Construct two counterfactual conditionals, and consider whether the relation between counterfactual conditionals and the laws of natural science is intrinsic or merely superficial. The sentences you construct should involve natural-science content and be as creative or original as possible.
1.Frege: If the density of iron were less than that of water, it would float on water.[①]
2.Einstein’s “first naive thought experiment” concerning relativity: If a person were to run along with a light wave at the speed of light, then he would find himself in a wave field that does not change with time. (But it seems that this would not happen!)[②]
3.Hawking’s discussion of the origin of the universe and the “anthropic principle”: “If the expansion rate at that moment one second after the Big Bang had been even smaller by one part in a hundred trillion, then the universe would have collapsed before it reached today’s scale.”[③]
4.Laplace’s demon: If there were an intelligent being with super-strong computational power, then given an initial condition, it could deduce, according to the laws of mechanics, every state of the entire universe in the past and future.
5.Poincaré’s “nighttime doubling”: If everything in the universe were to expand to twice its size last night, we would have no way of perceiving that this had happened.[④]
6.Newton’s first law: In the absence of external force, a body maintains constant velocity.[⑤]
7.The ideal-gas equation of state: For an ideal gas of mass M, the functional relation among the state variables pressure p, volume V, and absolute temperature T is pV＝vRT.……
Brief explanation and discussion:
First, the so-called “counterfactual conditional” refers to a hypothetical conditional sentence whose antecedent and consequent are both clearly taken to be unreal. However, the boundary between counterfactual conditionals and ordinary hypothetical conditionals is rather blurry; in fact, their features are fairly close, and in discussions in philosophy of logic they are often grouped together. Here, however, I will mainly discuss counterfactual conditionals, so most of the examples cited are relatively typical ones.
It is obvious that the above sentences not only directly involve natural-science content, but also have unique significance in the history of the development of natural science.
From these examples, it is plainly visible—not only that “counterfactual conditionals” may be meaningful, but also that the role they play in natural science can be said to be indispensable.
According to Frege’s idea, the first sentence expresses the following two thoughts: iron does not have a density lower than water, and if something has a density lower than water, it floats on water. Frege uses this to explain why certain counterfactual sentences are meaningful. But this example he gives seems too simple; this method of splitting “thoughts” is hard to use for analyzing cases such as Newton’s first law.
The feature of cases 2, 3, 6, and 7 is that their antecedents not only did not occur in reality, but also seem not even to have been potentially possible! That is to say, the antecedents of these counterfactual conditionals are not only “unreal,” but impossible—they are false not only in the actual world, but in all relevant possible worlds as well.
Among them, the function of items 2 and 3 is to some extent similar to that of a “proof by contradiction” — if A, then B; but B is impossible; therefore A is impossible. Proof by contradiction is important in scientific research. Typical cases similar to Einstein’s thought experiments include Galileo’s thought experiments on free fall and inertial motion, and so on. One may say that a certain kind of counterfactual conditional is not merely like statements such as “If the moon were made of pure plutonium, its mass would not exceed 100,000 kilograms” — hinting at some scientific inferences; rather, it may also become a link in scientific reasoning itself — in the form of proof by contradiction or a thought experiment.
Items 3, 4, and 5 are philosophical reflections on natural science; they are all very interesting, but I shall not expand on them here.
Items 6 and 7 are in fact scientific laws themselves! Item 6 is expressed in declarative form; if expressed as a conditional sentence, it would be: “If a body is not acted on by external force, then it will remain in uniform straight-line motion or in a state of rest.” But there is no essential difference from the declarative form. Here one may further ask: in most cases, is the deduction of scientific explanation, in some sense, always a “counterfactual sentence”? For conclusions established by scientific deduction often can only be “ideal states.” Of course, to say this is perhaps too extreme.
The relation between counterfactual conditionals and science should be “intrinsic”; it permeates every aspect of scientific research, thought, argumentation, laws, and so on. I believe that counterfactual conditionals are indispensable to science.
As for a further discussion of counterfactual conditions and their relation to “possible-world semantics,” I’ll write about that some other time.
[①]Frege: “On Sense and Reference,” trans. Chen Qiwei, in Chen Bo and Han Lin (eds.), Logic and Language—A Reader in Classical Analytic Philosophy, Orient Publishing House, 2005, p. 137
[②]Collected Works of Einstein, Vol. 1, The Commercial Press, 1976, p. 44
[③]Stephen Hawking, A Brief History of Time, Hunan Science and Technology Press, 2001, p. 113
[④]See William Poundstone, The Recursive Universe, trans. Li Daqiang, Beijing Institute of Technology Press, 2005, p. 71 and following
[⑤]Ernest Nagel, The Structure of Science, trans. Xu Xiangdong, Shanghai Translation Publishing House, 2002, p. 72
Latest comments
- apostar
2007-10-18 14:32:53 Anonymous 222.205.72.69
Brother, how much have you studied philosophy of logic? I’m just starting to learn it—could I ask you for some guidance?
- Gu Chu
2007-10-18 16:52:08
Philosophy of logic? Back then I only took Chen Bo’s course and read a little, so I can’t really say how much I’ve studied. Of course, discussion is welcome; if there are places where I’m weak, I can make up for them right away~
Translated from the Chinese original with AI assistance. The original text is authoritative.
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