In the original Star Trek, with the Starship Enterprise hurtling rapidly downward into the outer atmosphere of a star, Captain James T Kirk orders Lt Commander Montgomery Scott to restart the engines immediately and get the ship to safety. Scotty replies that he can’t do it. It’s not that he refuses to obey the Captain’s order or that he doesn’t happen to know how to restart the engines so quickly. It’s that he knows that doing so is impossible. ‘I can’t change the laws of physics,’ he explains.
We all understand Scotty’s point (although the Enterprise does somehow manage to escape). He cannot break the laws of nature.
That isn't Scotty's point at all. The laws of physics permit the engine restarting. The technology available to Scotty, to his best knowledge, does not. Tech obeys some laws of physics but is ignorant of other laws which is why we hope it will soon be superseded.
Nothing can.
No. A higher power can. But a more advanced civilization would have technology which would appear magical to us.
The natural laws limit what can happen.
For whatever type of force it deals with. But there may be a different force which is not subject to that limitation.
They are stronger than the laws of any country because it is impossible to violate them.
Only in the sense that the laws of stupidity are stronger than anything else as far as professional philosophers are concerned. They can kill and eat their students- thus defying the laws of the land- they can incessantly chop off their own head and shove it up their arse- thus defying various biological and physical laws- but they can't defy the law which requires them to always make the most self-defeating and stupid argument possible.
If it is a law of nature that, for example, no object can be accelerated from rest to beyond the speed of light,
No, that's a hypothesis- a useful one- not a Law, though, loosely speaking we might call it that. But, if positive mass can turn negative at c, then no violation occurs. We might then say 'energy conditions' are violated.
then it is not merely that such accelerations never occur. They cannot occur.
They can occur if for some currently unguessed at reason an 'energy condition' or something of that sort is violated or suspended.
There are many things that never actually happen but could have happened in that their occurrence would violate no law of nature.
We don't know that. It is an assumption. It may be that we live in a block universe, or a hologram, or something yet more arcane, and 'free will' is an illusion.
For instance, to borrow an example from the philosopher Hans Reichenbach (1891-1953), perhaps in the entire history of the Universe there never was nor ever will be a gold cube larger than one mile on each side.
If gold cubes form 'naturally', then one mile is not less likely than one centimeter. If such things are artefacts then there may be much larger cubes of this sort- if there are any at all.
Such a large gold cube is not impossible. It just turns out never to exist.
The same is true of a cube of cow-dung or one composed of shite published by philosophers.
It’s like a sequence of moves that is permitted by the rules of chess
or the rules of hitting people and running away
but never takes place in the entire history of chess-playing. By contrast, if it is a law of nature that energy is never created or destroyed, then it is impossible for the total energy in the Universe to change
just as it is impossible for the total uselessness of philosophy ever to change. One may try to avoid appearing like a drooling cretin by referring to prestigious things like gold, or chess, but it the word 'bullshit' can replace the predicates you use then, chances are, you are talking stupid bollocks.
The laws of nature govern the world like the rules of chess determine what is permitted and what is forbidden during a game of chess, in an analogy drawn by the biologist T H Huxley (1825-95).
But we know that the rules of chess have changed relatively recently. This is a silly analogy.
What all of the various laws (of Nature) have in common, despite their diversity, is that it is necessary that everything obey them.
No. Interesting observations are those which don't. They motivate research or confirm controversial, but, in view of the new observation, more 'parsimonious' theories which fit the data.
It is impossible for them to be broken. An object must obey the laws of nature.
No. We would be surprised if they were broken. Indeed we may be delighted. However, we may doubt that any 'disobedience' was involved.
In this respect, a law of nature differs from the fact that all gold cubes are smaller than a cubic mile,
A fact is information, which makes a true sentence true. We don't have access to any facts about gold cubes in the universe. Nor do we have access to true laws of nature. Thus we don't know what the difference between facts and laws. We may speculate that facts are heteronormative while laws are bisexual and tend to be obese. But this is pure speculation.
the fact that all the apples currently hanging on my apple tree are ripe, and other so-called ‘accidents’.
This is a stipulation this guy is making. He may believe it but we don't because it is wholly arbitrary. Indeed we may say 'poor chap, he teaches philosophy and thus can't not write shit. That would defy the Iron Law of Philosophy.
Prof Lange proceeds to engage in his profession's favorite parlor game- viz. making bizarre statements about things we 'normally do' in conversation.
there are lots of things that we would describe appropriately (in a given conversational context) as ‘impossible’ but that do not violate the laws of nature.
But there are lots of things which we imply are possible- e.g. Lange cramming his book where the sun don't shine- which violates all sorts of laws.
