Truth at the limit of a moving method
A paper on Quine against Peirce: defining truth as what inquiry converges on needs a notion of one theory being nearer than another. Statistics can supply that, and the standards deciding what counts as a method still move underneath it.
Written for a PHL233 paper assignment, submitted February 18, 2024. The assignment set a passage and asked two questions in 500 words: what is the author’s argument, and what is a reasonable objection to it. Rewritten here from the original, with the citations turned into inline links and a looser register; the argument is unchanged, and the paper as submitted is available as a PDF. The passage is Quine, Word and Object, page 21, from “Peirce was tempted to define truth” to “Any so-called pragmatic definition of truth is doomed to failure equally.” The copy I worked from is here.
Peirce wanted to define truth through scientific method. Keep investigating under some set of scientific principles, the sort that tells you a simpler theory beats a more complicated one, and the answers converge. His example is the velocity of light, measured through the transit of Venus, through stars, through oppositions of Mars, with the estimates moving steadily together toward one value. That value is the truth.
What Quine takes away
Quine’s objection comes in parts. There is no complete and agreed set of scientific principles governing what a scientific method is, so the question of what counts as one stays open. Not every method aimed at a given problem converges on a single theory. Even where methods do converge, nothing guarantees the convergence finishes in finite time.
Then the part the passage leans on. Peirce’s definition borrows the numerical notion of a limit, and a limit needs a distance: a sequence approaches a value because each term is nearer to it than the last. Between a theory and the ultimate truth about a problem there is no “nearer than” to appeal to. Without it the analogy collapses, and so does the definition built on it.
A distance can be supplied
I agree that Peirce’s argument has a hole, though Quine’s own is not airtight. “Faulty use of numerical analogy” is doing a lot of work without a definition behind it. Quine never says precisely what the numerical limit is, or how it relates to Peirce’s, before ruling the comparison out.
Statistics answers the narrow complaint. Repeated measurements of the velocity of light differ, and from those differences you can estimate a distribution, get an estimate of the true value from its parameters, check how measurements correlate, and quantify how reliable each one is. That gives you a “nearer than” after all: a measurement is nearer when it coheres better with the larger body of measurements.
Where it breaks anyway
The trouble is Peirce’s assumption that measurements from different methods converge into one statistically well-behaved distribution. The velocity of light may be constant across the observable universe and we may have a sharp estimate of it, but Peirce takes every scientific problem to be settled with the same certainty. Different theories of the same problem can predict sharply different values, each equally plausible on accuracy and biased in opposite directions. Statistics cannot recover a true value from that. It would report both as consistent with the data, while their opposite biases mean they cannot both be right.
The standards move
I do agree with Quine that no complete and agreed set of scientific principles is available now, and it may not be reachable in finite time. That leaves a larger problem behind it. Without a settled set, we cannot use those principles to certify that a given method is scientific at all, or to license its predictions as input to any statistical model of truth.
Take the velocity of light again. We cannot be certain that timing the eclipses of Jupiter’s satellites counts as a scientific method for measuring it. Future discoveries can change the principles we hold, and a method that qualifies today may not qualify afterwards. The principles have changed before and will change again, so the current set is neither flawless nor fixed.
A limit under a shifting standard
That is what defeats Peirce, and it is a different objection from Quine’s. The convergence Peirce needs is convergence of methods, and which procedures count as methods is decided by standards that themselves keep moving. A limit computed under a rule that changes while you compute it is not a limit. It is a sequence of different problems.
How the objection narrowed
I started out thinking Peirce fails for a simple reason: not every line of inquiry converges, and nothing guarantees it finishes in finite time. That is true and it is not much of an objection, since Peirce can always answer that we have not looked long enough.
The sharper problem is that nobody can say what a scientific method is. Without an agreed set of principles, the convergence has nothing definite to be a convergence of. What Quine himself leans on is narrower still: a limit needs a distance, and no distance runs between a theory and the truth.
For a while I thought that last one was answerable. Statistics does supply a nearness relation, in how well a measurement coheres with the body of measurements around it. Then it stopped being answerable, because two theories can fit the data equally well and be biased in opposite directions, which statistics reports as two acceptable answers that cannot both be right.
What I ended up believing is the point about moving standards, and it only becomes an objection once it is aimed at a procedure. That scientific principles change is a platitude. That the eclipses of Jupiter’s satellites might stop counting as a measurement of anything takes something away from Peirce.