How existence of God infers from principle of sufficient reason

[irichc]

1) The principle of sufficient reason bases its strenght in another one, not so well-known, the identity of indiscernibles. It can be formulated this way: if two things are identical, then they are the same thing (A = A).

2) From here, it follows the principle of sufficient reason, which enunciation may be: nihil est sine ratione, nothing exists without a reason.

3) If the identity of indiscernibles was false, that is, if we could find two identical things in different space-time coordinates, then God would had acted without a sufficient reason, arbitrarily. That would lead us to fall into indiscernible states and, finally, in the eternal recurrence fallacy.

4) Thus, if we deny the principle of sufficient reason, we are denying also the identity of indiscernibles, which is similar to contradict that A = A.

Daniel.

Philosophy forum (spanish):

http://boards1.melodysoft.com/app?ID=isegoria

[Philosoft]

Originally posted by irichc

2) From here, it follows the principle of sufficient reason, which enunciation may be: nihil est sine ratione, nothing exists without a reason.
If you actually mean "reason," you are begging the question. If, instead, you mean "cause," you are arbitrarily defining God, the unknown, as initial cause of the universe, the known. Either way, the premise fails.

[Clutch]

Sorry, I think I missed the argument bit.

First, what do you mean by "infers from"? This is a misuse of the word 'infer', and the content of your post does not enable one to decipher what your intention might have been.

Second, why would the existence of exactly similar but numerical distinct objects show anything about God? And how did God get into (3), anyhow?

You are helping yourself to all manner of strange and unfounded assumptions -- apparently just using phrases without really knowing what they mean. A good start at correcting this appearance would be to produce actual arguments. To give just one example: you should produce your purported proof of "Nothing exists without a reason" from the axiom of identity. Viz:

(1) For all x, x=x.

<Further premises and reasoning here, complete with identification of the theorems upon which the inferences rest.>
______

(n) Therefore, nothing exists without a reason.

Like that.

[Bill Snedden]

Originally posted by irichc
1) The principle of sufficient reason bases its strenght in another one, not so well-known, the identity of indiscernibles. It can be formulated this way: if two things are identical, then they are the same thing (A = A).

Actually, this is the rather well-known "law of identity."

Originally posted by irichc
2) From here, it follows the principle of sufficient reason, which enunciation may be: nihil est sine ratione, nothing exists without a reason.

And this is the also rather well known "ex nihil, nihil fit".

Originally posted by irichc
3) If the identity of indiscernibles was false, that is, if we could find two identical things in different space-time coordinates, then God would had acted without a sufficient reason, arbitrarily. That would lead us to fall into indiscernible states and, finally, in the eternal recurrence fallacy.

Well, no. Two things in "different space-time coordinates" would not be identical insofar as the law of identity pertains as an existent's location in space/time is part of its identity.

And what in the world is the "eternal recurrence fallacy?" Is this some appeal to the impossibility of an actual infinity?

Originally posted by irichc
4) Thus, if we deny the principle of sufficient reason, we are denying also the identity of indiscernibles, which is similar to contradict that A = A.

Hmmm...this sounds suspiciously like the Ontological and Cosmological arguments rolled into one...

Needless to say, I see no inference to God's existence here...

Regards,

Bill Snedden

[irichc]

If the existence of that plurality of identical particles or states could be proved, which is impossible, it will be also proved that Universe acts arbitrarily, putting them in two (or more) different places when nothing distinguishes one from another. It wouldn't be ONE coherent reason, but various (or infinite) mutually contradictory. Therefore, the principle of sufficient reason cannot be stated refering to multiple and sensible states, and must be stated refering to a simple and intelligible substance, that is, God.

Daniel.

Philosophy forum (spanish):

http://boards1.melodysoft.com/app?ID=isegoria

[Clutch]

If the existence of that plurality of identical particles or states could be proved, which is impossible, it will be also proved that Universe acts arbitrarily

(1) It is provable that exactly similar but numerically distinct particles or states exist.