It is impossible for me to wish you ‘Good morning’ in Finnish because I do not speak Finnish, to borrow an example from the philosopher David Lewis (1941-2001).
This is foolish. It is impossible for you to wish me good morning in English when you are wishing me good evening in English. This violates a 'law of nature' of an obvious sort. However, it is possible for you to wish me 'Good morning' in Finnish while telling me to go fuck myself in the Brahmin Dialect of Fulham Tamil. This is because I'm a native speaker of that dialect and have the right to interpret any stream of obscenities directed at me by my relatives as polite salutations in a Finno-Ugraic tongue. This is because those languages broke off from a proto-Dravidian stem 30,000 years ago. Also, Mummy loves me. She wouldn't tell me to fuck off and get a fucking job you stupid fuck. She must be saying 'Good morning' in Finnish. I too shall speak that delightful language.
But my doing so would not violate a law of nature: I could learn Finnish.
Not if you were dead. The reason more people don't speak the Fulham Brahmin dialect of Tamil is because listening to it for any length of time causes boredom related mortality. This, at any rate, is the reason my relatives give for avoiding my soirees.
accidents lack the kind of necessity that laws of nature possess,
we don't know that. This is just a stupid stipulation made for a stupid purpose
there are other facts that possess the kind of necessity that laws possess but are not laws – or, more accurately, they are not merely laws.
How can a fact possess 'necessity'? Something may be true without any information that this is so becoming available. Equally a type of information my become available without it confirming the truth of anything. How do 'facts' get to 'possess' anything? Can they also borrow stuff?
If a fact is a law, what truth is it confirming? Its own existence as a law? What about facts which are not merely laws? Are they confirming they are laws of an especially cuddly and lovable kind? Or is it the case that they possess cool sneakers?
While accidents are too weak to be laws because it would have been too easy to make them false, certain other facts are too strong to be merely laws because they are harder to break than even the laws themselves.
But an 'accident' is a fact. We may also say that a law which has been experimentally confirmed is a fact. It may be that there is a fact- e.g. that your soul is immortal- which is higher than any laws we might discover. But this is pure speculation.
For instance, the fact that all objects either contain some gold or do not contain any gold is a fact that has even more necessity than a law of nature does.
But a fact with even greater necessity is that the fact mentioned by Lange must be either utterly meaningless or else not a fact at all. Indeed, few would hold that a 'tautology' is a fact or that meaningfulness is enhanced by generating more and more tautologies.
It is still a fact even in the Star Trek universe, where the laws of nature are different (since starships routinely accelerate beyond the speed of light).
No. They go into 'hyperspace'.
For 4 to be a prime number is likewise impossible even in the Star Trek universe.
The Star Trek Universe is not constrained by any type of compossibility.
The laws of nature, then, fall somewhere between the accidental facts (which lack the laws’ necessity)
Why? Both may arise by some arbitrary process or through a 'law-less' choice sequence.
and the facts that possess a stronger variety of necessity than the laws do.
But tautologies are not facts. The following sentence is meaningless-
The laws are distinguished by having the variety of necessity that distinguishes the laws.
This could be said, with equal truth, of cats as well as the Nicaraguan horcruxes of my neighbor's cat.
But we must do better than that if we are to understand what a law of nature is.
But, being a philosopher, this dude can't do any better. He has wasted his life.
Philosophers do not aim to discover the laws of nature. That’s a job for scientists.
Philosophers do not aim to discover the Nicaraguan horcruxes of my neighbor's cat. That’s a job for the love child of Harry Potter and Nagini, the snake.
What philosophers aim to do is to figure out what sort of thing scientists are discovering when they discover the laws of nature.
What philosophers aim to do is to figure out what sort of thing Harietta Nagini is discovering when sje discovers a Nicaraguan horcrux which turns out to belong to my neighbor's cat.
The philosopher’s aim is not to help scientists do their job. Instead, the philosopher’s aim is to better understand the job that scientists are doing.
by babbling the same shite whether they are talking of Science or a Nicaraguan horcrux.
For instance, when scientists explain why something happens by appealing to a law of nature that they have discovered, what makes a law able to answer such a ‘Why?’ question?
The same shit as works for a Nicaraguan horcrux- i.e. talking stupid bollocks.
To understand scientific understanding is a job for the philosophy of science.
Just as to suck the dick of fellatio is a job for the philosophy of blow jobs.
Of course, it can be difficult to reach this philosophical understanding,
unless you are as stupid as shit
and I will ask you to bear with me as I guide you – step by step – towards understanding what a law of nature is. I hope that as a useful byproduct, you will also enjoy seeing how a philosopher utilises a few bits of logic (paging Mr Spock!) to grapple with the question ‘What is a law of nature?’ Hold on: I hope you will find the final result to be elegant and illuminating.
