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I have seen some creationists arguing that when evolutionary biologists use homologies (anatomical or genetic) as evidence for evolution, they are committing the fallacy of affirming the consequent. So both evolutionists and creationists would agree that if evolution is/were true, we would expect homologies. We do see homologies, therefore evolution is true. Now, of course this is an example of the fallacy of affirming the consequent.

A way that I see of solving this problem is to use Bayes' theorem. So if we have two mutually exclusive and jointly exhaustive hypotheses, with equal prior probabilities, say, evolution and creation ("E" and "C"), and an observation, say, homologies (H) then if one of the hypotheses entails the observation, that hypothesis is more likely, given the observation, than the hypothesis which does not entail the observation. More formally:

1) P(E or C)=1

2) P(E)=P(C)

3) (E->H)->P(H|E)=1 (since E implies H), (C-/->H)->P(H|C)=x;0

4) P(E|H)=p(H|E)P(E)/P(H), P(C|H)=P(H|C)P(C)/P(H) (Bayes Theorem)

5) Since P(H|E)=1, P(E|H)=P(E)/P(H), and since P(H|C) is a fraction, and P(H|C) is being multiplied by P(C), and for any numbers x and y, where y is a fraction, x multiplied by y is less than x, it follows that P(H|E)P(E)>P(H|C)P(C).

Hence our conclusion: P(E|H)>P(C|H)

So my questions are: 1. Is this proof correct? 2. Does this solve the problem of affirming the consequent, not only in the case of evolution, but also when dealing with other theories/hypothesis?

Frank Hubeny
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user8083
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    This isn't really any different than "We see humans and sponges share genetic information, therefore evolution is true." Of course, a Creationist could just as rationally say the Creator just reused the same genes. On another note, if you look at homologies from a genetic perspective, many structures that appear similar are actually the product of drastically different genetic code. That further undercuts the already invalid logic. –  Jan 10 '16 at 14:53
  • @BenPiper yes, but in order for them to make the claim that the creater chose to reuse genes, and therefore making homologies a prediction of creationism, they would have to add that to the creation hypothesis which would decrease its prior/intrinsic probability. – user8083 May 31 '16 at 05:35
  • Wikipedia defines "homology" in a way that wouldn't make sense at all without evolution, so it's technically true that the sentence "We do see homologies, therefore evolution is true." is a bit of circular reasoning. In fact you cannot even say "I observe homologies" if you don't already know about evolution, otherwise homologies are undefined. Might as well say "Evolution is true, therefore evolution is true". Which is tautologically true, but not a proof that evolution is true. On the other hand, I've never heard a biologist say "We do see homologies, therefore evolution is true." – Stef Jan 31 '24 at 16:10

6 Answers6

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Affirming the consequent

Scientists distinguish between the merit of explanations on the basis of (a) how accurately and (b) how widely they make experimentally-verified predictions.

This means empiricism is fundamentally based on affirming the consequent (and uses inductive reasoning), so you could argue empiricism is rather weak logically. However, you should note that having used A => B and B, science does not assert A is true, it labels A a good model for B.

Sadly, the media and popular opinion tend to conclude "scientists discovered that A is true". This common fallacy ("science is all true") leads to disillusionment when more data suggests a different conclusion.


Science is fundamentally not about truth, it is fundamentally about degree of statistical agreement.

This is why Newton is held as an eminent scientist, despite his theory of mechanics being demonstrably incorrect. Science doesn't care about correctness, it cares about degree of accuracy of prediction, and Newton was very accurate.

Reasoning statistically

Yes your derivation is correct. I would have presented (5) as:

P(H|E)=1, so by Bayes' theorem P(E|H) = P(H|E)P(E)/P(H), we have
P(E|H) = P(E)/P(H), but similarly, P(H|C)=x<1, so
P(C|H) = x P(C)/P(H), but P(C)=P(E) by prior assumption, so
P(C|H) = x P(E)/P(H) < P(E)/P(H) = P(E|H). Thus we have shown
P(C|H) < P(E|H).

but yours has the merit of being (a) briefer and (b) more explanatory.

Models that are validated empirically

This argument from Bayes' theorem explains why simple explanations making firm predictions are validated over ones which make more equivocal predictions, given similar accuracy. More generally, empiricism's statistical approach favours theories which readily make (preferably numerical) specific and universal deterministic predictions from measurable inputs over theories which make non-deterministic predictions or where it is complicated to find what the theory predicts.

This is absolutely the right approach to take in a scientific paper, since peer-reviewed empiricism is the validation tool for science - not logic, not "the truth", but statistical predictive accuracy.

