After all there are some indications that we shouldn't:

Who first studied "logical (ir)reversibility"?

And even the fundamental nature of symmetry is in question:

Is symmetry real?

Now we might suppose that there is a residual form of thought left over from religiously inspired expectation of, order and design. We may also think of how symmetry is merely that aspect of translation that preserves meaning.

But for all that we are still left with the question of how we came to an appreciation of the concept when the phenomenal world does not seem to provide the experience of it.

Question: How do monists (or physicalists) explain the conception of symmetry when there is no direct experience (or necessity) of its existence?

Symmetry isn't something we found in nature, we thought we did, but looking closer it wasn't there. Why then did we think it?

  • I don't have an expectation of symmetry, I just know that there is no equilibrium or balance without it. I'm often fond of equilibrium or balance, but not always. – Bread Jul 8 at 10:20
  • But we have "direct experience of its existence" : left/right hand, etc. – Mauro ALLEGRANZA Jul 8 at 14:21
  • This sounds like the Plato's question as to how we come to grasp perfect forms when sensible things are so imperfect. His answer was the myth of anamnesis. Kant replaced it with templates of pure reason. Demythologizing, we are born with some cognitive apparatus for which symmetry makes things more tractable. So it should be tried first, and kept when it works well enough. It is the same principle as "first search under the streetlight", it is reasonable regardless of whether what one is looking for is there. Better than first looking for a black cat in a dark room, even if it is there. – Conifold Jul 8 at 18:58
  • @Conifold I find the concept of anamnesis strangely compelling, but unnecessary for solving the paradox of knowledge. I think an organic explanation suffices: perceptions are conjugated into phenomena, experience builds knowledge, knowledge informs perception etc. Many mistakes are made, but quickly discarded... However this process doesn't quite explain our appreciation of symmetry, or abstractions in general. Particularly symmetry should have been discarded as a non-concept several orders of measurement precision ago. - Now I wonder: is it really that useful? – christo183 Jul 9 at 6:37
  • Experience is not the only thing that builds knowledge, Kant was right about that much. We have two inputs here, the phenomena and the representational apparatus, and the latter is, to a degree, hard wired, not into pure reason but into our brains. Its features can not be discarded, we are bound by them. It is because of that that our model of computation is a Turing machine, and symmetry is what makes Turing machines work better, it reduces complexity. Idealization generally is ubiquitous and attractive, not because of perfection, or experience, but because it lowers representational costs. – Conifold Jul 9 at 16:53

Why do we expect symmetry?

Because we see symmetry all around us: human faces have bilateral symmetry, as are their bodies; so are trees, and the leaves on trees show symmetry too.

Since symmetry is all around us we get to expect it. Moreover, one can argue, that there is a metaphysical necessity of such, since a world without symmetry of any kind, would be a world without patterns of any kind, and such a world is metaphysically impossible as its not founded upon a secure foundation but an insecure one, a chaotic one. And such a foundation, as metaphysicians have already pointed out, is simply not possible.

  • Which metaphysicians? And "not possible", or simply unpalatable? Because, as considered elsewhere, the more rigorous our epistemic undertaking, the less actual physical symmetry we find. Accordingly one would expect that more sophisticated thinking would try to contemplate a world without symmetry. Of course there is the matter of its usefulness, as raised by @Conifold. So essentially we thought we saw something in nature, then we found it may not be there after all, yet we keep it around for reasons... Where then, ontologically speaking, does symmetry come from? – christo183 Jul 10 at 5:41
  • "And such a foundation, as metaphysicians have already pointed out, is simply not possible." Would you mind saying a bit more about this? You mentioned that there are arguments that chaotic worlds without symmetry (I'm guessing in the mathematician's/physicist's more general sense of the word?) are metaphysically impossible, but I'm hoping you can expand and give an example of such an argument. – Adam Sharpe Jul 11 at 14:56
  • @Christo: Not possible and not just unpalatable. As Parmenides would have put it, is an unthought and not part of the way of truth. I was talking metaphysics not physics but perhaps you might want to have a look at high energy physics where the higher the energy the more physical symmetry is apparent. The weak force for example, becomes apparent through symmetry breaking. – Mozibur Ullah Jul 17 at 3:21
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    @Adam Sharpe: Have a look at the book Big Bang Big God where the author affirms that the metaphysical principle underlying physics is order and not unorder, and this, as it happens was a principle imported from theology. – Mozibur Ullah Jul 17 at 3:23
  • High energy physics is an interesting example. If we look at chronological progression of the physical universe, we start with a uniform (ordered?) state which coalesces asymmetrically... But I think I get your point: order entails symmetry. So if we expect order we must expect symmetry? – christo183 Jul 17 at 5:30

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