A law of nature is stuff that sciencey guys discover and then engineers figure out cool new tech some of which we get to buy.
To begin understanding the variety of necessity that distinguishes the natural laws (which, for simplicity, I will call ‘natural necessity’), let’s unpack the laws’ necessity
which does not exist to any greater or lesser extent than the necessity of anything at all.
in terms of the fact that the laws not only are true, but also would still have been true under various hypothetical circumstances.
To say 'it is true to say that if x then y' is equivalent to 'if x then y is a law' but 'necessity' has no purchase in any inquiry concerning x and y per se. Thinking otherwise immediately produces nonsense like the following
For instance, since it is a law that no object is accelerated from rest to beyond the speed of light, this cosmic speed limit would still have been unbroken even if the Stanford Linear Accelerator had now been cranked up to full power.
There is no such law. Why does the author mention SLAC? I thought the accelerator was shut down a decade ago. I get the feeling the author is bullshitting. I could equally well write 'Putin's clear hint regarding citing nuclear missiles in Venezuela raises questions about recent research in the field of Nicaraguan horcruxes. How might this affect Democratic solidarity in the face of the unfolding humanitarian disaster in Ukraine?'
On the other hand, since it is merely an accident that every apple currently on my tree is ripe, this pattern would have been broken if (for instance) the weather this past spring had been much cooler.
It is also an accident that no prankster switched all the apples on this dude's tree for pineapples in the hope that his dirty great beard would fall off.
I have just compared two ‘conditionals’ (that is, two if-then statements) that state facts about what would have happened under various circumstances that did not actually occur
So, they weren't facts at all.
– that is, two ‘counterfactual’ conditionals. We often assert counterfactual conditionals, as in ‘If I had gone to the market today, then I would have bought a quart of milk.’ (That I went to the market today – the falsehood in the ‘if’ position of the conditional – is the ‘counterfactual antecedent’.)
This is as much a fact as the proposition that if you had gone to the market today you would have been sodomized by a rabid ferret. You may deny it but you are a liar. Nobody goes to the market to buy milk though, no doubt, they end up buying it because they are disappointed they have been not attracted the sodomitical attentions of rabid ferrets.
The laws, having natural necessity, would still have been true even if other things had been different, whereas an accident is less resilient under counterfactual antecedents.
But one of those laws is that milk is only bought at markets by those whose anuses were not reamed by rabid ferrets.
An accident is invariant (that is, would still have been true) under some counterfactual antecedents. For instance, all of the apples on my tree would still have been ripe even if I had been wearing a red shirt this morning
No. If you were dead, though wearing a red shirt, you would have owned no trees. Ripe apples which belong to you cease to exist when you stop owning shit either by reason of death or because you have gone bankrupt both of which events may be caused by wearing a red shirt.
But an accident seems to have less invariance in some respect than a law.
Because it is a partial tautology.
After all, we use the laws to figure out what would happen if we were to pursue various possible courses of action – for instance, what would happen to an object’s acceleration if we doubled the object’s mass or doubled the force on the object. We can rely on the laws to tell us what would have happened under various hypothetical circumstances because the laws are invariant (that is, would have remained true) under those circumstances.
No. You need some intelligence to properly apply a law. Philosophers have no such thing. Thus we can on rely on them to talk bollocks incessantly.
Of course, we can find some counterfactual antecedents under which the laws are not invariant.
Me, maybe. You- fuck off.
Obviously, the laws would not still have remained true under counterfactual antecedents with which the laws are logically inconsistent (that is, under antecedents contradicting the laws). For example, the laws would have been different if an object had been accelerated from rest to beyond the speed of light.
No. The law would be the same. Mass would have become negative. The positive mass condition is not a requirement for the mathematical consistency of the theory.
But presumably, the laws would still have held under any counterfactual antecedent that is logically consistent with all of the laws.
No. If a higher power was going to suspend the law at time t, then no 'logical inconsistency' would arise in the higher order language.
I’ll use lower-case letters for statements that make no reference to lawhood, necessity, counterfactual conditionals, and so forth – what I will call ‘sub-nomic’ claims. (For instance, p could be the claim that all emeralds are green, but p could not stand for ‘It is a law that all emeralds are green.’)
