What a Paradox is, and is Not, and Why it Matters

I was inspired to write this one after watching this video “The Andromeda Paradox Even Confuses Physicists.” (https://www.youtube.com/watch?v=i7Rx6ePSFdk).

You can watch the video for a longer explanation, but the gist is that relativity and the speed of light cause something odd. If you are standing still while I am running past you, and we both observe the Andromeda Galaxy while I pass you, we will observe it in different states. Andromeda is about 1.5 million light years away, so when we observe it, we see it as it was 1.5 million years ago. Thanks to how relativity works if I am in motion (relative to you) that will cause me to see Andromeda a few days removed from how you, being stationary, will perceive it. This means that despite us being at the same location we will not be perceiving Andromeda in the same state. The example they use in the video is that one of us sees the launch of an alien invasion fleet while the other does not as the aliens would still be debating if launching the fleet is worth the trouble. Then they attempt to get into questions about determinism. Does this mean that the future is fixed? As in theory, one of us is seeing the future relative to the other . . . but not really as both us would actually be observing the distant past, just different points in the distant past. Naturally they muck up that discussion quite a bit.

The trouble here is that this is just not a paradox. It certainly seems odd, weird, perhaps even counter intuitive, but it is not a paradox. "A paradox is a seemingly sound piece of reasoning, based on apparently true assumptions, that still leads to a contradiction (Quine, 1976)."[1]. Expanding on Quine’s definition, and this definition is pretty standard, a paradox occurs when two or more elements within a thing (an idea, concept, situation,  etc.) have a contrary or contradictory relationship. Two or more things have a contrary relationship if they both cannot be true. If A is true then B is false, if B is true then A is false, or they can both be false. All the world’s religions have contrary relationships as they cannot all be true, one of them could be true, or they all could be false. An actual contradiction is much more restrictive. That’s if A is true then B is necessarily false and if B is true then A is necessarily false. The truth of one necessitates the falsity of the other and the falsity of one necessitates the truth of the other. With an actual contradiction it’s not possible that both A and B be false, because as soon as one is false the other is true. People do frequently confuse these terms and say there is a contradiction when the relationship in question is actually a contrary.

So an actual paradox will do something like affirm both A and non-A at the same time and in the same sense. The existence of a married bachelor is a paradox as no man can be both married and unmarried. I was a bachelor before I was 30 and then married my wife about a month before my 31^st birthday. This is not a paradox as the situation changed. I was not both married and a bachelor at the same time and in the same sense.

So the Andromeda paradox is not a paradox as there is a difference there. One person is in motion while the other is stationary. That difference means it is not a paradox. If both people were sitting in the same location and observed Andromeda in a different state that would be a paradox, but the fact that one of them is in motion means that there is a distinction, so there is no paradox. To help illustrate here’s a funny example of a time travel puzzle/paradox from a game I played along time ago. https://youtu.be/qJD_khJyiR4?si=l4I4IFoGCNr4EMqF&t=436

To further illustrate this one is not an actual paradox, but it still is pretty funny. https://youtu.be/RbNcYVrtbFE?si=UzTSG5MXw0UvqZNV&t=43

 Killing your past self would be a paradox as it leads to a contrary (how can you be alive to kill yourself if you are already dead?), but killing your future self does not do that . . . even though it’s obviously a bad idea. Unsurprisingly a lot of actual paradoxes occur in stories about time travel as it’s easy to come up with a paradox with time travel.

Now why does this matter?

Part of the problem here is that many contemporary physicists are not doing physics anymore, they are doing metaphysics, and many of them just don’t realize it. As Craig has said, “ . . . it is now widely recognized that the boundaries of science are impossible to fix with precision, and during the last few decades theoretical physics has become characterized precisely by its metaphysical, speculative character.”[2]  I’m not against people doing metaphysics. The better we get our metaphysics the better other things will be. And I’m not against physicists doing philosophy and metaphysics. I think it’s probably better if more people do philosophy and metaphysics. But your average physicist is not trained in philosophy and metaphysics or even very knowledgeable about them, as this fuss about the Andromeda “faux” paradox shows. By definition it’s not a paradox.