That's why "children prefer to leave their toys messy than tidy" isn't part of any major scientific model, whereas "the Higgs boson exists" is. The empirical evidence for the toys is overwhelming but hard to quantify and only nearly universal, whereas the evidence for the Higgs Boson is very localised and of comparatively incredibly rare frequency, but easy to analyse numerically.

Thus another too-common belief "all truth is science" is also fallacy.
It is one which, amusingly, would tend to be confirmed by empirical study (because non-numerical, multiple-option and generally hard-to-statistically-analyse truths already evaded being part of the scientific model)!

Can we use this method to decide between theories?

You have a lovely statistical argument in favour of a scientific theory (evolution) over a competing theory (young earth creationism). However, as always with science and statistics, you should be cautious about overgeneralising or misstating your conclusions.

It should come as no surprise that a statistical analysis favours a deterministic theory, as we just proved using no assumption other than E->H and C-/->H that P(E|H)>P(C|H). Don't allow your belief in evolution to encourage you to accept this kind of reasoning as a proof, since you'd be making the fallacy of affirming the consequent, about affirming the consequent!

To dissuade you, I'll give an example the other way around. I could compare evidence E of non-zero credit card bill with theory G: "the nasty green goblins will always cause the numbers to be non-zero on my credit card bill" and theory C:"I prefer to put purchases made at non-small businesses on my credit card to defer payment with "cashback" deducted, maintain a higher current account balance generally, and put the resulting spare money in an interest-earning savings account". Every month, using Bayes' theorem, P(E|C)<1 (albeit slightly) and P(move money into savings)<1 (significantly less slightly!), but P(E|G)=1, so I find that after a year or two, P(G|EEEEEEEEEEEE)>P(C|EEEEEEEEEEEE) by a wide enough margin to be statistically significant, so to behave empirically, I should accept the goblins model.

What can we conclude?

Don't let the green goblins near your credit card.

No, no, that's not it!

To reason this way has logical gaps (as you spotted, plus general inductive reasoning including assumptions about the immutability and uniformity of the universe), favours certain kinds of statements over others (Higgs vs toys), which can lead to misdiagnosis of the truth (credit card).

However, it's perfectly valid to use empirical statistical reasoning to decide between two scientific models. This way you deliberately favour the most statistically predictive theory, but remember, that means you have a good model, not necessarily the truth. (Your school education should have exposed you to a good few models that were the best explanation we had but were later surpassed. Be particularly sceptical about "most fundamental particle"!)

It's against the spirit of empiricism to go around believing in your models, in particular because you're less likely to come up with a new model if you do. However, we're all human, and instantly believing things we like the sound of is what we do.

How to invalidate your Bayesian argument

We've touched on how testing the consequent is intrinsically flawed logically (which doesn't make it bad science), so that we're never testing truth, we're testing accuracy, and at some examples where those are at variance. Now let's look at some popular other ways to logically invalidate your conclusions.

The numerical Bayesian conclusion after one application depends heavily on the assumed probabilities for your competing theories. This is why Bayesian statisticians like to refine their model time and time again, incorporating new evidence (whether inconsistent with previous data or not) into the calculation. You can come to radically erroneous conclusions by making radically erroneous assumptions at the start.

Even slight or subtle errors can flip your conclusions. In real life, a lot of time and money was wasted in initial attempts to find a plane crash, because of a forgotten erroneous initial assumption that a black box would be transmitting normally. Whilst later searches had been thorough, the model hadn't recorded that the first pass over nearby areas had just checked for the signal to speed things up. Correcting this altered the probability map substantially, and the wreck was quickly found in one of the new Bayesian hot spots.

Sadly, many people attempting to argue from evidence erroneously make drastic initial assumptions like P(Y)=0. (eg "I refuse to entertain that as a possibility without first seeing direct evidence" sounds reasonable to many.) This is both unnecessary and counterproductive, since it invalidates the very statistical argument they're trying to make and makes their reasoning circular, boiling it down to "no, that's nonsense" as both assumption and conclusion.

Another pitfall is to fail to consider possible overlaps and hence probabilistic interactions between your theories, credit to Chris Lively for this answer pointing that out.

Summary:

Science is not about truth, it's about accuracy. Empirical reasoning makes great science and concludes science is usually most accurate, but that's circular reasoning.

...which doesn't necessarily mean the conclusion is false! ((A-/->B)-/->not B) Note that empiricism concludes that the current scientific model is likely to be proven demonstrably false at some point in the possibly distant future, and replaced by something more accurate, but not necessarily closer to the truth.