So p has an 'extension' such that all the elements it picks out are green, but 'emerald' has no 'intension' with respect to that color. But a 'nomic operator' (i.e. one that stipulates 'it is a law that') can be wholly extensional. It is not truth preserving if it is not the case that the reason emeralds are green is not because no other type of emerald is permitted by the law (though that may be the case) or that no emerald can't be green because of some fact about chemistry. The problem here is that we have no reason to believe a 'nomic operator' is ever 'truth preserving' or, indeed, meaningful in any non-phatic way. In other words, saying 'it is a law that...' is like saying 'All right thinking people believe...' or 'As ordained by the great God fuck...' etc.
We have arrived at the following proposal for distinguishing laws from accidents: m is a law if and only if m would still have been true if p had been true, for any p that is logically consistent with all the facts n (taken together) where n is a law.
Thus it really is a law that only those not sodomized by rabid ferrets buy milk at the market. This is because logic tells us that if you are being sodomized by a rabid ferret, you lose the desire to buy milk. Your mind is on other things.
It may be argued that it would take extensive training and perhaps some gene manipulation to get ferrets to sodomize shoppers while rabid. It could not be argued that being fucked in the ass by a ferret which is foaming at the mouth is conducive to carrying on with your grocery shopping. Of course, if this were not the case for some class of person, a law of this type might be specifically promulgated so as to discourage the nuisance.
Let’s step back and take a look at what this means. This proposal captures
a rabid ferret up a hypothetical shopper's asshole
an important difference between laws and accidents in their resilience – that is, in their range of invariance under counterfactual antecedents.
The reverse is more likely. A natural law may fail to be experimentally verified because of impurities or difficulties with lab conditions. 'Accidents' may be highly resilient. Why does my hair always look like shit no matter how I style it?
However, this proposal cannot tell us much. That is because the laws appear in it on both sides of the ‘if and only if’.
But so does a lot of really stupid shit to do with Nicaraguan horcruxes and rabid sodomitical ferrets. It is foolish to think that logic can only be done with fancy stuff. If you can prove that God must be infinitely good you can also prove shit can be infinitely shitty.
The proposal picks out the laws by their invariance under a certain range of counterfactual antecedents p, but this range of antecedents, in turn, is picked out by the laws. (It consists of the antecedents that are logically consistent with the laws.) Therefore, this proposal fails to tell us what it is that makes m a law.
However, for any given law, there are other proposals which would be illuminating. They just wouldn't be philosophical.
This proposal also fails to tell us what makes the laws so important. The laws’ invariance under the particular range of counterfactual antecedents that the proposal mentions makes the laws special only if there is already something special about having this particular range of invariance. But the laws are what pick out this range. So if there is no prior, independent reason why this particular range of counterfactual antecedents is special, then the laws’ invariance under these antecedents fails to make the laws special. They merely have a certain range of invariance (just as a given accident has some range of invariance).
This is stupid shit. Laws are important only if they tell us what to do or what will happen in some useful context. They need not be irrefragable to fulfil this function.
In short, we have not yet managed to avoid the circularity that hobbled our initial thoughts about the laws’ particular brand of necessity But we have made progress: now we can see precisely what problem we have to overcome!
But it is the same as the one which arises with Nicaraguan horcruxes or rabid sodomitical ferrets
There is a way to overcome this problem. Our proposal was roughly that the laws form a set of truths that would still have held under every antecedent with which the set is logically consistent.
Why must all laws belong to a set of truths? There may be no fact associated with them. On the other hand, there may be no laws at all because the facts that are associated with them are 'sublatable'. As more fine-grained facts become available, a particular law may be superseded. As for logical consistency, it applies to statements about Nicaraguan horcruxes and sodomitical ferrets in a less misleading and time-wasting manner than when it tries to pass itself off as a contribution to epistemology.
In contrast, take the set containing exactly the logical consequences of the accident that all gold cubes are smaller than a cubic mile.
There are no 'logical' consequences. It is obvious that so long as gold cubes can be 'mushed together' the only 'accident' here is of a temporal and local nature- viz whether, in the local history of those concerned with the proposition, such a thing has happened or not. But this has nothing to do with logic or philosophy. If we really want to determine truth value in this context we'd have to debunk El Dorado type stories and Atlantis type stories and various mythological stories re. Mt. Meru etc. of a religious type.
Alternatively, we could have a sciencey discussion re. the likelihood of an asteroid which contains a gold cube of this type. We know there is a way it could happen- indeed there was some speculation that 16 Psyche has a core of this type- but this has nothing to do with logic or philosophy.
I really can't see what the author is doing here other than displaying his own imbecility.
This set’s members are not all invariant under every antecedent that is logically consistent with this set’s members. For instance, if a very rich person had wanted to have constructed a gold cube exceeding a cubic mile, then such a cube might well have existed, and so not all gold cubes would have been smaller than a cubic mile.
