Karl Popper & A Theory Of Everything
A Theory Of Everything (TOE): A scientific theory that can explain everything.
[quote=Karl Popper (Philosopher Of Science)]A theory that explains everything explains nothing.[/quote]
Suppose theory T is a TOE. Suppose also, like any good scientific theory, T entails an observable P. However, since T is a TOE, T also entails ~P.
1. T -> (P v ~P) [T explains everything]
The usual process by which a scientific theory is falsified via the prediction turning out to be false like so,
2. If scientific theory Y is true then prediction/observable Z is true
3. Prediction/observable Z is false
Ergo,
4. Scientific theory Y is false.
This simple technique to falsify a scientific theory fails in the case of the TOE T because it requires ~(P v ~P) to be true but ~(P v ~P) is the contradiction (P & ~P) and contradictions are never true. This is another way of saying a TOE can't be falsified and that means any TOE is unscientific.
WTF? :chin:
[quote=Karl Popper (Philosopher Of Science)]A theory that explains everything explains nothing.[/quote]
Suppose theory T is a TOE. Suppose also, like any good scientific theory, T entails an observable P. However, since T is a TOE, T also entails ~P.
1. T -> (P v ~P) [T explains everything]
The usual process by which a scientific theory is falsified via the prediction turning out to be false like so,
2. If scientific theory Y is true then prediction/observable Z is true
3. Prediction/observable Z is false
Ergo,
4. Scientific theory Y is false.
This simple technique to falsify a scientific theory fails in the case of the TOE T because it requires ~(P v ~P) to be true but ~(P v ~P) is the contradiction (P & ~P) and contradictions are never true. This is another way of saying a TOE can't be falsified and that means any TOE is unscientific.
WTF? :chin:
Comments (22)
Of course. Completely explaining a donut includes explaining the hole. :smirk:
Yeah, I can't help but agree, "completely" explaining the donut includes explaining the "(w)hole". Nice play on words, Amigo!
How? Don't you see anything wrong with a TOE that's supposed to explain everything? It (the TOE) could only do that if it were compatible, truth-wise, with both the truth and falsity of a prediction. In other words, it could never be falsified for to do that a contradiction would have to be true but that, as you know, is an impossibility.
I must confess though that I have serious misgivings regarding my analysis of the...er..."situation". I would deeply appreciate your help in making me wrap my head around this issue.
Where I am right now:
1. A TOE must, by definition, explain everything but does that include the scenario that, if T is the TOE and its prediction/observable is P, that both (T & P) is true and (T & ~P) is too. A comprehensive theory of thermodynamics (call it Y) exists and it explains both the hot (H) and the cold (~H) i.e. (Y & H) and (Y & ~H) but these two don't seem comparable in the way I compared them. The question that puzzles me is WHY?
2. What exactly does Karl Popper mean by "if a theory explains everything, it explains nothing"? My take on this is Popper's applying his falsfiability criterion here and deems any theory that, "explains everything", to be unfalsifiable, something that I attempted to outline in my OP.
What's going on here?
What Popper means is that a theory that explains everything is so general as to be useless. But the apparently similarity with a physical theory of everything is, I think, coincidence, it’s not what he was talking about.
Roger that! Will get back to you when I can.
Quoting Wayfarer
Good to know but why is it "useless"?
Sleep time.
The most interesting thing about mechanical theories is the point at which they fail. Physics is the science of...approximation.
Interesting. I had the exact same problem when I began thinking about the TOE and Karl Popper's statement. For some unknown reason, there's no good explanation of Popper's claim that if a theory explains everything, it explains nothing available on the www.
I tried a number of approaches, a few I'll mention below:
Suppose theory T is a theory that "explains everything". T should entail some observables (experimental findings) and suppose one of them is P.
Suppose T is just like your garden variety scientific theory. If that's the case, the following relationship should hold,
1. T -> P [T entails P]
2. T [T is true]
3. P [1, 2 MP]
4. T & P [2, 3 Conj]
Now, since T "explains everything,
5. T -> ~P
6. T [T is true]
7. ~P [5, 6 MP]
8. T & ~P [6, 7 Conj]
9. ~(~T v ~~P) [8 DeM]
10. ~(~~P v ~T) [9 Comm]
11. ~(~P -> ~T) [10 Imp]
13. ~(~T v ~P) [4 DeM]
14 ~(~P v ~T) [13 Comm]
15. ~(P -> ~T) [14 Imp]
Notice 1. T -> P is falsifiable only if ~P -> ~T but 11. ~(~P -> ~T) says no, that's not the case AND T -> ~P is falsfiable only if P -> ~T but 15. ~(P -> ~T) says that's not the case either. Ergo, the theory T that "explains everything" can't be falsified.