<Further premises and reasoning here, complete with identification of the theorems upon which the inferences rest.>
______

Therefore, the Universe acts -- and in particular, it acts arbitrarily.

See how that's gotta work? Arguments: Yay! Half-or-less-understood bafflegab: Yuck!

[irichc]

Originally posted by Clutch
(1) It is provable that exactly similar but numerically distinct particles or states exist.[/B]

"Against this it might be argued that a hidden variable interpretation would show that there are in fact several distinct particles each with their own locations, momenta and spins, although we cannot in fact re-identify a particle from one time to another".

"Against this has also been noted, e.g., Hacking (1975), that such a completely symmetrical situation of two spheres could be re-interpreted as one sphere in a non-Euclidean space. So what might be described as a journey from one sphere to a qualitatively identical one 2 units apart could be redescribed as a journey around space back to the very same sphere".

(from the www)

Daniel.

Philosophy forum:

http://boards1.melodysoft.com/app?ID=isegoria

[Clutch]

Oh, for pete's sake. Give an argument! How difficult is that to understand?

What do you mean by "two identical objects"? Do you mean that if 1=2, then God would be arbitary? (Presumably correct, by ex falso quodlibet.) Do you mean two objects with identical non-relational properties, but (obviously) distinct relational properties? Or what? How do the quotes you cribbed here, without comment or explanation of relevance (or citation), support the truth of the conditional premise in question?

I'm trying to take you seriously here, but you're making it difficult by not showing any interest in clarity or actual reasoning.

[SRB]

Originally posted by irichc
1) The principle of sufficient reason bases its strenght in another one, not so well-known, the identity of indiscernibles. It can be formulated this way: if two things are identical, then they are the same thing (A = A).

2) From here, it follows the principle of sufficient reason, which enunciation may be: nihil est sine ratione, nothing exists without a reason.



Quite apart from your conflation of the law of identity and the identity of indiscernibles (which are, ironically, two totally different things), there is no reason at all to suppose that (1) is true. Like Clutch, I challenge you to show how "nothing exists without a reason" can be inferred from "the law of identity is true." We are after a clear chain of reasoning, preferably with the relevant inferences given their appropriate names.

SRB

[Keith Russell]

Daniel said:
2) From here, it follows the principle of sufficient reason, which enunciation may be: nihil est sine ratione, nothing exists without a reason.

Nonsense!

Nothing doesn't exist--with or without a reason!

Keith.

[tronvillain]

Since this appears to be an attempt to prove the principle of sufficient reason rather than an attempt to prove the existence of God from the principle of sufficient reason, it is oddly titled. As Clutch has pointed out, it would be useful if you could actually show how the principle of sufficient reason follows from the law of identity, since it does not appear to. I am afraid this is one of the sadder arguments I have seen in a while, despite being clad in philosophical jargon.

Now, even if we do accept the principle of sufficient reason, the existence of God does not appear to follow.

[irichc]

I did it before. Read the message that starts like that:

"If the existence of that plurality of identical particles or states could be proved, which is impossible, it will be also proved that Universe acts arbitrarily..."

Daniel.

Forum of philosophy (spanish):

http://boards1.melodysoft.com/app?ID=isegoria

[Silent Acorns]

Principle of sufficient reason (PSR): every true statement has a sufficient reason why it is true

The Identity of Indiscernibles: no two distinct objects have exactly the same properties.

(there are other wordings, but these are the simplest)


irichc:

If the existence of that plurality of identical particles or states could be proved, which is impossible, it will be also proved that Universe acts arbitrarily, putting them in two (or more) different places when nothing distinguishes one from another. It wouldn't be ONE coherent reason, but various (or infinite) mutually contradictory. Therefore, the principle of sufficient reason cannot be stated refering to multiple and sensible states, and must be stated refering to a simple and intelligible substance, that is, God.

