What kind of fallacy is this?

It involves statements about the uniqueness of things like fingerprints, snowflakes, grains of sand, etc. First it establishes how many possibilities there are, down to the subatomic level. That number is invariably enormous. Then it’s stated that the number of these items in existence can’t possibly add up to that enormous sum. Therefore they must all be unique.

Obviously the argument ignores the fact that there can still be duplication, without fulfilling every possibility. duplication can occur at any time, without needing to exhaust all possibilities first.

I think this fallacy vaguely hints at “excluded middle” and “non-sequitur,” but not really satisfying either. Is there another fallacy that I’m ignoring?

Or isn’t it a fallacy at all?

Of course, teh acompanying question would be “what is the resolution/accuracy of the identification process that distinguishes between any two items?”

I.e. If I have a 20-megapixel picture of a fingerprint, then there are 2^20,000,000 possible values, even if that number is nowhere near the number of moleular combinations. But then, you have to conisder structure - typical fingerprints are meandering lines, so the pixel arrnagement is unilikely to be checkerboard. Eliminating a vast number of those possibilities. Similarly, snowflakes are connected and hexagonal structure based, eliminating circular or octagonal designs.

Actual name of this misdirection argument, good question. It puts an improper upper bound on the values being discussed. Too imprecise. Improperly stating the problem?

The Mad Sir Squeaks.

A specific example would be helpful.

I get a little irritated by the ‘Card Game’ approach to argumentation anyway. Maybe demonstrate the ‘obvious’ part of your argument instead of calling on a fallacy?

This sounds to me like the converse of the Pigeonhole Principle. The Pigeonhole Principle itself is valid: if you establish how many possibilities there are, and the number of items in existence is greater than the number of possibilities, there must be duplicates.

So I suppose the reasoning given in the OP could be considered an example of the Fallacy of the Converse.

Ok, here’s a simplified example:

You live on a tiny planet with one snowfall, ever. Only ten billion flakes. But theoretically there can be a trillion possible snowflakes. You conclude that every flake is unique, since you’ve used up only 10% of the possibilities.

But you don’t need to use up all trillion possibilities in order to find a perfect match. Flake #7 can be a perfect match to flake #6,204,379,058.

So what kind of fallacy is it, aside from non-sequitur?

Ok so let’s assume that (probably) there are at least two snowflakes that have the same shape. (At least, let’s assume that we are talking about that kind of scenario.)

The false conclusion is: all of the snowflakes are unique.

The false premise is: if the number of snowflakes is smaller than the number of all possible snowflakes, then all of the snowflakes are unique.

We can easily see why this premise is false, but I don’t recall if there is a name for this type of fallacy. On the other hand there are also examples where it is (probably) the case that all of the snowflakes are unique. In those cases the fallacy is appeal to probability. It’s not really the name of the fallacy that’s important anyway.

Your fingerprints are just like snowflakes. They’re both very pretty.

This sort of actually happened a couple years ago. After the Madrid terrorist train bombings a US citizen was investigated & arrested primarily due to a partial fingerprint match. Unlucky for him he was a commie-pinko lawyer who had not only converted to Islam but also specialized in defending terrorists. Anyway, his partial fingerprint was like a 90% match of a print found on evidence taken from the scene, but it turned out that this was just a coincidence. It showed that now that we have such huge databases fingerprints, especially partial ones, are not absolutely unique…

Can you cite any evidence where two people have identical fingerprints? (not partials obviously)

It can’t be a formal logical fallacy, because there’s no logical reasoning, just incorrect statistical reasoning.

If their logic is
Premise 1: “If there are more items than possibilities, two items must be duplicate”
Premise 2: “There are fewer items than possibilities”

Conclusion: There are no duplicates

Then the fallacy is denying the antecedent - assuming the reverse of the proposition just because the proposition isn’t positively true.

Your fallacy is the use of the word “must be”. In fact, it is so probable that they will be unique, that for practical purposes they can be presumed so. But even if there are only two snowflakes in the universe, it is a fallacy to assume that they “must be” different.

I agree with Dioptre that it’s probably not a logical fallacy, but a statistical one.

Brandon Mayfield is in fact a great example of confirmation bias-- the FBI decided early that he was guilty, so they interpreted all the evidence as confirming that. Seriously, when they found that his passport had been expired and there was no record of him leaving the country in years, they decided that proved he was involved, because only a terrorist would go to the trouble of traveling in secret, and only a high-level Al-Queda operative would be able to travel so secretly that the FBI couldn’t uncover any trace!
[Lots of other fallacies like guilt-by-association, etc., going on too]

This is relevant also with infinite sets.

A common conception is that given infinite “goes” at something, then whatever could happen, will happen (e.g. monkeys typing the complete works of shakespeare).
But in fact, as long as duplicates are allowed, and there is more than one possibility in each turn, there are infinite sets where any single possibility does not appear.

e.g. if you roll a die an infinite amount of times, it then there are infinite result sets that do not contain a 4. For example {1, 2, 1, 2, 1, 2…}

The chance of having such a result set is infinitesimal, however it cannot be logically concluded that that set does not exist, as it breaks no logical or physical rule to have such a result set.

I’ll chime in to point out that your simplified example is flawed as presented.

With ten billion flakes there are around 5 * 10^19 pairs of flakes. Divide by a trillion to get that we’d expect to see around 50,000,000 duplicate pairs of flakes in this particular snowfall.