AndrewC
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    "Science is fundamentally not about truth, it is fundamentally about degree of statistical agreement." <- This. Science is about making the simplest (Occam's razor) matching models of reality based on the data you have, it has nothing to do with truth whatsoever. If people would start realizing this, what a great day that would be. – David Mulder Aug 20 '14 at 07:54
  • @DavidMulder - That would be a very annoying day, since what we in practice mean by "true" is "statistically overwhelmingly likely according to mental models". Everyone "realizing" what you stated would be forced into nihilism, which is not a fun (or wise) place to be. – Rex Kerr Aug 20 '14 at 08:06
  • @RexKerr: Well, that would depend on whether you consider any claim on 'supernatural' revelation of truth (that sounds so terribly cheap) to be plausible/acceptable/worth considering. But rejecting all those claims one would indeed logically and sensibly end up with nihilism regardless whether that's fun or not. And just for the record, in practice 'we' (as in the majority) considers truth as something absolute, regardless of all modernist movements. And the problem lies therein that people are told that science gives such absolute truths which is readily accepted out of fear for nihilism. – David Mulder Aug 20 '14 at 08:37
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    @RexKerr No, you can have two radically different models, one true, one false, where the results of both agree to a good degree with experimental data, but the false one comes out on top in the statistical analysis. It's OK to conclude empirically that the green goblins are a better model for predicting whether my credit balance is non-zero, but it's not OK to conclude that it's the truth. Conflating truth and accuracy is bad science. Keeping them separate doesn't imply nihilism. I've edited my answer two try and emphasise this central distinction more in the summary, sorry if I obscured it. – AndrewC Aug 20 '14 at 12:10
  • I think you're missing my point. Taken to its logical conclusion this means there is no truth about any empirical matter. Which means we may as well reclaim the word truth to mean something less unobtainable (outside mathematical logic). Just because a process does not guarantee truth it does not mean that it is wholly unrelated to truth (as @DavidMulder claimed). – Rex Kerr Aug 20 '14 at 17:38
  • @RexKerr No it just means that empiricism doesn't prove truth. Redefining the word truth doesn't help you here, and I'm unwilling to label the goblins theory true when I know the other theory to be true. If you redefine the word to mean statistically valid I have to swap that round. Also, using the word true instead of accurate will cause more people, not less, to confuse the two concepts. There is truth about scientific questions, but for the reasons above, empiricism doesn't prove it. That's fine, because science is brilliant for its accuracy and doesn't need truth. Top scientists doubt. – AndrewC Aug 20 '14 at 17:55
  • You absolutely do not know the other theory to be true. You could be mistaken about your motives, your memories could be faulty, etc.. You have accumulated a good deal of evidence that makes the latter a good model. That's it. If you don't want to use "true" for that, don't, but it makes conversations awkward. (Basically it just means you avoid ever using the word "true" except when talking about math, just as you avoid using the word "theorem".) – Rex Kerr Aug 20 '14 at 18:10
  • If you call statistically verified "true", then Newtonian mechanics used to be true but isn't now. That makes truth non-constant, despite the unchanging underlying physical system, which is nonsensical, or you admit both Newtonian and relativistic which makes science self-contradictory. The good news is that neither is necessary, because science avoids falsehood by failing to address truth, and instead is a fantastically useful edifice with ever-more-accurate models. Why would you want to relabel accuracy truth, when accuracy is so successful? – AndrewC Aug 20 '14 at 18:18
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    @RexKerr Now you're arguing from nihilism! Of course I know the other theory is true. I'm me, and it was all about my habits and reasons for them. I didn't acquire evidence, I was there, being me! You may only have my plausible assertions, but I have knowledge. If you refuse to admit any knowledge, even knowledge about oneself, why are you so keen to throw the word "truth" around so freely? – AndrewC Aug 20 '14 at 18:47
  • That all empirical matters are tentative is one of the great philosophical results. But many are so meagrely tentative that there is no point altering one's language when speaking of them. You were there being you, you say. How do you know this? Maybe the whole thing was a dream or hallucination. You have some feeling that it was real, but are your feelings never mistaken (and how do you prove this with only a finite number of examples)? But nihilism is a silly (a very poor model; false) because we can create incredibly good and reliable models and cease worrying about p values. – Rex Kerr Aug 20 '14 at 19:18
