Paradox

Margaret Cuonzo

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First annotation on Nov 13th, 2025. Last on Nov 14th, 2025.

Chapter 2

The Quine/Duhem problem 2. Not e 3. Not {H, (A1, A2, A3, . . . , An)}
The simple Quine/Duhem paradox 1. No hypothesis can be tested in isolation from an indefinite set of auxiliary hypotheses. 2. In order to show that a hypothesis is mistaken, it is necessary to isolate that hypothesis from its set of auxiliary hypotheses. 3. Therefore, no hypothesis can be shown to be mistaken.
A group of philosophers of statistics claim to have a solution to the Quine/Duhem problem. These philosophers, known as Bayesians, get their name from the statistician Thomas Bayes. According to the Bayesians, an answer to the Quine/Duhem problem can be given if the hypothetico-deductive model of scientific testing is replaced with another model. According to the Bayesian model, evidence e confirms a hypothesis H to the extent that a scientist's degree of belief in H is higher given evidence e than what it was or would be without this evidence. As discussed in chapter 1, subjective probability is a measure of the subjective degree of belief ranging from 0 or complete disbelief to 1 or complete certainty. The scientist's degree of belief in the hypothesis without the evidence is called the prior probability of the hypothesis, and the scientist's degree of belief in the hypothesis after the evidence is called the posterior probability. So if the posterior probability of H is greater than the prior probability of H, the extent to which H is confirmed is the difference between the posterior and prior probabilities.
As Deborah Mayo asks in the title of an article critiquing the Bayesian approach, "What's Belief Got to Do with It?": Scientists do not succeed in justifying a claim that an anomaly is due not to H but to an auxiliary hypothesis by describing the degrees of belief that would allow them to do this. On the contrary, scientists are one in blocking an attempted explanation of an anomaly until and unless it is provided with positive evidence in its own right. And what they would need to show is that this evidence succeeds in circumventing the many ways of erroneously attributing blame. (1997, 228–229)
The most important objection concerns the Bayesians' reliance on the prior degree of belief of the scientist in his or her hypothesis before the hypothesis is tested. Assuming that scientists have such degrees of belief, and also assuming that these beliefs can be quantified into degrees, it is undesirable that the prior beliefs be taken as central to reasoning in science.
So, although beauty exists in the mind alone, there are certain properties in nature that give rise to it in those who have the capacity for experiencing nature correctly. Part of the development of this faculty for experiencing beauty, for Hume, involves being delicate, that is, being able to experience subtle differences among comparable works and small details. Practice, as discussed earlier, is important as well: freeing oneself of prejudice, especially with regard to fashion, must be done, but not at the expense of understanding that not every custom is a good one. Hume, for example, says, "Must we throw aside the pictures of our ancestors, because of their ruffs and hooped skirts? But where the ideas of morality and decency alter from one age to another, and where vicious manners are described, without being marked with the proper characters of blame and disapprobation, this must be allowed to disfigure the poem, and to be a real deformity" (1757, 18). Some of the jokes, for example, of television shows as beloved as the classic The Honeymooners, with the hapless husband Ralph Kramden shaking his fist at his wife, and threatening her with "Bam, zoom, right to the moon, Alice!" strike a more observant viewer as abusive and hardly a laughing matter. Finally, there is good sense, or the ability to reason effectively (15). These are activities that develop our aesthetic sense and make us better able to discern the beautiful.
In "The Semantic Conception of Truth and the Foundations of Semantics," Alfred Tarski (1944) gives a diagnosis of why the liar paradox arises. For Tarski, the trouble with statements such as What I am now saying is false arises because natural languages such as English, Spanish, and so on, are semantically closed. That is, the expressions of the language are used to describe the language itself. Expressions like is true, is false, is a sentence are both part of the language and used to describe the language at the same time. Like the famous M. C. Escher print of two hands in which each hand depicted in the drawing is drawing the other, the things that are created by something—in this case, the expressions of a language—are used to give a picture of the language itself.
The paradox can be applied to two nations going to war. In this case, usually, the "game" has been entered. According to Moaz, "Recklessness is the consequence of perfectly reasonable calculations involving the notion that escalation is perfectly controllable because war is something that nobody wants. Each side believes that it can frighten the opponent by manipulating the risks of war. But when the parties reach the threshold of war, they cannot back down because nobody can afford to become the loser" (1990, 110). Moaz also states: "Crises may escalate precisely because politicians are reasonable and prudent and precisely because they do all in their power to avoid confrontation. In a system of interactions where what one gets depends as much on what other actors do as on what one does, things may get out of hand precisely because each side tries to prevent them from getting out of hand" (103–104).
The first paragraph of William James's "What Pragmatism Means" nicely touches on this point: Some years ago, being with a camping party in the mountains, I returned from a solitary ramble to find every one engaged in a ferocious metaphysical dispute. The corpus of the dispute was a squirrel—a live squirrel supposed to be clinging to one side of a tree-trunk; while over against the tree's opposite side a human being was imagined to stand. This human witness tries to get sight of the squirrel by moving rapidly round the tree, but no matter how fast he goes, the squirrel moves as fast in the opposite direction, and always keeps the tree between himself and the man, so that never a glimpse of him is caught. The resultant metaphysical problem now is this: Does the man go round the squirrel or not? He goes round the tree, sure enough, and the squirrel is on the tree; but does he go round the squirrel? In the unlimited leisure of the wilderness, discussion had been worn threadbare. Everyone had taken sides, and was obstinate; and the numbers on both sides were even. Each side, when I appeared therefore appealed to me to make it a majority. Mindful of the scholastic adage that whenever you meet a contradiction you must make a distinction, I immediately sought and found one, as follows: "Which party is right," I said, "depends on what you practically mean by 'going round' the squirrel. If you mean passing from the north of him to the east, then to the south, then to the west, and then to the north of him again, obviously the man does go round him, for he occupies these successive positions. But if on the contrary you mean being first in front of him, then on the right of him, then behind him, then on his left, and finally in front again, it is quite as obvious that the man fails to go round him, for by the compensating movements the squirrel makes, he keeps his belly turned towards the man all the time, and his back turned away. Make the distinction, and there is no occasion for any farther dispute. You are both right and both wrong according as you conceive the verb 'to go round' in one practical fashion or the other." Although one or two of the hotter disputants called my speech a shuffling evasion, saying they wanted no quibbling or scholastic hair-splitting, but meant just plain honest English "round," the majority seemed to think that the distinction had assuaged the dispute. (1906/2008, 26)

Chapter 3

An influential argument in the philosophy of science is relevant to our discussion of paradoxes. It runs as follows: throughout the long history of science, most scientific theories have been proven false and the entities posited by these theories were proven to not exist. Based on this evidence from the past, it is rational to conclude that propositions of present (and future) scientific theories are false and the entities posited by the theories nonexistent, as well. Larry Laudan (1977) famously provided a long list of empirically successful theories—that is, generally accepted theories that could usually provide successful predictions—that were eventually rejected and their theoretical terms shown to not refer. The list includes the crystalline spheres of ancient and medieval astronomy, the humoral theory of medicine, the effluvial theory of static electricity, catastrophic geology and its commitment to a universal (Noachian) flood, the phlogiston theory of heat, the vibratory theory of heat, the vital force theory of physiology, the theory of circular inertia, theories of spontaneous generation, the optical ether theory, the electromagnetic ether theory, and many others.