Science, Phylogeny and Affirming the Consequent

Rum – “Y, therefore X” cannot be deduced from “if X, then Y.”

In logic this is known as affirming the consequent: Affirming the consequent - Wikipedia

My comment applies only to the logical formula in your post above, not to questions about the status or content of phylogenetic hypotheses.

Cheers, Paul.

The scientific method is often mistaken as affirming the consequent, in fact this is a well known issue among philosophers of science. This sort of objection applies to just about all the hard sciences, and amounts to an objection to science as a whole, as it is usually practiced by scientists in most fields.

Here is some helpful reading that should drive home the point.

To illustrate further, almost all scientific work quantum mechanics and relativity, astronomical work from Kelper and Newton to LIGO, can all be framed as “affirming the consequent.” So this objection is just not plausible.

A better question: why does what a philosopher calls a fallacy work so well in understanding the workings of the world?


Yes my argument would commit this fallacy if I jumped straight from the 1st premise to the conclusion. But I have a second premise, which renders the argument valid in form.


Because it is a fallacy. It wouldn’t matter if every scientist on Earth said otherwise. Freshman logic students can spin out an infinitude of counterexamples (illustrating the fallacy). This is not a hill on which to die.

Science works, but it does not do so by committing logical fallacies. The HD-method, for instance, works by modus tollens (if P, then Q; ~Q, therefore ~P), not by affirming the consequent.

At the Discovery Institute, it’s called “inference to the best explanation.”

My citation of this fact should not be taken as any acknowledgment that @pnelson accurately represented @Rumraket. You don’t need knowledge of the philosophy of science to see that he didn’t.


You missed the middle premise the argument, “if not X, then not Y”. Inadvertent quote-mining?


It doesn’t. The second premise has no bearing.

  1. If it is raining (X), then the driveway will be wet (Y).

  2. If it is not raining (~X), then the driveway will not be wet (~Y).

  3. The driveway is wet (Y). Therefore, it is raining (X).

No. Invalid logical form, as these counterexamples illustrate:

– Bob was washing his car in the driveway. Y is the case, and it’s not raining (~X).

– The water main broke in the street, flooding the driveway. Y is the case, and it’s not raining (~X).

You can devise other counterexamples. Premise (2) is irrelevant and does not avoid the fallacy.

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This is clearly false. The second premise, in this case, constrains the argument significantly. This is a shocking oversight on your part. A more interesting conversation (besides a conversation that tries to understand why you are misrepresenting @Rumraket) would examine each of the premises here, and it would do this exploration in the context of what @Rumraket actually wrote (key word: ‘supports’).


No that just means your 2nd premise is false. If it is not raining, the driveway will not be wet. But the driveway became wet even though it was not raining, hence the 2nd premise is false. The argument was valid, but not sound.

Edit: Validity and Soundness


@pnelson can you give us an example of hypothesis testing that is not, in your analysis, also an example of affirming the consequent?


That’s not a particularly good argument.

Yes, the conclusion does follow from the 2nd premise. However, that second premise is what is usually in contention. You should not stipulate to a premise that your opponent is likely to reject.

Thus, I partially agree with @pnelson here. But only partially.

If we look at the original argument made by @Rumraket it doesn’t actually fit this form. It is more like:

The distinction here is that it is not an argument about what is. Rather, it is an argument about what we can reasonably expect.

To say it differently, it is not an argument about whether X is true. Rather, it makes a pragmatic case that the evidence supports X.

Science is not truth-seeking. Science is pragmatic.


I’d like to hear about any perspectives on Polya and plausible reasoning as it relates to scientific inferences.

From Wikipedia: “To Polya, “a mathematical proof is demonstrative reasoning but the inductive evidence of the physicist, the circumstantial evidence of the lawyer, the documentary evidence of the historian and the statistical evidence of the economist all belong to plausible reasoning”. Polya’s intention is to teach students the art of guessing new results in mathematics for which he marshals such notions as induction and analogy as possible sources for plausible reasoning.“

No amount of appealing to the (apparent) practices of scientists can render affirming the consequent logically valid. That alone should tell you that any rational reconstruction of scientific inference which says “Hey, guess what – affirming the consequent actually works!” is doomed at the start.

