I'm fairly certain I've blogged on this topic before, or at least mentioned this tactic in passing at least once or twice, but I wanted to devote something like an entire post to this. We see this all the time from creationists; evolution doesn't happen in real life, they say, because there's no proof of it. When pressed, "proof" becomes synonymous with "transitional fossil." The absence of transitional fossils, then, is why evolution clearly isn't happening.
Here in lies the rub. I named this after Zeno's dichotomy paradox: according to Zeno's dichotomy paradox, you have Point A and Point B. Say that Point A is your car door, and Point B is your house door. Now, you're leaving your house to get to your car. According to Zeno, you will never reach your car door. In order to go between Point A and Point B, you have to go 1/2 way. But in order to 1/2 way, you have to 1/4 the way. But before you can go 1/4 the way, you have to 1/8 the way. But before you can do that, you have to go 1/16 the way, and then 1/32, and then 1/64, and then 1/128, and then 1/256, et cetera. Thus, since you're always going 1/2 of the 1/2 to get there, you can never reach your point. I've also seen this referred to as Zeno's arrow paradox; in order for an arrow to fly to its target, first it has to go 1/2 the way, but before that, it has to go 1/4, and you can see where this goes. It goes on like this for infinity.
Why is the transitional fossil argument creationists use identical to Zeno's paradox?
We have Species A (sA) and from it, evolved Species B (sB). Creationists claim evolution doesn't happen, because there's no evidence that Species A evolved from Species B. In order to find the evidence sA evolved into sB, we need to present a transitional fossil that shows traits of both sA and sB; call this fossil species sb. So we have sA --> sb ---> sB. No sooner do we do this, though, than we have a demand for another transitional fossil, between sb and sA. Call this one sab. So now we have sA --> sab --> sb --> sB. Then we get another request to find a transitional fossil between sA and sab, and so forth. In order to get from Point A to Point B, we have to travel halfway, but we must travel halfway to get there, and then travel halfway again to get to the quarter of the way, and so forth. The same paradox is at work here. You will continually get requests of a halfway species representing a transitional fossil, ad naseum, and when you can't present it, then Tada! God! Evolution is wrong, suck it, Darwinists! They are aware that the fossil record is incomplete; that's why eventually you're going to run into a situation where this "argument tactic" will prevail.
How do we go about solving the problem? Simple.
A heads up: I'm familiar with the logic, but I'm taking set theory for a spin for the first time. If I screw up the symbols, I would appreciate begin told. This is as much an exercise in trying to see if I understand set theory as it is me taking apart this "argumentative tactic".
The first thing you need to realize is that the continued requests for a transitional fossil are red herrings to distract from their main point. Zeno's Transitional Fossil rests on the core claim that follows:
If there are no transitional fossils, evolution is not true
is equal to
If there are no transitional fossils ← evolution is not true
I underlined If to distinguish this from an Iff statement, which is what this looks like on the surface (but isn't). What this statement tells us is that there are no transitional fossils, then evolution is not true. I can word the statement another way to make this clearer:
Evolution is not true if there are no transitional fossils.
So let's look at this in terms that we can make sense of.
A: There are transitional fossils
B: Evolution is true.
Since we're using logical operators here, though, we need to frame it like this:
This is a conditional THEN-IF. In order for it to be true, the THEN part has to be true. It doesn't matter if evolution is true or not; in order for the statement itself to be true, then the ¬A, or "there are no transitional fossils" must stand as true. So let's take a closer look at ¬A.
A means that there is a fossil record with transitional fossils. Negating it means that there isn't a fossil record without transitional fossil. So what we're looking, then, is this: let F stand for any fossil and let T stand for any transitional fossil. Let M stand for the entire fossil record.
A → (∃M [T ∈ M] ^ [F ∈ M])
And, for our case, to further define what's being said:
¬A → (∃M [T ∉ M] ^ [F ∈ M])
In English, then, the first one reads: A implies there exists set M where T is an element of M and F is an element of M. Or, that there are transitional fossils implies there exists a fossil record that includes both transitional fossils and traditional fossils.
The second one reads: ¬A implies there exists set M where T is not an element of M and F is an element of M. Or, there are no transitional fossils implies there exists a fossil record that includes only traditional fossils but not transitional ones.
So in order to prove that ¬A is true, we need to verify that there is indeed an entire fossil record (M) where there are no transitional fossils. The minute we prove that there are transitional fossils, then ¬A falls apart. And because of the way this works - there exists an entire fossil record without transitional fossils - all we need to do is prove that there is one transitional fossil in order to prove that ¬A is false, and that A is true, and the THEN-IF conditional becomes false since the THEN is false.
We begin by getting a solid definition of what a transitional fossil is.
