Take an argument built from this statement:

If the theory of evolution is not true, then we would see rabbits in the Precambrian. We don't see rabbits in the Precambrian thus the theory of evolution is true.

E: The theory of evolution is true
R: We would see rabbits in the Precambrian

~E⇒R
~R
E

So that is valid by way of modus Tollens, but when we see a rabbit, we don't have a valid argument for asserting that evolution is not true.

~E⇒R
R
~E

This is invalid by way of affirming the consequent.

R⇒~E
~R
E

This is invalid by way of Denying the antecedent.

I've got to be missing something here, someone please wake me up.

P.S. I don't deny evolution at all.

E⇒~R
R
~E

Okay, I think I answered my question.

But let's say rabbits are found in the Precambrian, wouldn't it only be natural to say that the assumption was wrong? That there is a perfectly good reason why rabbits can be found in the Precambrian and it is compatible with evolution?

Your original statement seems backwards and doesn't really make sense. It should be:

If we see rabbits in the Precambrian, then the theory of evolution is not true.

R: We see rabbits in the Precambrian
E: The theory of evolution is true

giving R -> ~E (and also E -> ~R as the contrapositive) instead of the reverse like you had. And ~R doesn't logically imply anything about E or ~E.

What is the assumption? Is it the entire statement: "If the theory of evolution is not true, then we would see rabbits in the Precambrian"? You can question whether this implication is true, but that falls outside of what the formal logic tells you.

For a statement of the form "If P then Q" then P is usually called the hypothesis, but it may also be called an assumption (especially when writing proofs in math). So your statement could also be interpreted as asking whether "the theory of evolution is not true" can be rejected.

Also, what is "natural" may not be a useful way of understanding the logic. You're right that it could be possible for evolution to be true and still see rabbits in the Precambrian, but there's nothing "natural" about it formally.

If you have already concluded that evolution must be true, then you would "naturally" reject the claim that "evolution is not true." But that's an entirely different issue (basically, it's a form of bias -- not that all bias is bad).

Yes, I see that we have moved outside of a question of validity and into questioning the truth value of the proposition "If the theory of evolution is true then we should not see the Rabbits in the Precambrian".

I suppose the question I am asking now, is no longer one of validity, it is about the concept of falsification in general, and it relates to what you said about bias. How does falsification protect against someone asserting that the original falsification theory was just not true, e.g., "Sure we found a rabbit in the Precambrian, yet rather than assume that the theory of evolution is false, we believe that -- contrary to what we originally thought -- rabbits in the Precambrian are perfectly compatible with evolution". It seems to set up a scenario where rather than throwing the theories out (which why would you if they seem to be working/accurately modeling the world) by way of falsification, the theory is simply amended to something that fits the new facts.

Which seems reasonable. The current "theory of evolution" doesn't care if it is correct or not, nor does it care if it never changes, it's simply meant to describe what we should see in the world.

I think we first attempt to adjust the model. If the observation leads to fundamental changes becoming necessary, a new theory may be required. That's how I understand it anyway.

For example, if it is confirmed that a neutrino can travel faster than C, we'll need to revise the model. Perhaps the information we learn for why the neutrino can travel faster than C will end up turning the current model upside down and a new theory may develop.

If rabbits are found in the precambrian evolution is in trouble and the hunt for a new hypothesis begins.

It's not clear because you're confusing evolution with common descent. There are really four separate hypotheses:

1. All life on Earth changes traits via natural processes (biological naturalism)
2. Evolution by natural selection as currently understood is that natural process (evolution)
3. All life on has descended from a single ancestor (common descent)
4. The picture we have gathered from the fossil record and other evidence is a correct account of the timing of the appearance of various forms of life. (the historical record)


Rabbits in the Precambrian is only a solid falsification of (4), and perhaps throws (3) into question given the timelines involved. It would cast doubt on the others, mostly because people hold god to be a viable alternative hypothesis, but it doesn't make them impossible.

This is a tough of question.

The best thing to do, perhaps, is to just study other types of discontinuities in scientific theories and look for both the philosophical shifts and the data that fed those shifts:

* Geocentric solar system to heliocentric
* Epicycles to ellipses
* Luminifereous ether (Michelson-Morely)

I hesitate to introduce evolution and microbiology into this list because I'm not as familiar with the history. I'm not sure that there was a "strong" competing theory at the time that was actively being pursued in some sort of scientific sense. So it wasn't really so much that the a former theory was "falsified" but rather that it was a new question that nobody had ever really thought deeply enough about to form a coherent theory. I could be entirely wrong about this, though.

Edit: I don't put special relativity into this list because it's not as if we abandoned Newtonian mechanics. It's more like special relativity was an augmentation of Newtonian mechanics.

Also, my physics bias is showing.

Maybe we are getting away from the original question.

I don't use the fancy terms, but when we start by assuming ~E ==> R, and we also assume ~R, then we deduce E by contrapositive, which is the same thing as modus tollens.

If we start by assuming ~E ==> R, and we also assume R, we cannot deduce ~E. Apparently that's called affirming the consequent--I just call it converse logical error.

If we start by assuming ~E ==> R, we cannot deduce that R ==> ~E. That's also converse logical error. Similarly we can't deduce that E ==> ~R. That's inverse logical error (what you're calling denying the antecedent).

I don't really see that you are missing anything. Maybe I am missing what the question is?

He could also check out http://en.wikipedia.org/wiki/The_Str...ic_Revolutions for a very well-regarded account of how this happens. The book was vaguely a response to Popper, but you don't need to have read his Logic of Scientific Discovery or really have any background in science or philosophy to read Kuhn's book.

All it means to be falsifiable is that there is a detectable difference between if it is true or if it is false. It is such a low standard that its hard to believe some hypotheses dont meet it.

edit. i don't think you understand about the rabbits in the Precambrian. if there were rabbits in the Precambrian evolution is wrong ... horribly wrong. that would do more damage to evolution than discovering Mark Antony owned a laptop would do to history.

I used evolution because it was the only theory that, off the top of my head, I knew (roughly) what would falsify it. I am not suggesting that there's any actual way to justify evolution if there are rabits in the Precambria.

There is an old view that scientific theories are based on induction. That is, we discover scientific laws by generalizing from a finite set of observations to a general principle. The problem with this view is that, depending on how seriously you take the Humean problem of induction, this process of generalization is unjustified.

Karl Popper accepted Hume's critique of induction and so attempted to explain the logic of science without relying on inductive logic. He proposed that we should view falsification instead of induction as the distinctive method of science. The basic idea is this: A scientific hypothesis is one that is refutable by a set of observations or an observable event. That is, such a hypothesis can be falsified. The process of scientific experiment is thus not a matter of verifying theories, where we prove them to be true, but rather it is a process of corroboration where we defeat potential inconsistencies with the hypothesis. The more times we fail to falsify a theory, the more corroboration it has and after enough such corrooborations, we will come to regard it as our (current) best theory. However, there is no verification or proof here--any set of observations will be consistent with more than one scientific theory and so cannot be used to decide between them.

The problem with this view is the one you bring up here. According to the arguments of Quine and physicist Pierre Duhem, any observation can be made consistent with a scientific hypothesis if you change enough of your background assumptions. Thus, it would seem that you can't falsify any particular hypothesis by appeal to empirical observations because the hypothesis can be made consistent with those observations if you change enough of your background assumptions.

As for the specific problems in your OP, TomCowley is right.