  • @RexKerr Actually, I agree with the entirety of that comment, (apart from the language redefinition bit). I should have said that my example was a demonstration that empirical conclusions could be false rather than true, so I asserted truth needlessly. (More irony!) I expect we're not going to convince each other over whether the distinction between accuracy and truth is important, but we can I hope agree that science is useful, and that the discussion has been entertaining. – AndrewC Aug 20 '14 at 20:09
  • I am fully agreed on those last two points. – Rex Kerr Aug 20 '14 at 21:12
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    @AndrewC Your "green-goblins" counterexample does not satisfy one of the conditions. Namely, the prior probability of G and C are not equal. The reason why this is the case is that, you have knowledge of cases where C holds, whereas you have never seen (i assume) green goblins. – user8083 Aug 22 '14 at 20:56
  • @user8083 The green goblins can be invisible when they want to be. I saw it on the TV. More seriously, I pointed out the problem with fixing the prior probabilities to suit your beliefs in the "How to invalidate your Bayesian argument section". if you fix the initial probabilities you're not taking account of the evidence. A good Bayesian approach repeats experiments multiple times, and quickly the evidence starts to dominate any unjustified initial fairness. It's only a humourous stark example to demonstrate the mathematical dependence on the certainty of the model. – AndrewC Aug 22 '14 at 21:39
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    Then how would you measure the prior probability of a hypothesis? Specifically in the case of creation and evolution. And by the way, the green goblins hypothesis is unfalsifiable and ad hoc. That's a big warning that you shouldn't take it seriously. – user8083 Aug 22 '14 at 22:40
  • @user8083 Revised model: the green goblins can't be invisible, the only reason I've never seen them is that they spend their time at my credit card company's data centre instead of in general society. Any sentence starting "I prefer..." Is very hard to falsify, just as it's hard to falsify empirically that I love my wife. Whether I am physically attracted to my wife is an answerable scientific question, but whether I love her is not. The key to the Bayesian approach is not the initial probability, it's the repeated inclusion of new data into the model. The flaw was only testing one outcome. – AndrewC Aug 23 '14 at 07:14
  • @user8083 Perhaps you'll prefer this eg: Bayes favours confident Colin who loudly predicted in 1960 that there would definitely be a black US president in the next 50 years, over probabilistic Pete who said the probability that the US would elect someone black would be 8% each time for 50 years. That probability closely matches the facts (1/12 elections), but Pete's theory only gives about a 64% probability that it would actually happen in that time, so single-shot Bayes says Colin wins. Bayes favours theories making correct confident predictions of unlikely outcomes. P(T|O)=P(O|T)P(T)/P(O) – AndrewC Aug 23 '14 at 07:58
  • Just to be clear, I'm using the word unlikely interchangably with infrequent in this bit of statistics. – AndrewC Aug 23 '14 at 08:47
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    Please consider taking longer discussions to chat! :) – Joseph Weissman Aug 29 '14 at 00:57
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    +1 for "science does not assert A is true, it labels A a good model for B." The rest of the answer is spot on, but that phrase does a great job of capturing a very important and difficult nuance of science in language which is accessable to a layman. – Cort Ammon Jul 19 '15 at 21:23
  • "Science is not about truth, it's about accuracy." - Accuracy in regards to what? If science is "not about truth" then accuracy doesn't matter either. –  Jan 10 '16 at 14:50
  • @BenPiper A scientific model is better than another when it makes predictions that match the observed data to a higher number of decimal places. This is accuracy. Whether or not the model is the truth or not is irrelevant - all that matters is how accurate it is. Both relativity and quantum mechanics are fairly implausible-sounding, and are considered unsatisfactory in the sense that there's no consistent model covering both, so it seems that at least one of them is not the truth, but that doesn't matter much as they fit the data very closely indeed and are the best models we have. – AndrewC Jan 10 '16 at 19:53
  • Understood. I was trying to make sense of the comment in light of statements made by some in the scientific community, e.g. "The theory of gravity is fact". If science is only concerned with accuracy of one model vs. another, then no one can use science to proclaim something as "fact." –  Jan 10 '16 at 21:12
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    @BenPiper Indeed. Although research-active scientists themselves are usually more familiar with the peer-approval consensus-based statistical verification nature of actual science, many science adherents seem to gloss over that and treat science as the truth, the whole truth and nothing but the truth. It's an amazing, fascinating, growing and changing, intricately detailed set of models that are accurate to a degree that's one of the crowning endeavours of the human race. We don't need to make it a hostage to future remarkable discoveries by asserting that it's the truth. – AndrewC Jan 10 '16 at 22:17
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AndrewC had a very good answer; however I wanted to add a few things.

