Formalizing a Proof of God by Leibniz(timlabs.org)
timlabs.org
Formalizing a Proof of God by Leibniz
https://timlabs.org/leibniz/
23 comments
I have 0 experience with theorem provers (and almost 0 with proofs in general) but am at least somewhat aware of their existence. This might be the first time I feel like I can actually follow the code. Might start learning Oak because of this post, so thanks!
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P8 Every body whatsoever has an infinite number of parts.
P3 Infinite power is an original capacity to move the infinite.
So anything moving anything has infinite power, in which case everything moving something has infinite power?
LE: I re-read the P3 premise: only movers that aren't moved themselves have infinite power. All movers that have bodies are moved themselves (P6), so they don't have infinite power.
P3 Infinite power is an original capacity to move the infinite.
So anything moving anything has infinite power, in which case everything moving something has infinite power?
LE: I re-read the P3 premise: only movers that aren't moved themselves have infinite power. All movers that have bodies are moved themselves (P6), so they don't have infinite power.
The mover only has as much power from the body moving it, so it would still be distributed - almost like a top-down message passing or request if needing more power to allocate the infinite.
> Leibniz uses "original capacity" here to distinguish primary from secondary causation, noting that "secondary causes operate by virtue of the primary". I take this to mean that if a mover is being moved by something else, its power is only by virtue of the thing moving it, rather than an original capacity. I therefore require that the mover not be moved itself, for the conclusion of this premise to apply.
I find this quite elegant actually. It's like an allowance of energy in a fractal pattern. Feels elegant!
> Leibniz uses "original capacity" here to distinguish primary from secondary causation, noting that "secondary causes operate by virtue of the primary". I take this to mean that if a mover is being moved by something else, its power is only by virtue of the thing moving it, rather than an original capacity. I therefore require that the mover not be moved itself, for the conclusion of this premise to apply.
I find this quite elegant actually. It's like an allowance of energy in a fractal pattern. Feels elegant!
> But if B is moved by another body, which in turn is moved by another body, and so on, then we face either an infinite regress or a cycle, with each body moving the next. To handle this, Leibniz invokes p4, taking together all bodies which are movers, and referring to the whole as C.
So the argument hinges on the composition of (all) moving objects and the premise that the composed body is also moving but cannot be moved by another body since all the bodies are in the composition.
Supposing the only objects in the universe are two objects moving each other (in a cycle), they are considered a single body moved by an immaterial body because their composition cannot move itself? So everything boils down to where does energy come from?
So the argument hinges on the composition of (all) moving objects and the premise that the composed body is also moving but cannot be moved by another body since all the bodies are in the composition.
Supposing the only objects in the universe are two objects moving each other (in a cycle), they are considered a single body moved by an immaterial body because their composition cannot move itself? So everything boils down to where does energy come from?
I think other bodies can move other bodies depending on how much energy it uses relative to its motion in that sense of the proof.
Think of it as a budget of initial size.
So the bodies are limited as a whole vs the incorporeal which is infinite and influences the bodies total energy distribution per allowance.
Think of it as a budget of initial size.
So the bodies are limited as a whole vs the incorporeal which is infinite and influences the bodies total energy distribution per allowance.
I think the distinction lies in God being that which cannot be moved, having infinite power is not enough to be God.
I think the post is more about what Oak can do as a proof language. Obviously, anyone can pick apart the argument.
It is fun to see these historical arguments formalized like this, but they should remember to mention how flawed these arguments have proven to be over time.
P3 has the same flaw as Zeno's paradoxes, where there is a false assumption that the sum of infinite things must itself be infinite. If this were true, calculus class would be much easier, as all of those infinite sums would have the same answer. Since we know that the sum of an infinity achieved by infinite division of a finite is a finite itself, we are unable to tell whether it would take infinite or finite power to move these infinite things.
P1 fails to account for the possibility of multiple gods or gods other than the one this proof is presumably about. No evidence is provided for the claims of incorporeality or infinite power, either, without which the proof could well be proving that something more powerful than god exists, but not necessarily that god does.
The entire proof, flaws aside, only endeavors to prove that something god-like once existed, but not that it still exists or has any relation to what people historically have called god.
P3 has the same flaw as Zeno's paradoxes, where there is a false assumption that the sum of infinite things must itself be infinite. If this were true, calculus class would be much easier, as all of those infinite sums would have the same answer. Since we know that the sum of an infinity achieved by infinite division of a finite is a finite itself, we are unable to tell whether it would take infinite or finite power to move these infinite things.
P1 fails to account for the possibility of multiple gods or gods other than the one this proof is presumably about. No evidence is provided for the claims of incorporeality or infinite power, either, without which the proof could well be proving that something more powerful than god exists, but not necessarily that god does.
The entire proof, flaws aside, only endeavors to prove that something god-like once existed, but not that it still exists or has any relation to what people historically have called god.
I think this is quite elegant and nice. Cool!
