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In the context of scientific inquiry, the term prediction means "The logical consequences of a set of premises". Consider the following premises :

Athena is taller than Zeno.

Zeno is taller than Apollo.

Apollo is taller than Plato.

Given (1)-(3) and the rules of inference in deductive logic. We can derive Athena is taller than Plato. Likewise, given the premises (axioms and definitions) of Euclidean Geometry, and the rules of inference in deductive logic, we can derive (5).

The sum of angles in a triangle is 180 degrees (two right angles, where a right angle is a one quarter of a full rotation.). And given the premises (definitions and laws) of classical mechanics and the rules of inference in deductive logic, we can derive (6).

(6) If you throw a stone straight up, it will go up in a straight line and come down in a straight line. It will not go up and stop there, go up and come down in a spiral, go up and come down in a slanting path, ...

We say that (4) is a prediction derived from (1)-(3), that (5) is a prediction derived from Euclidean Geometry (what mathematicians call a theorem), and (6) is a prediction from classical mechanics. To show that something is a prediction from a scientific theory, you need to articulate the premises (axioms and definitions) of the theory, and derive the alleged prediction from the premises using deductive logic.

I have not seen a single derivation/proof of this kind in any published research or textbook in macro evolutionary biology. Notice that I am not talking about 'proving' that evolutionary theory is true. That requires non-deductive logic. I am talking about proving that an alleged prediction is indeed a prediction. That requires deductive logic. Notice also that I am not talking about forecasting. e.g., Does evolutionary theory say whether or not humans will lose their legs by CE 4000?

Prediction in the sense outlined above concerned only with deriving one set of propositions from another set of propositions. It has nothing to do with foretelling, which is predicting future events, as distinct from predicting past events, or predicting the weight or height of a person from the age of that person.

I mentioned deductive logic in deriving predictions. The deductive logic can be classical deductive logic, probabilistic deductive logic, or defeasible (non-monotonic) deductive logic. In situations that demand non-monotonic logic, we may get the effect of what is called 'chaos' , 'non-linearity, 'strange attractors' or 'sensitivity to initial conditions'. For instance at the beginning of the twentieth century Poincarré discovered what is called the three body problem in classical mechanics. Even though the laws of classical mechanics are deterministic laws, the application of these laws to a situation in which a planet is caught in the gravitational attraction from two stars (instead of a single star) makes it impossible to predict a single trajectory/path for the planet unless we have infinite precision in our knowledge of initial conditions. (https://en.wikipedia.org/wiki/Three-body_problem)

Given that life is a Complex Adaptive System, it is impossible to make unique predictions of the sort made in classical mechanics with exactly two bodies. All that we can predict is the space of possibilities, and the most probable states within that space.) This is what we are asking of a theory of biological evolution worthy of being called a 'scientific theory'.

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    But biology produced many useful explanations and discoveries, like vaccine and this is science. Aug 27, 2022 at 16:11
  • Purely logical deduction of predictions from a set of axioms only seems practically possible in physics and chemistry, where we have some canonical set of mathematical laws that everything else is supposed to derive from. Wouldn't the same problem apply to geology, or the study of non-evolutionary aspects of biology like diseases? The reductionist thesis is that everything in these fields should in principle be deducible from physics + initial conditions, but that isn't possible in practice so scientists have to make due with more qualitative statements of theories in these fields.
    – Hypnosifl
    Aug 27, 2022 at 19:18
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    Is there a question here? If you are looking for mathematical deductions mathematical biology is a natural place to look, and there are plenty of axioms and definitions in population dynamics or genetics.
    – Conifold
    Aug 27, 2022 at 19:36
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    Biologists can accurately predict how long a given pesticide will be efficient on a given insect population from their rate of mutation and the frequency of their reproduction cycle (here is an abstract introducing such kind of predictions). The prediction can't be made with 100% accuracy because the observed phenomenon is extraordinarily complex and not yet fully understood, yet it is also the case of any non trivial physics problem (nobody can tell you with 100% accuracy how much fuel a given plane will consume from Paris to Shanghai).
    – armand
    Aug 28, 2022 at 2:19
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    A side point: your example of "taller than", the conclusion cannot be inferred with logic alone; you also need a theory that says "taller than" is transitive. As to the rest, you are mistaken if you think deduction give some special certainty of correctness because deduction is only valid, not certain. That means the conclusion is only true if the premises are true, and you can't ultimately derive the premises from deduction. Aug 28, 2022 at 9:44

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You are conflating the deductive certainty of mathematical methods, and perhaps certain conclusions one can draw from the material conditional, say of the transitivity of volumes in space as a general rule, with the broader notions of scientific methods.

The sciences use mathematics, and some mathematical claims have deductive certainty, generally in some foundational sense, but as a whole, mathematical modeling when applied to real-world, stochastic phenomena of the physical universe are approximations, and therefore reach only tentative conclusions. Statistical predictions, for instance, are expressed with confidence intervals, and therefore are inherently inductive. And the biological sciences are very indebted to probabilistic and approximate mathematical techniques. None of these is deductively certain.