This is nonsense. We might be able to get a 2 mile gold cube today iff Society worked together to achieve this for some religious reason- e.g. to avert doomsday. But no 'rich person' could command such an operation on a whim because 'rational expectations' & something like Ricardian Equivalence forecloses that option. Suppose there is only one rich guy. He pays us to do something which is as stupid as shit and which will shrink the production possibility frontier. We will take his money and laugh at him as he scratches his head and wonders why that stupid shit aint coming to pass.
Yet the antecedent p that a very rich person wants such a cube constructed is logically consistent with (that is, does not contradict) all gold cubes being smaller than a cubic mile.
How badly have you wasted your life if you end up writing a sentence like the above? Why not just say being anally raped by a rabid ferret is logically consistent with writing this shite coz of the Nicaraguan horcrux of my neighbour's cat?
Let’s capture this idea by defining what it would be for a set of facts to qualify as ‘stable’.
The set of facts isn't self consistent. This is because the 'fine graining' is different or else there is some law were are not aware of.
Suppose we are talking about a (non-empty) set 𝚪 (gamma) of sub-nomic truths that is ‘closed’ under logical implication. (In other words, the set contains every sub-nomic logical consequence of its members.)
In which case, either logical implication is not nomic or not true or else it is a member of gamma. If it is nomic and not true then gamma can't be closed. If is true and nomic then there is no 'chain' (defined as a partial order on 'almost nomic' sub-nomic truths) between it and any set of sub-nomic proposition (otherwise gamma is not closed). But in this case, 'logical consistency' is not intensional for gamma or else no nomic truth can avoid circularity or be non-arbitrary- i.e. can be associated with a unique preorder of gamma.
Thus gamma can't exist (because, by stipulation, it is non-empty).
𝚪 is ‘stable’ if and only if for each member m of 𝚪 and for any p that is logically consistent with 𝚪’s members, m would still have held if p had held. In short, a set of truths is ‘stable’ exactly when its members would all still have held under any counterfactual antecedent with which they are all logically consistent.
It is possible that gamma is a singleton- like Alonzo Church's 'slingshot'. But then 'stability' is the property of the one big Truth which every true proposition expresses, nomic or not.
In contrast to our previous proposal, stability does not use the laws to pick out the relevant range of counterfactual antecedents.
But logical consistency may be a law and stability may be defined by it. In other words, circularity might still obtain.
Stability avoids privileging the range of counterfactual antecedents that is logically consistent with the laws.
Only because you say so. But why should we believe you?
Rather, each set of truths
which may have been constituted by a law
picks out for itself
maybe only because of that law
the range of counterfactual antecedents under which it must be invariant in order for it to qualify as stable.
under that law
The fact that the laws form a stable set is therefore an achievement that the laws can ‘brag about’ without presupposing that there is already something special about being a law.
unless logical consistency is a law.
In contrast to the set containing all and only the laws, consider the set containing all and only the fact that all gold cubes are smaller than a cubic mile (together with its logical consequences).
That isn't a fact. It is a hypothesis.
That set is unstable: its members are all logically consistent with some very rich person wanting a gold cube larger than a cubic mile,
I'm a very poor person and want such a cube. But what has wanting a thing got to do whether it truly exists? There be some scientific reason why, like a Uranium cube, no Gold cube can attain this size. However, that scientific reason would be defeasible.
and yet (as we saw earlier) the set’s members are not all invariant under this counterfactual antecedent.
We saw no such thing. Endlessly repeating stupid lies has no magical effect save upon grad students stupid enough to need a credential to earn a little money as stupid liars.
Let us look at another example. Take the accident g (for ‘gas’) that whenever a certain car is on a dry flat road, its acceleration is given by a certain function of how far its gas pedal is being pressed down.
Acceleration or momentum or velocity is an 'accident' but no functional relationship seeking to capture an alethic structural causal model (SCM) is an 'accident'. In this case we know that acceleration is not a function of the gas pedal if there is no petrol in the tank or the wheels have fallen off.
Had the gas pedal on a certain occasion been depressed a bit farther, then g would still have held.
As a hypothesis, sure, but a hypothesis is not an 'accident'.
Can a stable set include g?
It is not true. So, the answer is no.
Such a set must also include the fact that the car has a four-cylinder engine, since had the engine used six cylinders, g might not still have held.
Why not? What affects g is whether there is gas in the tank and whether the wheels haven't fallen off.
(Once the set includes the fact that the car has a four-cylinder engine, the counterfactual antecedent that the engine has six cylinders is logically inconsistent with the set, so the set does not have to be invariant under that antecedent in order to be stable.)