My translation:

1) If two objects can be distinct and identical in all respects, then the universe would contradict itself
2) Therefore, the universe would be true without sufficient reason.
3) Therefore, PSR can't be stated in reference to objects
4) Therefore PSR must be stated in reference to something else
5) This something else must be a simple and intelligible substance.
6) I call this substance God.
7) Therefore, PSR necesitates God.

I believe that this is the essence of your reasoning.

My problem is is that I don't see how (3) follows from (1) and (2), or how (5) follows from (1)-(4).

[HRG]

Originally posted by irichc
I did it before. Read the message that starts like that:

"If the existence of that plurality of identical particles or states could be proved, which is impossible, it will be also proved that Universe acts arbitrarily..."



And quantum theory (including the experimental check on Bell's inequality) indicates strongly that the universe does "act arbitrarily", as you call it, and that its regularities are only statistical.

Reality is not bound by philosophical speculations.

BTW, you might consider the scattering of two or more identical bosons off each other. It is impossible to say which outgoing particle corresponds to a specific incoming particle.

Regards,
HRG.

[Keith Russell]

HRG:

Still if the two outgoing particles occupy different spaces, travelling in different directions, and/or at differing rates of speed, we can clearly tell that they are in fact two different particles, even if we can't tell which one was which before the impact.

(I may not be able to tell two twins apart, but I still know that there are two of them.)

Keith.

[beyelzu]

i am just happy to see that i am not the only one who finds no logic in irichc's arguments.

[irichc]

Originally posted by Beyelzu
i am just happy to see that i am not the only one who finds no logic in irichc's arguments.

Try reading some Leibniz works.

Daniel.

[HRG]

[QUOTE]Originally posted by Keith Russell
HRG:

Still if the two outgoing particles occupy different spaces, travelling in different directions, and/or at differing rates of speed, we can clearly tell that they are in fact two different particles, even if we can't tell which one was which before the impact.

(I may not be able to tell two twins apart, but I still know that there are two of them.)

Keith.

But you can follow the "trajectory" of one of the twins (perhaps you have marked him with a red dot) and identify him after the interactions. You cannot do that with bosons.

In any case, what about the coherent state of Bose-Einstein condensation (which is not an eigenstate of the number operator, to be technical, so you cannot even tell how many individual particles are there in the condensate soup) ?

My point is simply that quantum reality should at least make us reconsider all the "obviously true" statements about identity, sufficient reasons etc.

Regards,
HRG.

[Sagan]

1) The principle of sufficient reason bases its strenght in another one, not so well-known, the identity of indiscernibles. It can be formulated this way: if two things are identical, then they are the same thing (A = A).

2) From here, it follows the principle of sufficient reason, which enunciation may be: nihil est sine ratione, nothing exists without a reason.

3) If the identity of indiscernibles was false, that is, if we could find two identical things in different space-time coordinates, then God would had acted without a sufficient reason, arbitrarily. That would lead us to fall into indiscernible states and, finally, in the eternal recurrence fallacy.

4) Thus, if we deny the principle of sufficient reason, we are denying also the identity of indiscernibles, which is similar to contradict that A = A.

Daniel.

Philosophy forum (spanish):

http://boards1.melodysoft.com/app?ID=isegoria



With respect, I must say that this medieval philosophizing is, to say the least, out of date. Four problems, by no means an exhaustive list.

1) You are speaking of metaphysical principles of logic. It turns out that Nature hasn't read Aquinas. (I'll explain below.)

2) Even by the rules of metaphysical logic, this argument fails because (2) is a non-sequitor. You have merely asserted that it follows from (1).

3) Your attempt to apply metaphysical rules to the natural world fails because you (a) introduce space and time, which are not implicit in A=A, and (b) you skip over the question of whether a thing is identical with itself.

4) Even assuming none of these problems existed, you have no justification for concluding that God exists. Aristotle, the originator of this line of argument, didn't. We could postulate many varieties of Prime Mover.