Interesting to see the connections between various philosophies on the debate of "unmoved mover" this is basically the crux between Christianity/Ancient Greek/Ancient Vedic.
Thanks for sharing.
Interesting to see the connections between various philosophies on the debate of "unmoved mover" this is basically the crux between Christianity/Ancient Greek/Ancient Vedic.
Thanks for sharing.
It's a nice exercise but doesn't this ultimately proof that using these formalized proofs is flawed? That this system can be made to 'proof' anything, as long as the premises are logical by themself?
Or am I reading too much in the mathematical term 'proof'? Because it sounds more like 'verifiable reasoning' to me.
Or am I reading too much in the mathematical term 'proof'? Because it sounds more like 'verifiable reasoning' to me.
You already hit the important part with "as long as the premises are logical". Since the premises here are flawed, the proof falls apart. It isn't a flaw in formalized proofs. Getting flawless premises is the challenge for trying to use this for philosophical proof - the concepts are typically not as well defined as, say, what you see in geometry class.
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A "quick" "summary" by Feser is:
1. The Principle of sufficient reason (PSR) holds that there is an explanation for the existence of anything that does exist and for its having the attributes it has.
2. If PSR were not true, then things and events without evident explanation or intelligibility would be extremely common.
3. But this is the opposite of what common sense and science alike find to be the case.
4. If PSR were not true, then we would be unable to trust our own cognitive faculties.
5. But in fact we are able trust those faculties.
6. Furthermore, there is no principled way to deny the truth of PSR while generally accepting that there are genuine explanations in science and philosophy.
7. But there are many genuine explanations to be found in science and philosophy.
8. So, PSR is true.
9. The explanation of the existence of anything is to be found either in some other thing which causes it, in which case it is contingent, or in its own nature, in which case it is necessary; PSR rules out any purported third alternative on which a thing's existence is explained by nothing.
10. There are contingent things.
11. Even if the existence of an individual contingent thing could be explained by reference to some previously existing contingent thing, which in turn could be explained by a previous member, and so on to infinity, that the infinite series as a whole exists at all would remain to be explained.
12. To explain the series by reference to some further contingent cause outside the series, and then explain this cause in terms of some yet further contingent thing, an so on to infinity, would merely yield another series whose existence would reman to be explained; and to posit yet another contingent thing outside this second series would merely generate the same problem yet again.
13. So, no contingent thing or series of contingent things can explain why there are any contingent things at all.
14. But that there are any contingent things at all must have som explanation, given PSR; and the only remanning explanation is in terms of a necessary being as cause.
15. Furthermore, that an individual contingent thing persists in existence at any moment requires an explanation; and since it is contingent, that explanation must lie in some simultaneous cause distinct from it.
16. If this cause is itself contingent, then even if it has yet another contingent thing as its own simultaneous cause, and that cause yet another contingent thing as its simultaneous cause, and so on to infinity, then once again we have an infinite series of contingent things the existence of which has yet to be explained.
17. So, no contingent thing or series of contingent things can explain why any particular contingent thing persists in existence at any moment; and the only remanning explanation is in terms of a necessary being as its simultaneous cause.
18. So, there must be at least one necessary being, to explain why any contingent things exist at all and how any particular contingent thing persists in existence at any moment.
19. A necessary being would have to be purely actual, absolutely simple or noncomposite, and something which just is subsistent existence itself.
20. But there can in principle be only one thing which is purely actual, absolutely simple or noncomposite, and something which is subsistent existence itself.
21. So, there is only necessary being.
22. So, it is this same on necessary being which is the explanation of why any contingent things exists at all and which is the cause of every particular contingent thing's existing at any moment.
23. So, this necessary being is the cause of everything other than itself.
24. Something which is purely actual, absolutely simple or noncomposite, and something which just is subsistent existence itself must also be immutable, eternal, immaterial, incorporeal, perfect, omnipotent, fully good, intelligent, and omniscient.
25. So, there is a necessary being which is one, purely actual, absolutely simple, subsistent existence itself, cause of everything other than itself, immutable, eternal, immaterial, incorporeal, perfect, omnipotent, fully good, intelligent, and omniscient.
26. But for there to be such a thing is for God to exist.
27. So, God exists.
For the details see the twenty pages of chapter five ("The Rationalist Proof") in his book Five Proofs of the Existence of God:
* https://www.goodreads.com/book/show/35592365-five-proofs-of-...
Also covered are: Aristotle, Neo-Platonic (Plotinus), Augustinian, and Thomistic.
(The above is the summary which I've transcribed. I think I've typed it out correctly, but there could be some typos.)
1. The Principle of sufficient reason (PSR) holds that there is an explanation for the existence of anything that does exist and for its having the attributes it has.
2. If PSR were not true, then things and events without evident explanation or intelligibility would be extremely common.
3. But this is the opposite of what common sense and science alike find to be the case.
4. If PSR were not true, then we would be unable to trust our own cognitive faculties.
5. But in fact we are able trust those faculties.
6. Furthermore, there is no principled way to deny the truth of PSR while generally accepting that there are genuine explanations in science and philosophy.