Phew :sweat: :sweat:
"Explains everything" is the maximal, complete, 1-to-1 map of the territory, which is merely the terrority itself, and therefore useless as a map. The only "ToE" is the everything itself, thus useless as a theory. That's how Popper's statement speaks to me.
:up:
As the good Kantian that he was , Im sure all we’d need to do to please Popper is adjust the TOE so that it acknowledges we can never reach the thing in itself, and instead aim to approximate absolute truth as asymptotic limit via progressive falsification.
Thanks for alerting me to the paradox. I failed to notice that a theory that explains everything, explains nothing was one, a very interesting paradox indeed.
Quoting Pantagruel
It's been about 2 - 3 months since I gave the issue you raise here some thought. Back before physics and mathematics became subjects in their own right, philosophers like Heraclitus and Lao Tzu conceived of the world as a interaction between opposites (light vs dark, hot vs cold, good vs evil and so on).
When science began studying such phenomena with the aid of mathematics, it was discovered that (some) opposites could be, in a sense, united under one banner For instance, hot and cold were simply different positions on a numerical scale of the kinetic energy of particles. In other words, hot and cold, a particular instance of so-called opposites were actually different manifestations, albeit extreme ones, of the same underlying phenomenon (heat/kinetic energy of particles).
That's to say opposites are an illusion of sorts and imply, at least from a scientific and mathematical standpoint, either a misunderstanding or gross oversimplification of reality, the world.
Nevertheless, from a phenomenological perspective, opposites (dualistic, yin-yang thinking) are how the world appears to us and ergo, on that score should be given the respect they're due.
Quoting Pantagruel
Examples?
Quoting Daemon
Kindly expand and elaborate.
Quoting 180 Proof
If you have the time, please go through what I have to say under To All vide infra.
Quoting Joshs
Well said! :up:
@Wayfarer & @Banno
To All
A. I reckon that what Karl Popper meant by "a theory that explains everything" is a scientific theory that can't be falsified because it doesn't matter what the observational results are, such a theory will, as claimed, "explain everything".
The usual way science is done is positing a theory Y, making a prediction Z based on Y. This yields the following conditional,
1. Y -> Z
If Z is observed, the theory is said to have been confirmed but not necessarily that it's true (fallacy of affirming the consequent). However, if Z fails i.e. the prediction fails, the following is true,
2. ~Z -> ~Y
The theory Y is now falsified.
If, as I suspect, "a theory that explains everything" is one that can't be falsified, the option expressed in 2. ~Z -> ~Y should be unavailable to us. In other words, false that ~Z -> ~Y or,
3. ~(~Z -> ~Y) [we can't falsify Y with ~Z)
4.~(~~Z v ~Y) [3 Imp]
5. ~(Z v ~Y) [4 DN]
6. ~Z & ~~Y [5 DeM]
7. ~Z & Y [6. DN]
8. Y [assume for conditional proof]
9. ~Z [7 Simp]
10. Y -> ~Z [8 - 9 conditional proof]
Take a look now at lines 1 and 10. They are,
1. Y -> Z
10. Y -> ~Z
11. Y [assume for CP]
12. Z [1, 11 MP]
13. ~Z [10, 11 MP]
14 Y -> (Z & ~Z)
Initially I thought a theory Y that "explains everything is, taking 1 and 2, together, 14. Y -> (Z & ~Z) but this is clearly not someone in faer right mind would claim [no one would claim a contradiction]. Ergo, a theory Y that "explains everything" would entail either a prediction Z or the contradictory ~Z but definitely not both (Z & ~Z). That is,
15. Y -> (Z v ~Z) [Y is a theory that "explains everything"]
The way to falsify Y would then be,
16. ~(Z v ~Z) -> ~Y
and then,
17. (~Z & ~~Z) -> ~Y [16 DeM]
18. (~Z & Z) -> ~Y [17 DN]
19. (Z & ~Z) -> ~Y [18 Comm]
Observe line 19 carefully. The antecedent (Z & ~Z) is false (contradiction) but we know line 19 is true. That means, the consequent ~Y has to be false (a true conditional with a false antecedent must have a false consequent). If ~Y is false, Y has to be true. Put simply, we're unable to falsify Y using the standard technique [see lines 2 and 16].
