This quote confuses me. At first I read it as a restatement of the famous Lord Kelvin quote on the topic—if you don’t have numbers, your understanding “is meager and unsatisfactory.” Hooray for that as far as it goes. But the second half seems to suggest, reversing another famous quote, that it is better to be precisely wrong than vaguely correct.
I favour D’Arcy Thompson’s view. If you are precisely wrong, it will be easy for evidence to refute you and make you less wrong. But if you are already vaguely right, how will you attain to being precisely right? How will you discover that you are actually vaguely wrong, if your wiggle room lets you explain away contrary evidence? As Francis Bacon wrote, “Truth arises more readily from error than from confusion.”
Being vaguely right is only better when you need to decide an action now and have no opportunity to improve your knowledge. But being precisely right is better still. “Weak Bayesian evidence” is worth as much as a penny lying in the road: if you need to pick up a penny, you need a lot more than a penny.
But in fact, that is not the sort of vague rightness that the quote you linked to is about. Here is its context:
The terms of ordinary language fall into the same classes as those of science: they stand for things, classes of things, parts, or qualities, or activities of things; but they are far less precise in their signification. As long as popular thought is vague its language must be vague; nor is it desirable too strictly to correct the language whilst the thought is incorrigible. Much of the effect of poetry and eloquence depends upon the elasticity and indirect suggestiveness of common terms. Even in reasoning upon some subjects, it is a mistake to aim at an unattainable precision. It is better to be vaguely right than exactly wrong. In the criticism of manners, of fine art, or of literature, in politics, religion and moral philosophy, what we are anxious to say is often far from clear to ourselves; and it is better to indicate our meaning approximately, or as we feel about it, than to convey a false meaning, or to lose the warmth and colour that are the life of such reflections. It is hard to decide whether more harm has been done by sophists who take a base advantage of the vagueness of common terms, or by honest paralogists (if I may use the word) who begin by deceiving themselves with a plausible definiteness of expression, and go on to propagate their delusions amongst followers eager for systematic insight but ignorant of the limits of its possibility.
Popular thought, poetry, eloquence, manners, fine art, literature, politics, religion and moral philosophy. Is our “vague rightness” in such matters anything more than an illusion, a subjective sense of “meaningfulness” when we utter our words that has as much backing as a sub-prime mortgage?
ETA: That last sentence of the extended quote is rather good, and deserves to be quoted on its own. ETA again: except the final phrase: such people are up against the limits, not of its possibility, but of their own capacities.
If you are precisely wrong, it will be easy for evidence to refute you and make you less wrong.
This seems to imply that we should delegate decision-making to a system that is certain the sky is rgb(0,255,0) over a system that assigns the bulk of its probability to various shades of blue. But, if we know that the sky really is some shade of blue, the system with the less precise prior that the sky is blue will do better than the system that precisely thinks it’s (bright lime!) green as new evidence becomes available.
I can’t imagine that this is actually what’s meant by the original quote or your reply. What is D’Arcy Thompson’s view?
As soon as we adventure on the paths of the physicist, we learn to weigh and to measure, to deal with time and space and mass and their related concepts, and to find more and more our knowledge expressed and our needs satisfied through the concept of number, as in the dreams and visions of Plato and Pythagoras; for modem chemistry would have gladdened the hearts of those great philosophic dreamers. Dreams apart, numerical precision is the very soul of science, and its attainment affords the best, perhaps the only criterion of the truth of theories and the correctness of experiments. So said Sir John Herschel, a hundred years ago; and Kant had said that it was Nature herself, and not the mathematician, who brings mathematics into natural philosophy.
[ETA: Here, p.122, is the context for the reference to Herschel.]
And he goes on to rebuke the life sciences for having been slow to follow the same course. He suspends judgement on whether the mysteries of the mind and consciousness can be solved by physical science, “But of the construction and growth and working of the body, as of all else that is of the earth earthy, physical science is, in my humble opinion, our only teacher and guide.”
This seems to imply that we should delegate decision-making to a system that is certain the sky is rgb(0,255,0) over a system that assigns the bulk of its probability to various shades of blue.
I think that is a perverse reading of Carveth Read’s maxim.
This quote confuses me. At first I read it as a restatement of the famous Lord Kelvin quote on the topic—if you don’t have numbers, your understanding “is meager and unsatisfactory.” Hooray for that as far as it goes. But the second half seems to suggest, reversing another famous quote, that it is better to be precisely wrong than vaguely correct.
I favour D’Arcy Thompson’s view. If you are precisely wrong, it will be easy for evidence to refute you and make you less wrong. But if you are already vaguely right, how will you attain to being precisely right? How will you discover that you are actually vaguely wrong, if your wiggle room lets you explain away contrary evidence? As Francis Bacon wrote, “Truth arises more readily from error than from confusion.”
Being vaguely right is only better when you need to decide an action now and have no opportunity to improve your knowledge. But being precisely right is better still. “Weak Bayesian evidence” is worth as much as a penny lying in the road: if you need to pick up a penny, you need a lot more than a penny.
But in fact, that is not the sort of vague rightness that the quote you linked to is about. Here is its context:
Carveth Read, Logic: Deductive and Inductive, p.351.
Popular thought, poetry, eloquence, manners, fine art, literature, politics, religion and moral philosophy. Is our “vague rightness” in such matters anything more than an illusion, a subjective sense of “meaningfulness” when we utter our words that has as much backing as a sub-prime mortgage?
ETA: That last sentence of the extended quote is rather good, and deserves to be quoted on its own. ETA again: except the final phrase: such people are up against the limits, not of its possibility, but of their own capacities.
This seems to imply that we should delegate decision-making to a system that is certain the sky is rgb(0,255,0) over a system that assigns the bulk of its probability to various shades of blue. But, if we know that the sky really is some shade of blue, the system with the less precise prior that the sky is blue will do better than the system that precisely thinks it’s (bright lime!) green as new evidence becomes available.
I can’t imagine that this is actually what’s meant by the original quote or your reply. What is D’Arcy Thompson’s view?
Here’s some context for D’Arcy Thompson:
[ETA: Here, p.122, is the context for the reference to Herschel.]
And he goes on to rebuke the life sciences for having been slow to follow the same course. He suspends judgement on whether the mysteries of the mind and consciousness can be solved by physical science, “But of the construction and growth and working of the body, as of all else that is of the earth earthy, physical science is, in my humble opinion, our only teacher and guide.”
I think that is a perverse reading of Carveth Read’s maxim.