When beginning to compare theories it's best to begin by looking at your assumptions. In this case you are assuming that both creation and evolutionary theories are mutually exclusive. The second major assumption is that they have equal probabilities.

Covering the first point, there are creationist theories that do not preclude evolution. There are also evolutionary theories that do not throw out the possibility of initial creation. In other words there is a middle ground between the two which is not accounted for in your application of the Bayes theorem because you are starting from a highly over simplified viewpoint.

Ignoring that, the second issue has to do with assuming that each option has equal probability. This is simply impossible to determine. On the evolutionary side, we have a certain amount of physical evidence which is interpreted to have a certain meaning. This meaning might be correct, it might not be. We've certainly had many instances in history where a scientific "discovery" was made which turned out to be completely wrong as new information surfaced, and we've had many instances where the initial hypothesis has turned out to be as close to "settled" as it gets. However in this particular case, science is still learning about our past: and there are gaps. The gaps don't mean that evolution is any less valid, but it certainly means there are points that need further discovery.

On the creationist side, what "proof" could there possibly be other than the creator coming down and demonstrating in front of a world wide audience how man was formed? Maybe finding a barcode written at an atomic level? Even if either of those happened, it would still be contested. In other words, we have no real way of identifying that which was created versus that which may have "naturally" formed. However, absence of proof is meaningless. Now there are irreducible complexity arguments that, frankly, I'm not even remotely qualified to make an opinion on.

What is the likelihood that evolution is the sole means by which life arose on Earth? Is it still solely "evolution" if it was helped by some external source - even something as innocuous as an asteroid hitting the planet? What if that asteroid was hurled by a super intelligent race (or being) which knew it would be a catalyst to start life? Where do we even draw the line? There are just too many questions here.

The point is, we can't assume that either option has equal probability initially because there are in fact more than two options and those grey areas are not mutually exclusive. We also can't assume the probabilities are the same because there is a tremendous amount we don't know; which is further ambiguated by the extremes of both sides attempting to narrow the arguments of their opponents.


  1. Is this proof correct?

I'd have to say no as the comparison you are attempting to make is starting from false assumptions.

  1. Does this solve the problem of affirming the consequent not only in the case of evolution, but also when dealing with other theories/hypothesis?

Again, no. If "other theories" include starting from false assumptions then Bayes won't help you. Honestly we may as well substitute "my big toe" for 'E' and a "can of spam" for 'C' and be able to derive the exact same amount of meaning from the equation.

NotMe
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  • +1 Indeed, yes I completely glossed over any kind of created/guided evolutionary process, a(nother) hole in the argument. – AndrewC Aug 20 '14 at 05:55
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    The use of initial probabilities which come from nowhere when using Bayesian methods is one of the key criticisms the Frequentist statisticians have of the Bayesian statisticians, another argument that shows no sign of being resolved, but which I could/should have raised. – AndrewC Aug 20 '14 at 06:40
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    When I have time, I'd like to take the point you made I alluded to in the previous comment and list it among more common errors, explained in the context of the Bayesian method as erroneously assuming P(E and C)=0, along with invalidly starting with P(E)=0 or P(C)=0. I guess you could say they're only invalid if you're reasoning statistically, so to be fair this is more of a problem for someone trying to prove not-C, particularly since it seems presentations of that argument use these assumptions more often anyway. – AndrewC Aug 20 '14 at 06:50
  • Prior probabilities are determined by simplicity. In the case you mentioned, of creationist theories that involve evolution; these hypothesis have the disadvantage that they are less simple than just creation and just evolution. We assign equal prior probabilities to both hypothesis simply because we have no reason to think of one hypothesis being intrinsically more likely than the other. – user8083 Aug 20 '14 at 21:20
  • You're missing the point with regards to the proof. I only used evolution and creation as an example. But, the idea was to provide a statistical model for determining which hypothesis has a greater likelihood in a total disjunction of hypothesis. This requires that: 1. We have a total disjuction of hypothesis for some observations. 2. The more likely hypothesis is the one which inplies the observation, and has a probability greater than or equal to the probability of all other hypothesis. – user8083 Aug 20 '14 at 21:24
  • @user8083: I'm pretty sure I see what's going on. You start off by giving an example of a fallacy of affirming the consequent. This is followed by stating you want to solve this problem using Bayes. Then you commit the exact same fallacy within the setup of the Bayes theorem by applying the above fallacy and receiving the completely expected result. This is then offered as proof that you've somehow solved something. – NotMe Aug 21 '14 at 00:30
  • What I was trying to show is that by starting off on the wrong foot by artificially ignoring known possibilities (ie: C may also imply H; which means that H isn't a useful determinant ), no amount of mathematical reasoning will fix it. – NotMe Aug 21 '14 at 00:35
  • I never claim to have solved anything. This is an attempt to solve a problem. If we define C as the claim that "an omnipotent, omnisicient being created life and diversity on earth" i dont see how that could imply H, since (by definition of omnipotence: god can choose to do or not do whatever is logically possible) this being can either choose to create homologies or not. – user8083 Aug 21 '14 at 02:28
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Why are homologies evidence for evolution instead of common design?

Better question: Why are homologies stronger evidence for evolution than common design?

