachelor") is contained in the concept of the predicate ("is an unmarried man").
As I read him, Quine's attack is based on the idea that the notion of "analytic" is mysterious and inexplicable, so you might as well dispense with it. He tries to show that when you try to explicate analyticity, you have to appeal to a notion of synonymity; and synonymity is itself best explained in terms of analyticity.
So Quine wants to say that all truths are synthetic.
Second dogma: actually two dogmas in itself. Firstly, "radical reductionism" -- the idea that each meaningful statement (such as "The book is on the table") can be expressed in terms of direct sense experience and logic. Secondly, the related idea that a statement can individually be proven true or false.
Can Carnap break Quine into pixels?
The radical reductionist tries to turn everything into the form: "Quality q is at point-instant x, y, z, t". However, says Quine, there's always going to be something mysterious; for instance, the connective "is at" can never be reduced to sense experience and logic.
As for the idea that sentences are individually provable, Quine doesn't so much give an argument as a countersuggestion. "[O]ur statements about the external world face the tribunal of sense experience not individually but only as a corporate body… The unit of empirical significance is the whole of science."
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So there are no unquestionable truths (no truth is true simply by virtue of its meaning). And knowledge cannot be reduced to sense experience (there's always something extra that you bring to the table).
It's not clear to me that these two ideas are themselves established; and it's not clear that, if established, they'd be enough to ground Quine's web of knowledge. Richard Rorty in fact remarks (Philosophy and the Mirror of Nature, 1979) that for such a view as Quine's (or Sellars') there can be no positive argument, only suggestion -- and the best you can do is address the concerns of critics. The same would go for Quine's epistemological anti-foundationalism. But I'll jot down some thoughts on these things another time.
Some implications of Quine's picture might be:
-- "Indeterminacy of translation". Beliefs can't be proven or disproven by themselves because they're connected to an entire web of beliefs. Similarly, individual English sentences don't have individual meanings. So you can never give a sentence-to-sentence exact translation (though you can give sentences that, in the particular context, will likely have the same practical effect).
-- "Ontological relativity". There is no clear way to choose one ontology (that is, a particular set of beliefs about what exists) over another. If you have a taste for neatness, maybe the best you can do is commit to the simplest set of beliefs that will make sense of your experience. But even then, the notion of "simple" is ambiguous. Believing in an external world is in some ways simpler than, in radical reductionist fashion, restricting yourself to talking about sense experience. Believing in the square root of minus one is in some ways simpler than only believing in rational numbers.
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Comment by Damo
But does it equals 5 or 3 should we build aircraft based upon that premise?
I'm happy with my delusions of certainty about numbers. Call it faith.
Comment by Adrian
Philosophy Blog
Well, the Quinean response (if I'm interpreting him properly) is that we CAN build aircrafts on that basis, provided we make enough change to the rest of our beliefs. If the aircrafts fall out of the sky, then we haven't made enough changes to the rest of your beliefs.
Numbers are funny things though. I mean, when you ask the question, "Do numbers exist?", the answer is ambiguous.
I think Quine was a formalist (rather than a realist or an intuitionist) with respect to maths. That is, to put it grossly, he viewed maths as an abstract game of symbols that just happen to have real world applications.
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Oh, here's a cute thing (if I remember properly) from Bishop Berkeley.
1x0=0
2x0=0
Therefore 1x0 = 2x0
Then divide both sides by zero, and you get
1 = 2
Comment by Passer-By