Another way to look at it is as below,
Suppose we do observe the contradiction Z & ~Z,
20. Z & ~Z
21. ~Y [19, 20 MP]
You might then believe that Y has been falsified [line 21].
Not so fast!
22. Z [2o Simp]
23. Z v Y [22 Add]
24. ~Z [2o Simp]
25. Y [23, 24 DS]
Y is true [line 25, ex falso quodlibet]
In other words, Z & ~Z (contradictions), as expected and as warned, leads to all kinds of nonsense but, more importantly, Y can't be falsified and if you insist that it has been, you'll have to accept it's true as well. Z & ~Z is a no-go area. ~Y can't be proven or Y can't be falsified.
B. A TOE isn't a theory that's compatible with both what it predicts and a failure of that prediction. In other words, given a TOE T, prediction P, it's not the case that, T -> (P v ~P). T would "explain everything" except the predictions it makes that fail to come true.
You know, people's minds seems to be like containers, their shapes, sizes, capacity, so on are determined by how much they know (and don't know), their overall attitude, their experiences, etc. When someone gives faer point of view on an issue, like this one - Popper's statement, naturally that what the fingers type would be a reflection of the "container" which held the issue, the mind that processed the data. Take my opinion on the issue as idiosyncratic at best or foolishness at worst. I'm responding to "...even incoherent..." I have a lot to learn (so little time). :smile:
[quote=180 Proof]"Explains everything" is the maximal, complete, 1-to-1 map of the territory, which is merely the terrority itself, and useless, therefore, as a map. The only "ToE" is the everything itself, thus useless as a theory. That's how Popper's statement speaks to me.[/quote]
Thanks for asking me to reread your post. I had an Aha moment! How right you are, assuming I understood you that is. The idea behind thinking, its purpose, its defining character, is to map reality. I suppose it's like taking mirror and capturing an image of what's out there and what's in here ( :point: :broken: ). Necessarily then, if only out of regard for the mind and appreciation of its distinctness, the map shouldn't be merely the territory. Did I get you or am I, as usual, holding the wrong end of the stick? :chin:
There's something fundamentally wrong about map = territory because then there's no map. The whole point of mapping, conceptually modeling the world is to get our hands on a map that aids the navigation of the territory and this requires that the map to be distinct from the territory i.e. they must retain different identities based on how each is defined. If map = territory, it implies, I just realized, for whomsoever this is true, that this rather unfortunate (fortunate?) person actually doesn't have a map and thus "...watch the world unfold as it will in order to find out what happens..."
A TOE would be, in re the map-territory metaphor, one that would have, like you said, a 1-to-1 corrrespondence with reality, all that's in it and all that happens in it. The problem would be that such a map would be impossible if ever there are contradictions. The TOE in question, if it is a TOE, entails a contradiction and if it does, it necessarily is false. Now I get why mathematicians are scared silly by contradictions; it implies their axioms are inconsistent i.e. one/more of them are false.
The question is, what if the territory - the world - does have contradictions? Do we discard classical logic which collapses under the weight of a single contradiction? If the answer is no, by token of ex falso quodlibet, the map is no longer of any use for then "everything is true".
Rambling here. Would appreciate your input. Thanks.
Worse than that: anything at all – true, false, nonsensical – "follows" from a contradiction (re: principle of explosion).
Only propositions convey truth-values and therefore can "have contradictions". Maps, not territory, "have contradictions"; believing otherwise is to mistake the map for the territory (misplaced concreteness). Proof: the absence of even a single contradictory fact, event or thing in the world. :fire:
"What if" indeed, Fool. Alice's 'Wonderland out of "In the beginning there was" Jabberwocky'. :sweat:
"Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned." ~Ibn Sina
Well, here's @Pop from @Frank's interesting discussion about IIT:
Quoting Pop
If you ask @Pop to explain anything, the response is "it's information".
He's the guy you should be talking to. And maybe Fritjof Capra too.