Let me try to elucidate. Metaphysical logic, like mathematics, often finds precise analogues in the natural world. But not always. In the case of the identity principle, one of the most surprising discoveries in quantum physics is that nature violates this principle shamelessly. Superposition, in which A both is and is not until such time as it decoheres, provides one instance. If your argument were valid, this would appear to prove that "God had acted without sufficient reason." However, your argument appears to lack formal validity, and so tells us nothing one way or another. Furthermore, you cannot expect informed people to take seriously medieval axioms like, "nothing exists without a reason." Says who? It is logically possible that everything exists without a reason. To assume otherwise is to add yet another flaw to your argument: circularity.

If you really want to make a logical argument in which we are asked to deduce the existence of God from knowledge about the natural world, you will need a long, long list of premises that envelope the current state of scientific knowledge. You will also need axioms that clearly define God. However, Christian philosopher Richard Swinburne has attempted this in The Existence of God, so you needn't go to the trouble.

Regards,

[Jinto]

Didn't we just go through this (http://www.iidb.org/vbb/showthread.php?t=86501)? :rolleyes:

[corn]

The principle of sufficient reason can not be used to prove God. It can only be used to disprove God if two identical 'objects' are found differing on in number.

If the God exists assuming he is of the Christian variety then the principle of sufficient reason must be true. It is fitting for God at all times to create the most perfect action due to his omni max nature. The sufficient reason is that the action is most perfect or best possible. Im not sure if all perfect actions must be actualised but an action must be perfect to be actualised. Now if two actions were equally perfect then God would need a reason to actualise one over the other. He cannot act randomly or arbitrarily as doing so would remove his power.

If God created this world, by Gods nature this is the best possible world. If this world contains within it two identical objects differing only in number, then another possible world exists where those objects are reversed. So when God is actualising a world he cannot actualise the best possible world because there are two such worlds. God must choose between them, as he cannot act randomly then he cannot act, and would not have created anything.

Something exists, so for God to exist, two identical objects differing only in number cannot exist. If they do then God cannot exist. If they don’t, nothing is shown about God.

[HRG]

I did it before. Read the message that starts like that:

"If the existence of that plurality of identical particles or states could be proved, which is impossible, it will be also proved that Universe acts arbitrarily..."



The identity of all photons, of all protons, of all electrons etc. has been demonstrated (Planck's radiation law, Bose-Einstein condensates etc.), and the universe does act arbitrarily. Deal with it.

I'm really sorry, but the universe is not bound to behave in a certain way just because you think it should.

Regards,
HRG.

[corn]

The identity of all photons, of all protons, of all electrons etc. has been demonstrated (Planck's radiation law, Bose-Einstein condensates etc.), and the universe does act arbitrarily. Deal with it.

I'm really sorry, but the universe is not bound to behave in a certain way just because you think it should.

Regards,
HRG.


The earth was once flat.

[HRG]

The earth was once flat.

Yes, and diseases were caused by demons ;)

But nobody ever demonstrated that it was so.

Regards,
HRG.

[corn]

and the universe does act arbitrarily. Deal with it.

I'm really sorry, but the universe is not bound to behave in a certain way just because you think it should.

Regards,
HRG.

How was it demostrated that something acts arbitrarily?

[ex-xian]

Everyone, please keep the discussion civil and on topic. Also, please keep in mind the EoG specific guidlines,
Any argument that focuses on an individual or group of individuals. This means not just users here but also groups of people. Even if it could be proven that all theists/atheists have an IQ of 24 or less, this is entirely irrelevent to a logical argument.
Posts which consist of no argument whatsoever. Note that this does not mean "no good argument."
Posts which consist of only sarcastic quips or one liners.
Any further violations will be deleted.

Thank you

[ex-xian]

As has been noted before, the law of identity and the identity of indiscernibles are not the same thing. The law of identity states an object is identitical to itself, Ax, x=x.