 Is this just me being too nitpicky about how people use words? No, because how we use words matters. We need to strive to be clear in our terms so that everyone else understands what we mean.

Nearly every time philosophers have found a paradox, they attempt to solve it. And this is typically done by attempting to find a distinction that saves us from the contrary/contradiction (such as the fact that one person is in motion while the other is stationary) or by going back and rejecting some part of the reasoning that got us here (in this case relativity physics and the speed of light). Philosophy has a history of dealing with paradoxes, real and apparent, since at least as far back as Zeno’s paradoxes. Here’s a much more recent example at meeting of the American Philosophical Association.   https://youtu.be/Yp1khHlGR5o?si=8dL5oEm6Q9vSuzUe

So all this jabbering about the Andromeda paradox is at best a waste of time as there is no problem to solve here. There are good reasons to accept relativity physics, good reasons to accept how the speed of light works, and lo and behold no contrary or contradiction when we put them together, so there is no problem. If these physicists had a significant knowledge of the philosophy and the metaphysics the claims they are making fall under, they would realize this is no more of problem than it is when a plane “paradoxically” flies despite the existence of gravity.

Now I am in no position to start doing astrophysics, quantum physics, or even take anything more than a very basic crack at classical physics. But having studied philosophy and metaphysics I am in a good position to say, “This is a contradiction and therefore a problem to be solved, and that is not a contradiction and therefore it is not a problem.” And there simply is no contradiction or contrary within the Andromeda Paradox so it’s not a paradox and thus you are wasting your time and mine if you claim it is.

Using clear and correct terms to describe things really matters. There are many practical examples of this were “experts” use terms incorrectly and mislead people.

Very often issues regarding fertility treatments such as IVF are lumped into discussions on abortion. But these things are simply not the same and arguably not even in the same class. If you are in favor of IVF and get your way there will be more babies in the world. If you are in favor of abortion and get your way there will be less babies in the world. The two are not the same and treating them as such is foolish and objectively wrong. This is not to say that you cannot have ethical concerns about both. I have ethical concerns about both government corruption and the prevalence and ease of access to pornography, but the two are not the same, and it would be dumb to treat them as such.

When you dig into the dismissals that legitimate, well credentialed scientists make about Christianity, religion, and philosophy you often find this disconnect as well. The late Stephen Hawking and Lawrence Krauss have both claimed the universe came from nothing, and Krauss used that to try and undermine cosmological arguments for God’s existence. But they don’t actually mean “nothing” in the true sense of “no thing,” and this is clear when you read them in context. “Nothing” is as Plato said, “what rocks dream about.” If there are laws of physics like gravity, then you don’t have nothing, you have something (the law of gravity). Even if there is no matter, but there are still physical laws, that is still something, not nothing. However, neither of them seemed to grasp this point. I strongly suspect it’s because they lacked education and training in philosophy and metaphysics and as such, they made the basic mistake of equivocation.

When they argue for evolutionary theory at a popular level many evolutionary biologists make a similar error as they fall into arguing for Physicalism and/or Naturalism and seem to be unable to comprehend that those philosophical worldviews are not identical with evolutionary theory.

And all this is akin to what is going when on physicists talk about the Andromeda “paradox;” it’s just not a paradox. And while you could argue that that particular example is mostly benign, this type of problem causes big issues elsewhere and is symptomatic of the underlying lack of education and training in philosophy that many other disciplines have. When you do not or cannot get simple, easy things like the definition of words right, then it’s difficult to see why anyone should take you seriously when you make claims about complicated and difficult things.

And don’t even get me started on how bad about this many theologians are.

[1] I pulled this definition from this entry in the Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/self-reference/. I’m sure there are other, better and more precise ways to define “paradox” but this makes the point quite well.

[2] William Lane Craig, Systematic Theology Vol 1, 6.