Short answer: Evolution (descent with modification) actively predicts and explains homologous structures, and a lack of homologous structures among related organisms would be evidence against evolution. At best, a theory of common design is compatible with homologies but neither predicts nor requires their existence or lack thereof (as a designer is free to either re-use patterns or start over). Therefore, the extensive homologies that we find in nature are considered to be evidence in favour of evolution and are neutral with respect to a common designer.

Longer answer:

There have been a LOT of species on our planet over the past few billion years.[citation needed] Several hundred years ago, humans studying plants and animals discovered something truly bizarre: a nested hierarchy of traits that suggested there was some objective way that animals and plants could be grouped.

For example: Did you know that if you look at an animal with hair or fur, that animal's skull will have one temporal fenestra - but if the animal has scales or feathers the skull will have either two or (in the special case of turtles & tortoises) none at all?

Evolution depends on heredity - the passing on of characteristics from one generation to the next. Each generation of a species will be mostly like the one before, with only slight differences. A novel feature that arises in one population will only be seen in that population and its descendants - it will not and cannot arise in the exact same way in a completely separate lineage, even where convergence would encourage superficial similarity.

For example: Bats are mammals (specifically rodents), and have inherited the basic number and arrangement of bones that all other mammals have. Each individual bone might be bigger or smaller than the corresponding bone in another mammal's skeleton, but we should find far more similarities than differences, and the similarities should be strongest between species that are more closely related. This is indeed what we find - the bones bat wings are homologous to the ones in our arms and hands.

The basic body plan that bats, rats and humans share is derived from the earliest of tetrapods, and looking around us we can see that the basic body plan has been largely conserved. However, if we were to look at a trait that arose independently in different lineages - say, wings/flight - evolution predicts:

  1. Each group that evolved flight (bats, birds and the now-extinct pterosaurs) will have skeletal structure made up of bones that are homologous to the other groups - bats, birds and pterosaurs all inherited the same basic tetrapod skeletal toolkit.
  2. There will be significant differences in how each lineage honed in on flight - each lineage will have inherited its own legacy of mutations and selection pressures to arrive their current wing design - there's no 'going back', 'redo' or 'starting from scratch' option available if evolution is the only force at play.

Examining the different wing structures, this is indeed exactly what we see! Even though all 3 lineages have wings, the devil is, as they say, in the details:

  • Pterosaurs have wings built from an extension of the 5th digit ('pinky finger') to create a wing.
  • The 3rd and 4th digits in a bird's 'hand' have fused together and elongated to create their wing frame, and birds no longer express the 1st and 5th digits.
  • Bats retain all 5 'distinct' digits, with digits 2 through 5 elongated and used to make their wing.

This prediction of homology is rather unique to evolution. If biological creatures were designed & created in some kind of workshop instead, there is no reason why the designer would be forced to work within the constraints of heredity.

As a comparison, cars are, quite clearly, designed and manufactured objects. Designers can borrow ideas from other models (which would be called 'horizontal transfer' in biology) or radically reinvent just about anything about the vehicle. When the engineers sit down to design the 2016 Volkswagon Beetle, there's nothing to stop them from moving the engine from the front to the back. If cars were subject to evolution instead, such a radical change would be impossible.

Coming back to the idea of a common designer as an alternate hypothesis, our knowledge of design from other fields makes the observed strict reliance on homologous structures and simultaneous lack of horizontal transfer and back-to-the-drawing-board redesigns combines to be weak evidence against this hypothesis. This 'common designer' is not behaving in any way like any designers any of us know.

Homology is only one of the many lines of evidence that lead us to the conclusion that the theory of evolution is a mostly correct description of biological diversity.

Dave B
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Taking 'intelligent design' and 'evolution' as philosophical hypotheses about the origin of life; then homologies in nature are evidence for both hypotheses; but of course this is not the only evidence used.

Mozibur Ullah
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Some notes on your question.

(1) You assign probabilities to theories, which doesn't make sense. Probabilities are specific numbers that obey the calculus of probabilities. They are made in the light of explanations that give an account of why the probabilities have the specific values they have. As a result explanations do not have probabilities. An explanation is either true or false. An explanation may say that some specific event E has some probability p(E) and if the relative frequency of E differs from p(E) that is a problem for the theory.

(2) Many evolution supporters may think that structural and genetic homologies support their theories. They are wrong because support doesn't exist. In reality, you can't prove any position or show it is probable, i.e. - support it. Any argument requires premises and rules of inference and it doesn't prove (or make probable) those premises or rules of inference. If you're going to say they're self evident then you are acting in a dogmatic manner that will prevent you from spotting some mistakes. If you don't say they are self evident then you would have to prove those premises and rules of inference by another argument that would bring up a similar problem with respect to its premises and rules of inference.

