Describing the impossible

[Dr H]

When we say something is impossible in reality, I think that we are often referring to our descriptive language rather than any actual limitations reality might have.

A common example is that, "A married bachelor is impossible". What we are really saying here is that if you present me with a person that I would label as being a bachelor, I would never also label them as married, and vice versa. So this is essentially a restriction I’m imposing on my own labelling system. It’s not a statement about what can and can’t occur in reality.

Well . . . what they're really saying is that certain qualities pertain to a "bachelor" which are mutually exclusive with certain qualities which pertain to someone who is "married".  It's more than just the labels; it's acknowledgement of certain characteristics and rules which have been lumped together under certain labels for the sake of convenience -- ie., brevity of expression.

Another example more linked to reality itself is, "A square circle is impossible". Assuming we're not just talking about abstract theory, we are referring to patterns we might spot in reality. If we see some sort of shape, we use a label to identify it. What the statement above is saying is that if I map out a shape that I would call a circle, I would never also call it a square, and vice versa. It’s again a restriction on my labelling system only.

When we make scientific statements, we would be talking in looser terms. We might say it is impossible for energy to be destroyed. I would translate this as meaning we have never yet had any evidence for energy being destroyed, and all our models indicate that this would not make sense. We're not claiming that it is literally impossible. At least, I hope any given scientist would not say that. If it did happen, we’d just have to rework our models and understanding. So we're saying it is impossible as long as our models prove to be accurate.

You are describing, I think, just a linguistic variation of the paradox of self-reference.  That is, your examples involve language used as language, rather than language used as a means of describing the world.  The question is whether language defines reality, or whether reality exists independently of language.

If language defines the world, then I agree with your observations to a point.  One of the properties of language is that we can create words and alter meanings as it suits us, subject, to some extant, to social consensus.  So if I define "circle" as "the set of all points in a plane equidistant from a single fixed point", and I define "square" as "the curve traced out in a plane by a point that moves so that its distance from a given point is constant" -- well then, voila!, the square circle becomes linguistically possible.

If, however, "circle' and "square" exist either as independent objects in the world, or if they can exist as concepts independent of language, things are not so simple.   Do you really believe that you create reality through language?

Even linguistically a problem arises in that we employ language to ostensibly communicate information to one another, and and such communication can only occur if we are agreed at least to come extent on the accepted definitions for certain terms.  
If you say to me "The dog has a light blue collar," when your intended meaning is "you are about to be run over by a train," I'm going to end up as a smear on the tracks.  Likewise with the unique definition of "square" given above.  Using that definition you can claim till the cows come home that a "square circle" is possible, but I'm thinking that assertion isn't going to be widely accepted, because most people are agreed upon a very different definition for square.

We can similarly deconstruct the idea that, "It is impossible for god to make a rock he can’t lift".

I pull this one out, because it is different from the others in that it is not clear that the central object -- "god" -- is a real referent.  First define "god" by ascribing what properties such an entity necessarily has to have.  Only then can we begin to decide on the truth value of the extended claim about what a "god" might be able to make and/or lift.