But if there is no gas in the tank, g won't hold.
But since the set includes a description of the car’s engine, its stability also requires that it include a description of the engine factory, since had that factory been different, the engine might have been different. Had the price of steel been different, the engine might have been different. And so on.
It's beginning to look like there is only one very big true fact which contains all the information about the Universe.
This ripple effect propagates endlessly.
Which is cool if what you are doing is mysticism. Faith is founded on a mystery which Reason can't begin to contemplate.
Take the following antecedent (which, perhaps, only a philosopher would mention!): had either g been false or there been a gold cube larger than a cubic mile. Under this antecedent, is g preserved? Not in every conversational context.
Socioproctology is the conversational context by which assholes are identified and winnowed from discourse.
This counterfactual antecedent pits g’s invariance against the invariance of the fact about gold cubes.
only in the sense that rabid ferrets are invariably ass raping Marc
It is not the case that g is always more resilient.
Or more cuddly or inclined to suck you off.
Therefore, to be stable, a set that includes g must also include the fact that all gold cubes are smaller than a cubic mile (making the set logically inconsistent with the antecedent I mentioned, and so the set does not have to be invariant under that antecedent in order to be stable).
Maybe this is meant to be a joke.
A stable set that includes g must also include even a fact as remote from g as the fact about gold cubes.
Presumably the axiom of pairing is used to assert the existence of a stable set which is unique by the axiom of extensionality. We then need the axiom of regularity or else the axiom of induction. But if the stable set is a singleton what is the point? There is no binary relation or ordinality or inner product space or metric or measure.
The only set containing g that might be stable is the set of all sub-nomic truths. (Let’s call it the ‘maximal’ set.)
How is this useful? We can define the shitty set as that which causes everyone to shit so copiously as to extinguish the universe. But what have we actually achieved?
Every non-maximal set of sub-nomic truths containing an accident is unstable.
and thus unable to cause everybody to shit themselves very copiously
We have now found a way to understand what makes a truth qualify as a law rather than an accident: a law belongs to a non-maximal stable set.
and thus cause the extinction of the universe by reason of copious shitting
No set containing an accident is stable (except, perhaps, for the maximal set, considering that the range of antecedents under which it must be invariant in order to be stable does not include any false antecedents, since no falsehood is logically consistent with all of this set’s members).
ultimately the universe will be extinguished by everybody shitting copiously. It's gonna happen any day now.
We saw earlier that the sub-nomic facts that are laws should be distinguished from two other sorts of sub-nomic facts. On the one hand, accidents are easier to break than laws. Unlike the accidents, laws possess natural necessity. On the other hand, some facts are even more necessary (harder to break) than the laws, such as the fact that all objects either contain some gold or do not contain any gold.
This depends on how 'object' is defined. Some tradeable objects contain gold under a contingency.
It may be, 'at the end of Time', an all-wise robot may order, or codify, all human knowledge in terms of necessary and sufficient conditions and binary relations and unique preorders and inner products and so forth. We don't know whether this is possible but it is a nice Sci-Fi type idea. However, nothing we can say about that ideal world has any bearing on our own. The purpose of Science has been defeated by our having emigrated to fantasy land.
Such a fact possesses an even stronger variety of necessity than natural necessity. (Let’s call it ‘broadly logical’ necessity.)
But that logic would be very greatly in advance of our own. It's notion of necessity may be incomprehensible to us.
By thinking of natural laws in terms of stability, we can understand how the laws differ from both the accidents and the broadly logical necessities.
We often think we understand stuff which we later realize was nonsense pure and simple. Thus when someone says to me- 'Look, let me break it down for you quick and dirty. Just think of a Nicaraguan horcrux in terms of a placebo in a drug trial for overcoming caffeine addiction and you can start to understand why your neighbor's cat couldn't possibly have a Guatemalan horcrux. It's like the Yoneda lemma but restricted to grassmannian functors.'
Hearing something of this sort, I tend to grimace and then reluctantly admit that I can see where you are coming from but...fundamentally... we need to be thinking outside the box of category theory. I mean grassmannian functors for the holy sake of fuck! Is that we have come to? I thought the whole point of socioproctological topology was that we wanted to get away from that type of question begging bullshit.
The odd thing is I have a sneaking feeling I said something really profound back there.
Let’s investigate whether there are any other non-maximal stable sets besides the set of laws. Consider the set of all and only the sub-nomic truths possessing broadly logical necessity. It includes the truths of mathematics and logic.
These are theorems. But the theories behind the theorems can conflict. There can't be a set of all sets of theorems because the thing corresponds to no well formed formula. More significantly, what we would have is valid formula independent of truth value.