The identity of indiscernables, while similiar, is a distinct concept. It states that given two objects, if they have identical properties, then they are the same object. That is, given A with properites a1, ..., an and B with properties b1, .., bn, if a1=b1, ..., an=bn, then A=B. I've never seen it expressed formally and I can't figure out how to express an arbitary number of predicates...maybe Clutch can do it...maybe
x,y [~(x=y) -> (Px & ~Py) V (~Px & Py)].

The converse, the indiscerbility of identicals, states that if x=y, then they have all properties in common....maybe...
x, y {x=y -> [(Px ->Py) & (Py -> Px)]}

One of these, identity of indiscernibles or the indiscerniblity of identicals, is also called Liebnitz' Law...but I forget which is which.

I've even seen the name "identity of indiscernibles" used in mathematics. Let d be a metric on X; then, for x, y in X, if d(x,y)=0 then x=y. Also, there's an interesting article (http://home.ican.net/~arandall/Indiscernibles/) about QM and the indentity of indiscernibles.

[wiploc]

nothing exists without a reason.

So god doesn't exist?

crc

[HRG]

How was it demostrated that something acts arbitrarily?

Quantum theory tells us that nature is indeterministic at its fundamental levels.

Regards, HRG.

[HRG]

As has been noted before, the law of identity and the identity of indiscernibles are not the same thing. The law of identity states an object is identitical to itself, Ax, x=x.

The identity of indiscernables, while similiar, is a distinct concept. It states that given two objects, if they have identical properties, then they are the same object. That is, given A with properites a1, ..., an and B with properties b1, .., bn, if a1=b1, ..., an=bn, then A=B. I've never seen it expressed formally and I can't figure out how to express an arbitary number of predicates...maybe Clutch can do it...maybe
x,y [~(x=y) -> (Px & ~Py) V (~Px & Py)].

This simply says that identity can be defined in second-order predicate calculus, where you can quantify not only over objects, but also over predicates.

Thus: x = y <=> (for all predicates P) (P(x) = P(y)) - pretty close to what you wrote.

In set theory, this is known as the Axiom of Extensionality: two sets are identical if and only if they have the same elements.

Regards, HRG.

[ex-xian]

This simply says that identity can be defined in second-order predicate calculus, where you can quantify not only over objects, but also over predicates.

Thus: x = y <=> (for all predicates P) (P(x) = P(y)) - pretty close to what you wrote.

In set theory, this is known as the Axiom of Extensionality: two sets are identical if and only if they have the same elements.

Regards, HRG.
The way you wrote it, as a biconditional, implies both the identity of indiscernibles and the indiscernibility of identicals. I found this formulation on the Standford Encyclopedia of Philosophy website:
(∀F)(Fx ↔ Fy) → x=y for identity of indiscernables and
x=y → (∀F)(Fx ↔ Fy) for indiscernability of identicals.

(BTW, the vb code recognized the universal quantifier and the condition and biconditional symbols when I copied and pasted. Is there a way to write them here?)

[HRG]

The way you wrote it, as a biconditional, implies both the identity of indiscernibles and the indiscernibility of identicals. I found this formulation on the Standford Encyclopedia of Philosophy website:
(∀F)(Fx ↔ Fy) → x=y for identity of indiscernables and
x=y → (∀F)(Fx ↔ Fy) for .

What I wanted to stress is that identity becomes a defined relationship (not a primitive one) in higher-order logical calculus. Indiscernability of identicals is already part of the axioms for identity.


(BTW, the vb code recognized the universal quantifier and the condition and biconditional symbols when I copied and pasted. Is there a way to write them here?)

Sorry, I have no idea :o

Regards,
HRG.

[ex-xian]

What I wanted to stress is that identity becomes a defined relationship (not a primitive one) in higher-order logical calculus. Indiscernability of identicals is already part of the axioms for identity.

I (think I) see your point. I had only quantified over variables and you're telling me,in your other post, that one can also quantify predicates. I was just being picky in saying that Leibniz gave differnt labesl to the identity of indiscernibles and its converse.

