Describing the impossible

[polymath257]

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.

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

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.

A square circle is possible if you use the taxicab metric.

[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.

[Whateverist]

The conservation of energy is actually backed by Noether's theorem.  It's not purely empirical.

But surely the measured result is primary and the theorem descriptive, no?

[ignoramus]

Well, some things are impossible, at least in a definitional sense.  To take rob's first example, we define 'bachelor' as 'an unmarried adult male'.  Thus, a 'a married bachelor' is definitionally impossible.  Things of this sort are more than a labelling issue, they are a cognitive function issue.  The only way to make married bachelors possible is to redefine 'married', 'bachelor' and 'impossible'. Until and unless we are willing to do so, a married bachelor is, in every sense that matters, an impossibility.  Others:

-Canine cats

-Arctic tropics

-Wet desert

-Uneaten meal

-Non-alcoholic ethanol

Boru

Agree with the last one. Boru can be impossible at times!

[bennyboy]

You mean a pregnant virgin is impossible? 

The xhristards will be very upset!

Actually, a pregnant virgin IS possible.

[BrianSoddingBoru4]

Well, some things are impossible, at least in a definitional sense.  To take rob's first example, we define 'bachelor' as 'an unmarried adult male'.  Thus, a 'a married bachelor' is definitionally impossible.  Things of this sort are more than a labelling issue, they are a cognitive function issue.  The only way to make married bachelors possible is to redefine 'married', 'bachelor' and 'impossible'. Until and unless we are willing to do so, a married bachelor is, in every sense that matters, an impossibility.  Others:

-Canine cats

-Arctic tropics

-Wet desert

-Uneaten meal

-Non-alcoholic ethanol

Boru

Agree with the last one. Boru can be impossible at times!

Just 'at times'?  I'll try harder...

Boru

[ignoramus]

You mean a pregnant virgin is impossible? 

The xhristards will be very upset!

Actually, a pregnant virgin IS possible.

IVF!

Does the term virgin need to involve a dick?

[polymath257]

The conservation of energy is actually backed by Noether's theorem.  It's not purely empirical.

But surely the measured result is primary and the theorem descriptive, no?

Not actually. What happens is when a *new* theory is presented, Noether's Theorem is used to *derive* the expression for energy in that new theory. That is then used to make predictions based on conservation of that new quantity.

In essence, energy is *defined* to be the conserved quantity in Noether's theorem when the lagrangian is time invariant.

---

So in the case of energy being created or destroyed, I don't think scientists ever claim that it is "impossible." The merely say that it cannot be created or destroyed in an isolated system (as far as they know). The parenthetical "as far as we know" is assumed to follow all statements of scientific law, so it is never said in order to avoid redundancy.

Dark energy, for instance, may be a case of the universe breaking the first law of thermodynamics. Or it may just be an innate instability in spacetime. Scientists are still puzzling it out.

In fact, the conservation of energy in General Relativity is problematic. The basic equations are NOT time invariant, so Noether's theorem does NOT give a conserved quantity.

And this makes some sense because energy is the time coordinate of the energy-momentum vector and in curved spacetime, the translation of this vector to a common point (for various places where there is energy) may not be well-defined. The divergence theorem has to take curvature into consideration.

[Whateverist]

But surely the measured result is primary and the theorem descriptive, no?

Not actually. What happens is when a *new* theory is presented, Noether's Theorem is used to *derive* the expression for energy in that new theory. That is then used to make predictions based on conservation of that new quantity.

In essence, energy is *defined* to be the conserved quantity in Noether's theorem when the lagrangian is time invariant.

I can already hear the theists asking where comes your/our faith in that equation.

[bennyboy]

Actually, a pregnant virgin IS possible.

IVF!

Does the term virgin need to involve a dick?

My understanding is that if the hymen is intact, the girl is a virgin.  So I suppose if a virgin were really fooling around a lot, some loose swimmers might find their way home.