This set is stable since its members would all still have held under any broadly logical possibility. For instance, 2 plus 3 would still have been equal to 5
Not in base 3
even if there had been a gold cube larger than a cubic mile – and even if there had been a means of accelerating an object from rest to beyond the speed of light.
There is a nice little argument demonstrating that, for any two stable sets, one of them must entirely contain the other. The stable sets, however many there are, must fit one inside the other like a series of matryoshka dolls. The argument’s strategy is to consider a counterfactual antecedent like the one involving g (concerning the gas pedal) and the fact about gold cubes – namely, an antecedent pitting the invariance of the two sets against each other. Here’s how the argument goes.
First, assume that there are two stable sets, 𝚪 and 𝚺 (sigma), where neither set fits completely inside the other. In particular, suppose that t is a member of 𝚪 but not of 𝚺, and s is a member of 𝚺 but not of 𝚪. Now we can show that this assumption must be false because it leads to a contradiction. (Ready? Here we go…)
Let’s start with 𝚪. Since s is not a member of 𝚪, the counterfactual antecedent not-s is logically consistent with 𝚪, and hence so is the counterfactual antecedent (not-s or not-t). Therefore, since 𝚪 is stable, as we have assumed, every member of 𝚪 would still have been true, if (not-s or not-t) had been true. In particular, t would still have been true, if (not-s or not-t) had been true. So t and (not-s or not-t) would both have been true, if (not-s or not-t) had been true. Hence, if (not-s or not-t) had been true, then not-s would have been true; s would have been false.
Now we can make the analogous argument regarding 𝚺. Since t is not a member of 𝚺, the counterfactual antecedent not-t is logically consistent with 𝚺, and hence so is the counterfactual antecedent (not-s or not-t). Therefore, since 𝚺 is stable, as we have assumed, no member of 𝚺 would have been false, if (not-s or not-t) had been true. In particular, it is not the case that s would have been false, if (not-s or not-t) had been true. But now we have arrived at a contradiction with the result reached at the end of the previous paragraph. So we have proved that the initial assumption is impossible: there cannot be two stable sets, 𝚪 and 𝚺, where neither fits completely inside the other.
What we have just demonstrated is that the stable sets must form a nested hierarchy.
That's fine. Nested hierarchies exist in math. The problem is that we have no way of knowing whether there can correspond to 'truths', 'laws', etc.
There are at least three members of this hierarchy: the truths with broadly logical necessity (the smallest of the three), the set of laws (which also contains all the broadly logical necessities), and the maximal set (which contains all the sub-nomic truths). There are no stable sets larger than the set of laws but smaller than the maximal set, since any such set would have to contain accidents, but we have already seen that no set containing accidents (except for the maximal set) is stable.
The problem is that we don't know any members of any of these sets. We may assert that we know but an assertion is not knowledge. Confining ourselves to mathematical objects, we soon run into all sorts of ontological problems. The problem is not that we can't each suggest some scheme, the problem is that 'naturality' or 'non-arbitrariness' does not obtain at some point or another. Thus all you can have is a 'transfer principle' for useful stuff between models.
We can now understand what makes the natural laws necessary
Though we don't know what they are and also don't know what their being necessary actually entails. Will we projected into an alternative universe if they are broken? What about sufficiency? Which set pf natural laws are sufficient to explain the Universe?
and how their variety of necessity differs from broadly logical necessity. By the definition of ‘stability’, the members of a stable set would all still have held under any sub-nomic counterfactual antecedent with which they are all logically consistent. That is, a stable set’s members would all still have held under any sub-nomic counterfactual antecedent under which they could (ie, without contradiction) all still have held.
But only by stipulation. This is like defining the set of rabid ferrets as those whose failure to sodomize customers permits some to purchase milk.
In other words, a stable set’s members are collectively as resilient under sub-nomic counterfactual antecedents as they could collectively be. They are maximally resilient. That is what makes them necessary.
But do they exist? Could we know an example of one? We don't know.
There is a one-to-one correspondence between non-maximal stable sets and varieties of necessity. A smaller stable set is associated with a stronger variety of necessity because the range of antecedents under which a smaller stable set’s members are invariant, in connection with that set’s stability, is wider than the range of antecedents under which a larger stable set’s members are invariant, in connection with that set’s stability. Stability associated with greater invariance corresponds to a stronger variety of necessity – that is, greater unavoidableness.
This may capture a naive intuition we might have but it isn't useful. Indeed, it is mischievous.
Scientists discover laws of nature by acquiring evidence that some apparent regularity is not only never violated but also could never have been violated.