The most famous transitional fossil is this critter right here:
This is archeopteryx. Archeopteryx has features of both birds and theropods, as the link shows: it has a large toe, it has teeth, and the arm shape is very theropod-esque. The rigid, boned tail is also indicative of theorpods. Meanwhile, it had feathers, a strong breast bone for anchoring the massive muscles needed to fly, and had something like a beak. It features elements of both the ancestor group (theorpods) and the descendent group (birds). This makes archeopteryx a transitional fossil. To insist on anything else is a dishonest diversionary tactic (something creationists are infamous for).
Of coures, archeopteryx isn't the only transitional fossil. Not by a long shot. For completeness, let me introduce you to a transitional fossil I guarantee you that no Creationist has ever heard of: archimylacris. This little bugger may perhaps be distantly related to several heads of the creationist movement, being the ancestor of modern cockroaches. It's also the ancestor to modern mantises and termites; if you look at it, you can see traits of all three insects in it, plus the original species it evolved from/with, aphthoroblattina.
But given the way the statement is framed, only one of these has to be a transitional fossil in order for the statement to be wrong. Since it's clear that archeopteryx meets the requirements, that's all we need. ¬A is not true, since there are transitional fossils, thus ¬(A ← B) is a false statement and the argument falls apart.
What follows next depends on the creationist you're using this against. 90% of them will up and leave and never come back, especially if you're debating with them online. They won't bother replying, because they're ideologically driven and can't admit to the truth that their argument is wrong. The rest are going to aim for one of two tactics, both of which are to be expected but are highly dishonest, intellectually:
Nitpicking: a version of moving the goal-posts, they're going to redefine "transitional fossil" or give you some half-assed reason why it's not, when it meets all of the requirements you set forward in the beginning, and you're going to find yourself drawn into an argument over why these are not transitional fossils by people's fullest extent of biological knowledge begins with Genesis 1 and ends at Genesis 2.
Red Herring: This is where Zeno's Transitional Fossil comes in. The core of this argument was that if there are no transitional fossils, evolution is not true. We've already proved there are transitional fossils; the argument is dead. However, rather than acknowledge that, you get "yeah, well, you can't provide a transitional fossil between Point A and 1/2A-B!" The proper response here is "I don't need to; your argument is already invalid since all I needed was one to prove that transitional fossils exist."
Anyway, I hope I didn't screw up the symbols. I'm still new to this set theory stuff. I have a firm grasp of the logic behind it, but framing it in this sense was a new experience for me. Until next time, good luck!
Here in lies the rub. I named this after Zeno's dichotomy paradox: according to Zeno's dichotomy paradox, you have Point A and Point B. Say that Point A is your car door, and Point B is your house door. Now, you're leaving your house to get to your car. According to Zeno, you will never reach your car door. In order to go between Point A and Point B, you have to go 1/2 way. But in order to 1/2 way, you have to 1/4 the way. But before you can go 1/4 the way, you have to 1/8 the way. But before you can do that, you have to go 1/16 the way, and then 1/32, and then 1/64, and then 1/128, and then 1/256, et cetera. Thus, since you're always going 1/2 of the 1/2 to get there, you can never reach your point. I've also seen this referred to as Zeno's arrow paradox; in order for an arrow to fly to its target, first it has to go 1/2 the way, but before that, it has to go 1/4, and you can see where this goes. It goes on like this for infinity.
Why is the transitional fossil argument creationists use identical to Zeno's paradox?
We have Species A (sA) and from it, evolved Species B (sB). Creationists claim evolution doesn't happen, because there's no evidence that Species A evolved from Species B. In order to find the evidence sA evolved into sB, we need to present a transitional fossil that shows traits of both sA and sB; call this fossil species sb. So we have sA --> sb ---> sB. No sooner do we do this, though, than we have a demand for another transitional fossil, between sb and sA. Call this one sab. So now we have sA --> sab --> sb --> sB. Then we get another request to find a transitional fossil between sA and sab, and so forth. In order to get from Point A to Point B, we have to travel halfway, but we must travel halfway to get there, and then travel halfway again to get to the quarter of the way, and so forth. The same paradox is at work here. You will continually get requests of a halfway species representing a transitional fossil, ad naseum, and when you can't present it, then Tada! God! Evolution is wrong, suck it, Darwinists! They are aware that the fossil record is incomplete; that's why eventually you're going to run into a situation where this "argument tactic" will prevail.
How do we go about solving the problem? Simple.
A heads up: I'm familiar with the logic, but I'm taking set theory for a spin for the first time. If I screw up the symbols, I would appreciate begin told. This is as much an exercise in trying to see if I understand set theory as it is me taking apart this "argumentative tactic".
The first thing you need to realize is that the continued requests for a transitional fossil are red herrings to distract from their main point. Zeno's Transitional Fossil rests on the core claim that follows:
"Evolution is not happening because there are no transitional fossils."We can distill this even further:
"If there are no transitional fossils, evolution is not true."At first glance, this looks like a typical IF-THEN statement. That's the same trick I fell for the first time I started looking at this, and I got all the way to the end of several very complicated logical statements before I realized that this isn't the case at all; this isn't IF-THEN. Let's frame it like this:
If there are no transitional fossils, evolution is not true
is equal to
If there are no transitional fossils ← evolution is not true
I underlined If to distinguish this from an Iff statement, which is what this looks like on the surface (but isn't). What this statement tells us is that there are no transitional fossils, then evolution is not true. I can word the statement another way to make this clearer:
Evolution is not true if there are no transitional fossils.