(3) Knowledge is created by spotting a problem with some current idea, guessing solutions to that problem, criticising the guesses until only one is left and then looking for a new problem with that solution. In the light of this, homologies are relevant to judging whether you should adopt evolution or intelligent design.

If biological evolution is true then there should be structural and genetic homologies and if such homologies don't exist the theory is false. So looking for such homologies tests evolution and evolution has passed that test. The existence of such homologies is a problem that evolution that evolution has solved.

What about design theories? Design theories don't predict anything at all about structural or genetic homologies. The designer could have designed every species with a different genetic code, some species might use DNA, others could use information stored in a flash drive in the form of a text file, still others could store the information in the form of a program written in Clojure, or common lisp, or Ruby, or Python, or C++. He could have made every specimen of every species with blueprints he holds so that no species would have a genetic code. A designer could have constructed roads and made every species with wheels. And that's just a designer acting according to the laws of physics. If we postulate that god was the designer the situation gets even worse. God could have designed the laws of physics to be anything he liked. So there is no constraint on what god could do. Design theories don't pick out any particular state of affairs as the only possible state of affairs and so they explain nothing. As a result of this, they also predict nothing and no prediction can be considered a test of any design theory.

For more on epistemology see "Realism and the Aim of Science" by Karl Popper. For more on many of the issues in this question see "The Beginning of Infinity" by David Deutsch, especially chapters 1,4 and 13.