7. But there are many genuine explanations to be found in science and philosophy.
8. So, PSR is true.
9. The explanation of the existence of anything is to be found either in some other thing which causes it, in which case it is contingent, or in its own nature, in which case it is necessary; PSR rules out any purported third alternative on which a thing's existence is explained by nothing.
10. There are contingent things.
11. Even if the existence of an individual contingent thing could be explained by reference to some previously existing contingent thing, which in turn could be explained by a previous member, and so on to infinity, that the infinite series as a whole exists at all would remain to be explained.
12. To explain the series by reference to some further contingent cause outside the series, and then explain this cause in terms of some yet further contingent thing, an so on to infinity, would merely yield another series whose existence would reman to be explained; and to posit yet another contingent thing outside this second series would merely generate the same problem yet again.
13. So, no contingent thing or series of contingent things can explain why there are any contingent things at all.
14. But that there are any contingent things at all must have som explanation, given PSR; and the only remanning explanation is in terms of a necessary being as cause.
15. Furthermore, that an individual contingent thing persists in existence at any moment requires an explanation; and since it is contingent, that explanation must lie in some simultaneous cause distinct from it.
16. If this cause is itself contingent, then even if it has yet another contingent thing as its own simultaneous cause, and that cause yet another contingent thing as its simultaneous cause, and so on to infinity, then once again we have an infinite series of contingent things the existence of which has yet to be explained.
17. So, no contingent thing or series of contingent things can explain why any particular contingent thing persists in existence at any moment; and the only remanning explanation is in terms of a necessary being as its simultaneous cause.
18. So, there must be at least one necessary being, to explain why any contingent things exist at all and how any particular contingent thing persists in existence at any moment.
19. A necessary being would have to be purely actual, absolutely simple or noncomposite, and something which just is subsistent existence itself.
20. But there can in principle be only one thing which is purely actual, absolutely simple or noncomposite, and something which is subsistent existence itself.
21. So, there is only necessary being.
22. So, it is this same on necessary being which is the explanation of why any contingent things exists at all and which is the cause of every particular contingent thing's existing at any moment.
23. So, this necessary being is the cause of everything other than itself.
24. Something which is purely actual, absolutely simple or noncomposite, and something which just is subsistent existence itself must also be immutable, eternal, immaterial, incorporeal, perfect, omnipotent, fully good, intelligent, and omniscient.
25. So, there is a necessary being which is one, purely actual, absolutely simple, subsistent existence itself, cause of everything other than itself, immutable, eternal, immaterial, incorporeal, perfect, omnipotent, fully good, intelligent, and omniscient.
26. But for there to be such a thing is for God to exist.
27. So, God exists.
For the details see the twenty pages of chapter five ("The Rationalist Proof") in his book Five Proofs of the Existence of God:
* https://www.goodreads.com/book/show/35592365-five-proofs-of-...
Also covered are: Aristotle, Neo-Platonic (Plotinus), Augustinian, and Thomistic.
(The above is the summary which I've transcribed. I think I've typed it out correctly, but there could be some typos.)
This is just one more bad variation of the "prime mover" argument. Your step 24 is where a whole bunch of woo is injected.
> Because there must be a root cause, this root cause must be jesusy
The logic is in "not even wrong" territory. Why does being "purely actual, absolutely simple or noncomposite" imply "fully good"? Because you've abandoned reason and are just making up definitions. Define "good", please and thanks, and how that has any connection at all to a "root cause", however you want to define it.
> Because there must be a root cause, this root cause must be jesusy
The logic is in "not even wrong" territory. Why does being "purely actual, absolutely simple or noncomposite" imply "fully good"? Because you've abandoned reason and are just making up definitions. Define "good", please and thanks, and how that has any connection at all to a "root cause", however you want to define it.
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Ah right. I missed the fact that you mentioned Feser. I examined the argument first, but shouldn't have bothered since you mentioned him. I've read his blog, and it's chock full of the bizarre reasoning such as above.
> <lots of words>
> A implies B without a single shred of justification
> <some more words>
> Therefore Jesus
I'd recommend not bothering with any of that. It's honestly not worth anybody's time except as a curio for how to dress up nonsense to look reasonable.
> <lots of words>
> A implies B without a single shred of justification
> <some more words>
> Therefore Jesus
I'd recommend not bothering with any of that. It's honestly not worth anybody's time except as a curio for how to dress up nonsense to look reasonable.
Leibniz' arguments essentially amounts to a 17th century "because I am unable to understand or comprehend another reason, including the nature of the universe, the nature of thinking and thought of an independent agent, and 'because this is a convenient reason'".
Its premised on:
- 1. The ontological argument;
- 2. The cosmological argument;
- 3. The argument from eternal truths and;
- 4. The argument from the pre-established harmony, which is more commonly known as the argument from design.