Of course, none of what I'm saying is a radical claim, and this all goes back to the Hume's scandal of induction. The sciences are essentially a series of epistemological techniques that not only accept fallibilism (IEP), but embrace it, particularly applied science which relies heavily on the engineering methodology for acquiring knowledge.

I am talking about proving that an alleged prediction is indeed a prediction. That requires deductive logic.

No. Prediction is inherently inductive because it admits contingency by definition. So, your claim that scientific prediction requires deductive certainty is contradictory. Prediction and estimation are inherently contingent enterprises, and as such cannot be deductive, which is inference characterized by certain conclusions, at least. From SEP, Inductive Logic:

In a deductive logic, the premises of a valid deductive argument logically entail the conclusion, where logical entailment means that every logically possible state of affairs that makes the premises true must make the conclusion true as well. Thus, the premises of a valid deductive argument provide total support for the conclusion. An inductive logic extends this idea to weaker arguments. In a good inductive argument, the truth of the premises provides some degree of support for the truth of the conclusion, where this degree-of-support might be measured via some numerical scale.

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  • Re your last paragraph: deductive logic may be used to test correctness of premises used by your scientific theory. If you deduce from these premises something that contradicts evidence this means your theory is based on false premises. In this sense you might talk about predictions based on deduction too. Anything deduced from premises of your theory and not yet experimentally tested can be viewed as a prediction of your theory. Aug 28, 2022 at 6:44
  • @მამუკაჯიბლაძე I certainly will concede that if one accepts a reasonable model of scientific methods such as the hypothetico-deductive predictions are drawn from the theory, sure. But I think the OP is conflating the act of formulating predictions with the act of checking a prediction. To verify something is a prediction is merely to assess that it claims something is true in the future. "Tomorrow I will win the lottery" is easy to determine is a prediction without deduction. It references events in the future...
    – J D
    Aug 28, 2022 at 13:57
  • and were I to use combinatorial logic to get there, even if the combinatorial theory is deductive, the act of the prediction in such a manner is to marry the combinatorial theory to attempting to make a claim about inherently unpredictable outcomes. So, the theory is deductively certain, but the prediction about the state of my winning and losing isn't. Prediction, estimation, and even measurement inherently introduce contingency, and give science it's empirical quality.
    – J D
    Aug 28, 2022 at 14:00
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You have not been looking carefully enough.

Nested hierarchies are a rather obvious prediction of evolution. Once "family trees" are observed in organisms, the idea that such will be observed among all life is direct.

However, the prediction is not morphological family trees, but genetic family trees. Morphological family trees were observed first, and genetic family trees inferred. With the advent of genetic sequencing it is now possible to observe the predicted genetic family trees.

Such genetic family trees have been observed. Indeed, once predicted and looked for, nested genetic hierarchies are found in numerous species to such a degree that they permit correcting of relation patterns inferred from morphology.

Indeed to such a degree that it is possible to trace the passage of genes from continent to contient over time. And to observe the extension of nested hierarchies over this time.

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Science does not deal in proofs - which are about valid logical inferences from accepted premises. Science deals with evidence, and using it to distinguish between proposed models to account for phenomena. Prediction is just one kind of evidence.

You can see some of the issues from the fact that we don't live in Euclidean space, we live in Minkowski space, so corners of triangles in fact don't add up like that, but this only becomes apparent at high speeds or near large gravity fields. A sufficient magnetic field can stop even diamagnetic objects falling, especially if they are small, and stones with iron in or that have become charged like amber rubbed with a cloth, even more so. And electrostatic effects are involved in dust storms.

Are there other models that can account for specific phenomena, like say the details of the fossil record? Then if you can come up with alternative models, what evidence do they have supporting them and counting against other models?

Axiomatising in science is different to in logic or mathematics, in science it is about showing different theories relate, and establishing the domain of applications of foundational principles. See Does reality have axioms? and Is there a reason to believe that our universe obeys internally consistent rules?

Also, consider The Unreasonable Ineffectiveness of Mathematics in most sciences

There are certainly controversies within an evolutionary account. Lamarckism was dismissed, but now we have evidence for epigenetic mechanisms that can cause such effects. Abiogenesis is a tricky thing to account for, and find evidence for an account - it's likely statistical computer simulations will be involved. For all we know now it could have happened on Mars before Earth formed, and the collision collision that created the Moon happened which mostly stripped Mars of water & could have seeded Earth. The lack of visible aliens in the cosmos, while many Earth-like planets formed even in our galaxy billions of years ago, is another kind of evidence that we can relate to the likelihood of specific 'hard steps' to get to intelligent life, like emergence of multicellularity - on current knowledge it is hard to account for the seeming rareness of life.

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  • Lack of visible evidence of ET? The ONI has issued a report claiming they have more than 100 cases of encounters consistent with ETH. ; )
    – J D
    Aug 28, 2022 at 17:29

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