The history of science is replete with failures of affirming the consequent. Take the Copernican Revolution, for instance:

What was the problem here? Besides affirming the consequent, defenders of the Aristotelian / Ptolemaic geometry missed what UC-Irvine philosopher of science Kyle Stanford called an “unconceived alternative,” namely, that the stars were MUCH farther away from Earth than anyone realized.

Scientific inference is very messy and hard to model using propositional logic. If I had to lay money on it, however, I’d say that most problems arise (or, conversely, successes occur) when either (a) the majority misses an unconceived alternative, or, worse, insists it doesn’t exist, OR (b) someone is brave or just crazy enough to search for and find a true unconceived alternative. The discovery of H. pylori as the causative agent of ulcers is a beautiful example.

But these are cases involving the truth of empirical premises, and their possible existence, not logical form.

I think what you (mean to) appeal to, Josh, is what’s known as “convergent realism.” On some mornings, I am a convergent realist. Blood really does circulate. The core and mantle of the Earth really are hotter than its crust, and so on.

On other mornings, I am an anti-realist curmudgeon, and follow Larry Laudan (1981, p. 45):

…ever since antiquity critics of epistemic realism have based their scepticism upon a deep-rooted conviction that the fallacy of affirming the consequent is indeed fallacious. When Sextus or Bellarmine or Hume doubted that certain theories which saved the phenomena were warrantable as true, their doubts were based on a belief that the exhibition that a theory had some true consequences left entirely open the truth-status of the theory. Indeed, many non-realists have been non-realists precisely because they believed that false theories, as well as true ones, could have true consequences.

The first thing I learned from my atheist mentor Adolf Grünbaum, as an undergrad in the philosophy of science program at Pitt, is that one can infer true conclusions from false premises. That is just about the most liberating insight one can take away from the entire corpus of the philosophy of science.

Larry Laudan, “A confutation of convergent realism,” Philosophy of Science 48 (1981):19-49.

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Yes, stating the argument using the concept of expectations (of data) given hypotheses is better and conforms more to how science is actually done in practice.


I would be interested in an answer to @swamidass’s actual question.

Can you give us an example of hypothesis testing that is not, in your analysis, also an example of affirming the consequent?

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This is abductive inference, which makes sense:

Abductive inference (logically) is not affirming the consequent.

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Josh’s question, and your repetition of it, is so profoundly wrong-headed that the only appropriate answer to it is silence.

My point is that your objection applies to all hypothesis-driven research.

The reason why is that hypothesis-driven research is often mistaken for “affirming the consequent.” I provided references to scholarly work that shows this is a well known debate among philosophers of science.

Unless you can make a distinction (not ad hoc) that limits your reasoning to a more targeted, it amounts to a wholesale objection to hypothesis testing.

My question is mean to help you clarify your position, to make sure I’m not strawmannirg you. If I was wrong, you should have no difficultly producing dozens of examples of hypothesis testing that are not subject to your objection of seeming like “affirming the consequent.”


In this one matter I agree with Paul. Science has nothing to do with affirming the consequent. Then again, neither did the original point he complained about. Nobody is claiming that “we see X if Y is true, we see X, therefore Y”; the claim, if stated in similar language, is “we see X if and only if Y is true, we see X, therefore Y”. (Though as has been pointed out, science doesn’t work by formal logic, so there are much better formulations.) In the original case, we expect nested hierarchy from common descent and from nothing else we can think of, so if we see nested hierarchy we infer common descent. Paul doesn’t believe that, but he hasn’t advanced any justification.


I agree.

Correct. But that is sometimes how hypothesis testing is misunderstood.