No. The regularity may have evolved or arisen after a phase transition or something of that sort. Much progress has been made because of thinking along these lines.
For instance, when every ingenious effort to create a perpetual-motion machine turned out to fail, scientists concluded that such a machine was impossible
No. Scientists found a theoretical reason to reject the very notion. Some cranks kept at it though.
– that energy conservation is a natural law, a rule of nature’s game rather than an accident.
It may be an accident arising out of some arbitrary symmetry breaking in the very early universe.
In drawing this conclusion, scientists adopted various counterfactual conditionals, such as that, even if they had tried a different scheme, they would have failed to create a perpetual-motion machine.
This does not accord with the facts. Anyway, perpetual motion is possible- e.g. in a quantum ground state- it's just that no energy can be extracted from them.
That it is impossible to create such a machine (because energy conservation is a law of nature) explains why scientists failed every time they tried to create one.
But it doesn't explain why time crystals exist. The bigger question is whether any 'isolated system' can exist. If not, we could have perpetual motion machines or extract 'zero-point' energy.
Laws of nature are important scientific discoveries.
But they are defeasible. We don't believe any existing law will survive in its present form as our tech gets better and more 'truths' are available to us- thus permitting better laws to be 'discovered'.
Their counterfactual resilience enables them to tell us about what would have happened under a wide range of hypothetical circumstances. Their necessity means that they impose limits on what is possible. Laws of nature can explain why something failed to happen by revealing that it cannot happen – that it is impossible.
That is no explanation. Being able to do something useful if not everything that would be useful is what distinguishes the expert whom we consult. The guy who just says 'it's impossible!' is given the cold shoulder.
We began with several vague ideas that seem implicit in scientific reasoning:
but didn't do any scientific reasoning whatsoever. That's why we ended up with this shite.
that the laws of nature are important to discover, that they help us to explain why things happen, and that they are impossible to break.
Actually, knowing the law, knows what to tinker with so as to do something which may have appeared impossible.
Now we can look back and see that we have made these vague ideas more precise and rigorous.
Have we though? Talking incessantly of Nicaraguan horcruxes can somehow hypnotize you into thinking they are real but they aren't at all.
In doing so, we found that these ideas are not only vindicated, but also deeply interconnected. We now understand better what laws of nature are and why they are able to play the roles that science calls upon them to play.
Has this dude actually come up with any scientific discovery? If not why should we care whether he understand science better or Nicaraguan horcruxes better or rabid sodomitical ferrets more intimately?
My comment on Lange's article was as follows-
We understand Scotty to mean ‘it is not feasbile for agents of type A to perform operations of type B at this time and place’. We don’t understand Scotty to mean it is impossible to break laws of physics. A superior being could do so- indeed, that happened a lot on that show.Unwritten laws exist both in jurisprudence and every other type of field where ‘adjointness’ is a feature, and it may be that they can’t be specified till ‘the end of time’. Nevertheless, provided they permit ‘orientation’ or solve a coordination problem, they are useful.
Can an event break a law of nature? Yes. Moreover, that event could be unique and not regulated by any law whatsoever. Indeed, it appears, for any set of natural laws currently specifiable, some ‘unlawlike’ event is necessary for a Nature to exist such that it abides by laws. Indeed, this notion is built into the very idea of law in all ancient systems of thought. One way round this is to say that ‘tie-breaking’ events split Universes. Another is that the opposite happens, converging Universes create ‘uncorrelated asymmetries’.
Currently we don’t have a representation of Category theory which captures ‘naturality’- i.e. non arbitrariness (which could be considered the sine qua non of ‘law’)- for physical isomorphisms. Thus it is impossible for philosophy to do what the author claims. All that has happened is that some law of logic has been egregiously violated. No discovery has been made.
From a pragmatic point of view, we understand a scientific discovery when we find a useful application for it- i.e. we have concrete ‘model’ of it which generates something extra- resources, information, analogies- which allow us to gain even greater knowledge. We can now see that CS Pierce anticipated much we now associate with Tarski or model theory or even ‘univalent foundations’. But, once we see this, we also see that the Socratic dialogs are much richer than we were taught to believe precisely because they give us respite from the tiresome business of philosophy saying it is doing something very very special and thus represents a very special type of education for very special little flowers.
Consider- a set of truths is ‘stable’ exactly when its members would all still have held under any counterfactual antecedent with which they are all logically consistent. From an argument similar to Church’s ‘slingshot’, we are faced with the possibility that there is only one such proposition. But that means the calculus of relations has no purchase. This is a useless type of truth. One may as well just point to a God at the end of Time or to an omniscient turtle which is the hypokeimenon or other such gibberish.
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