So let's look at this in terms that we can make sense of.
A: There are transitional fossils
B: Evolution is true.
Since we're using logical operators here, though, we need to frame it like this:
¬(A ← B) or ¬A ←¬B(not) There are transitional fossils, (not) Evolution is true.
This is a conditional THEN-IF. In order for it to be true, the THEN part has to be true. It doesn't matter if evolution is true or not; in order for the statement itself to be true, then the ¬A, or "there are no transitional fossils" must stand as true. So let's take a closer look at ¬A.
A means that there is a fossil record with transitional fossils. Negating it means that there isn't a fossil record without transitional fossil. So what we're looking, then, is this: let F stand for any fossil and let T stand for any transitional fossil. Let M stand for the entire fossil record.
A → (∃M [T ∈ M] ^ [F ∈ M])
And, for our case, to further define what's being said:
¬A → (∃M [T ∉ M] ^ [F ∈ M])
In English, then, the first one reads: A implies there exists set M where T is an element of M and F is an element of M. Or, that there are transitional fossils implies there exists a fossil record that includes both transitional fossils and traditional fossils.
The second one reads: ¬A implies there exists set M where T is not an element of M and F is an element of M. Or, there are no transitional fossils implies there exists a fossil record that includes only traditional fossils but not transitional ones.
So in order to prove that ¬A is true, we need to verify that there is indeed an entire fossil record (M) where there are no transitional fossils. The minute we prove that there are transitional fossils, then ¬A falls apart. And because of the way this works - there exists an entire fossil record without transitional fossils - all we need to do is prove that there is one transitional fossil in order to prove that ¬A is false, and that A is true, and the THEN-IF conditional becomes false since the THEN is false.
We begin by getting a solid definition of what a transitional fossil is.
So what we're looking for is a species that exhibits traits of both the ancestral species and the species that derived from it. It's going to be, then, a combination of sorts.A transitional fossil may be defined as a fossil
which exhibits traits common to both ancestral
and derived groups. This is especially important
when groups are sharply differentiated (from: here).
The most famous transitional fossil is this critter right here:
This is archeopteryx. Archeopteryx has features of both birds and theropods, as the link shows: it has a large toe, it has teeth, and the arm shape is very theropod-esque. The rigid, boned tail is also indicative of theorpods. Meanwhile, it had feathers, a strong breast bone for anchoring the massive muscles needed to fly, and had something like a beak. It features elements of both the ancestor group (theorpods) and the descendent group (birds). This makes archeopteryx a transitional fossil. To insist on anything else is a dishonest diversionary tactic (something creationists are infamous for).
Of coures, archeopteryx isn't the only transitional fossil. Not by a long shot. For completeness, let me introduce you to a transitional fossil I guarantee you that no Creationist has ever heard of: archimylacris. This little bugger may perhaps be distantly related to several heads of the creationist movement, being the ancestor of modern cockroaches. It's also the ancestor to modern mantises and termites; if you look at it, you can see traits of all three insects in it, plus the original species it evolved from/with, aphthoroblattina.
But given the way the statement is framed, only one of these has to be a transitional fossil in order for the statement to be wrong. Since it's clear that archeopteryx meets the requirements, that's all we need. ¬A is not true, since there are transitional fossils, thus ¬(A ← B) is a false statement and the argument falls apart.
What follows next depends on the creationist you're using this against. 90% of them will up and leave and never come back, especially if you're debating with them online. They won't bother replying, because they're ideologically driven and can't admit to the truth that their argument is wrong. The rest are going to aim for one of two tactics, both of which are to be expected but are highly dishonest, intellectually:
Nitpicking: a version of moving the goal-posts, they're going to redefine "transitional fossil" or give you some half-assed reason why it's not, when it meets all of the requirements you set forward in the beginning, and you're going to find yourself drawn into an argument over why these are not transitional fossils by people's fullest extent of biological knowledge begins with Genesis 1 and ends at Genesis 2.
Red Herring: This is where Zeno's Transitional Fossil comes in. The core of this argument was that if there are no transitional fossils, evolution is not true. We've already proved there are transitional fossils; the argument is dead. However, rather than acknowledge that, you get "yeah, well, you can't provide a transitional fossil between Point A and 1/2A-B!" The proper response here is "I don't need to; your argument is already invalid since all I needed was one to prove that transitional fossils exist."
Anyway, I hope I didn't screw up the symbols. I'm still new to this set theory stuff. I have a firm grasp of the logic behind it, but framing it in this sense was a new experience for me. Until next time, good luck!
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