alanf
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  • "You assign probabilities to theories, which doesn't make sense. Probabilities are specific numbers that obey the calculus of probabilities. They are made in the light of explanations that give an account of why the probabilities have the specific values they have." No. Im assigning probabilities to hypothesis. – user8083 Aug 27 '14 at 20:12
  • I am using the term theory as synonymous with hypothesis. You can substitute hypothesis if you prefer. – alanf Aug 28 '14 at 08:46
  • Okay. I dont see why we cant assign probabilities to hypothesis. Each hypothesis has a prior plausability (probability). You've defined what a probability is, but i dont see how that would make assigning probabilities to hypothesis non-sensical. – user8083 Aug 28 '14 at 14:17
  • @alanf You appear to be objecting in principle to the Bayesian iterative method for refining probabilities. The frequentist movement (including Fisher) object for similar reasons. The frequentists may be more "right", but the Bayesians are more emprical. – AndrewC Aug 29 '14 at 00:21
  • Bayes' theorem is a correct statement about probabilities of events, not of theories. If you don't know the probability of some specific kind of event and want to find it Bayes' theorem may be useful if you have the appropriate explanation. But it is impossible to assign probabilities to explanations because an explanation is an account of how reality works and such an account is necessary to find probabilities. I'm not a frequentist. See "The Beginning of Infinity" by David Deutsch, Chapter 8, or this http://vimeo.com/5490979 which has a part about probability. – alanf Aug 29 '14 at 09:17
  • Explanations are causes. Causes are events. Hence, i see no problem in assigning probabilities to explanations. – user8083 Aug 29 '14 at 15:53
  • Explanations are not causes: they are accounts of what obtains in reality and why. A causal explanation is about causes: it is about what causal relationships hold and why. An event can cause another event, but it would not do so unless certain causal relationships hold and such relationships are not events so the assertion that causes are events is a fudge. Probabilities are descriptions of some aspects of what obtains in reality, so a probability can only be assigned in the light of an explanation, it cannot be assigned to an explanation. – alanf Sep 01 '14 at 08:55
  • Hm, no... Please give me an example of a non causal explanation. And even if there are non causal explanations, evolution is a causal explanation, i.e. Evolution causes homologies. And evolution is an event. The same goes for creation. – user8083 Sep 01 '14 at 13:36
  • An example of a non-causal explnation 1+1=2. – alanf Sep 02 '14 at 08:25
  • Evolution is not an event, or a cause. Anywhere in the universe where genes undergo variation and selection, evolution takes place. So there is no bounded region of spacetime you can point to that is the only region where evolution has taken place since it might happen elsewhere, so it is not an event. Evolution is also not a cause, it is an explanation of the sorts of causes that can lead to biological complexity. Creation also would not be an event because it also purports to explain the conditions under which biological complexity can arise. – alanf Sep 02 '14 at 08:45
  • How is 1+1=2 an explanation? – user8083 Sep 02 '14 at 12:45
  • Two issues. First, 1+1=2 is a stand in for any mathematical result. Maths doesn't cause anything it is simply about stating certain abstract relationships and it involves non-causal explanations. Second, 1+1=2 is a highly non-trivial explanation which is why people have to be taught that 1+1=2 and why some people have trouble learning it. For example, you have to understand something about the idea of a number, of the number 1, the number 2, the operation of addition and how those ideas are related to one another. – alanf Sep 02 '14 at 12:57
  • Yes, but that doesn't answer the question. If 1+1=2 is an explanation, then what is it an explanation of? An explanation is an answer to a 'why' question. It wouldn't make any sense to ask 'why is 1+1?' or 'why is 1+1=2.' So tell me, what does 1+1=2 explain? – user8083 Sep 03 '14 at 18:14
  • It does make sense to ask why 1+1=2. The answer has to do with properties of integers in general, properties of 1 and 2 in particular and properties of the operation +. – alanf Sep 04 '14 at 10:30
  • Yes but in that case "1+1=2" isnt the explanation, its what your explaining (by the properties of 1 and 2 and the propeties of the operation). – user8083 Sep 04 '14 at 11:21
  • You could say that, but the explanation of why 1+1=2 would still be non-causal. – alanf Sep 04 '14 at 12:52
  • Okay, i'll grant you that there are non-causal explanations. But this doesn't make it non-sensical to assign probabilities to hypothesis. Check out this paper by Elliot Sober http://joelvelasco.net/teaching/3865/sober-bayesianepistemology.pdf You need to assign probabilities to hypothesis to make sense of notions such as evidential confirmation, evidential disconfirmation, and evidential irrelevance. – user8083 Sep 05 '14 at 19:05
  • Evidence does not proves ideas true or raise their probability, so confirmation is impossible. Evidence can be relevant to an idea just by contradicting it without assigning probabilities to the theories involved. Evidence can be irrelevant by virtue of your idea not making any predictions about it. The theory of evolution makes no predictions about the mass of the Higgs boson. Since assigning probabilities to theories is unnecessary to assess them and has been criticised you should discard it. – alanf Sep 05 '14 at 23:23
  • That's a bare assertion. Since the theory of evolution doesn't make any prediction about the mass of the higgs boson, its probability is unaffected by the higgs boson, hence p(E|HB)=P(E) (where 'E' stands for any statement about evolution, and 'HB' any statement about the mass of the higgs boson) and vice versa P(HB|E)=P(HB). Confirmation is only impossible if you can't assign probabilities to hypothesis, but you haven't demonstrated that yet. – user8083 Sep 06 '14 at 01:36
  • If the hypothesis contradicts the observation, we can say that the hypothesis entails the negation of the observation. so P(H|O)<P(H) (provided that P(H)>0) which by definition, means that O is evidentially relevant to H. – user8083 Sep 06 '14 at 01:45
  • The probabilities are numbers. There has to be some account of where the numbers come from. But those numbers are supposed to be attached to abstractions that make statements about the whole of physical reality. (Even mathematics does this since physical objects can't violate mathematical truths.) So there is nowhere for the numbers to come from. And in any case they are unnecessary and undesirable in the light of the criticism of justificationism which you haven't addressed. – alanf Sep 07 '14 at 09:44
  • If you believe that justification isn't binary, i.e. there are degrees of justification, and thus some hypothesis can have MORE justification than other hypothesis, then you are automatically assigning a probability to that hypothesis. Furthermore, one way to assign probabilites to hypothesis is to 'measure' their simplicity in comparison to others, and see which ones make less claims. There is no way to make sense of degrees of justification without the use of probabilities. – user8083 Aug 16 '15 at 01:01
  • Justification is impossible, see http://philosophy.stackexchange.com/questions/77/can-you-prove-anything-in-philosophy/14750#14750 – alanf Aug 16 '15 at 11:54
  • If justification is impossible why do you adhere to justificationism? (if you do). – user8083 Sep 02 '15 at 21:21
  • I don't. See the answer I referred to for a short account of how knowledge is created. – alanf Sep 03 '15 at 10:06
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The main problem with the argument is in the first line:

So if we have two mutually exclusive and jointly exhaustive hypotheses, with equal prior probabilities, say, evolution and creation ("E" and "C"), and a observation, say, homologies (H) if one of the hypotheses entails the observation, that hypothesis is more likely, given the observation, than the hypothesis which does not entail the observation. More formally:

1) P(E or C)=1 [my emphasis]

Alvin Plantinga raises doubt that "E" and "C" are "mutually exclusive and jointly exhaustive hypotheses". Rather than evolution being inconsistent with Christian belief he claims: (page 12)

What is not consistent with Christian belief, however, is the claim that this process of evolution is unguided - that no personal agent, not even God, has guided, directed, orchestrated, or shaped it.

So it is doubtful that P(E or C) = 1. We would need two contradictory hypotheses such as the following:

  • Evolution is guided.
  • It is not the case that evolution is guided.

However, both of these hypotheses would imply the same homology evidence.


Plantinga, A. (2011). Where the conflict really lies: Science, religion, and naturalism. OUP USA.

Frank Hubeny
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