Incidentally, metric spaces also have both properties. Again, let d be metric on X. Then, in addition other properites, for x and y in X,

d(x,x)=0 and
if d(x,y)=0 then x=y.

Which is saying d(x,y)=0 iff x=y.

Sorry, I have no idea :o

I may start a thread to ask about this...it's always irritated me to write "Ex, Ax, => or ->, and ,<-> or <=>."

[corn]

Quantum theory tells us that nature is indeterministic at its fundamental levels.

Regards, HRG.

I might be mistaken, but i have always assumed that you cant demonstrate somethings non existence. You cant demonstrate that something occurred without reason. How could this be done? It seems identical to assuming God exists.

I can't find a better explanation for the Universe. Therefore, God exists.
I can't find a better explanation why things occur. Therefore, it is arbitrary.

[HRG]

I (think I) see your point. I had only quantified over variables and you're telling me,in your other post, that one can also quantify predicates.

Yes. The sad story is that this second-order predicate calculus cannot be axiomatized, in contrast to first-order P.C. (per Gödel's Completeness theorem).

I was just being picky in saying that Leibniz gave differnt labesl to the identity of indiscernibles and its converse.

Incidentally, metric spaces also have both properties. Again, let d be metric on X. Then, in addition other properites, for x and y in X,

d(x,x)=0 and
if d(x,y)=0 then x=y.

Which is saying d(x,y)=0 iff x=y.

True. But that's just the definition of a metric.

Regards, HRG.

[HRG]

I might be mistaken, but i have always assumed that you cant demonstrate somethings non existence. You cant demonstrate that something occurred without reason.

Given the excellent success of quantum theories, it is not my burden of proof to demonstrate that something occurred without reason.

How could this be done? It seems identical to assuming God exists.

I can't find a better explanation for the Universe. Therefore, God exists.
I can't find a better explanation why things occur. Therefore, it is arbitrary.
The indeterminacy of quantum theories is not just based on our ignorance of possible causes. It is expressed by the fact that there are states with non-zero mean-square deviations of specific observables, and buttressed by the experimental verification that Bell's inequality doesn't hold (it would hold if there was a deterministic cause behind specific quantum phenomena).

Regards, HRG.

[corn]

[QUOTE]Given the excellent success of quantum theories, it is not my burden of proof to demonstrate that something occurred without reason.

My intention was not to ask you in particular to demonstrate quantum theory, nor am i arguing that quantum theory is not successful. Entire Quantum theory does not fall apart if the world is not in deterministic. So I am failing to see your point.

The success of a theory does not shift burden. I still have no burden in proving some things non existence. Just like you will never have the burden in proving Gods non existence.

The indeterminacy of quantum theories is not just based on our ignorance of possible causes. It is expressed by the fact that there are states with non-zero mean-square deviations of specific observables, and buttressed by the experimental verification that Bell's inequality doesn't hold (it would hold if there was a deterministic cause behind specific quantum phenomena).

I am relatively ignorant in quantum mechanics and thankfully you have reinvigorated my desire improve that ignorance somewhat.

From what I understand the fact that Bell's inequality does not hold, does not demonstrate that the lack of a deterministic cause behind quantum phenomena. All it demonstrates is that Bell's inequality does not hold. It is theorized that there is no deterministic cause, but not demonstrated.

[Gary Welsh]

3) If the identity of indiscernibles was false, that is, if we could find two identical things in different space-time coordinates, then God would had acted without a sufficient reason, arbitrarily. That would lead us to fall into indiscernible states and, finally, in the eternal recurrence fallacy.

Here is where you go wrong, just sort of arbitrarily slipping God into the argument in the above premise. What is your argument? If we don't find two identical things in two separate space-time coordinates, that somehow establishes that a god exists? Can this also be used to prove leprechauns? Just curious.

[HRG]

My intention was not to ask you in particular to demonstrate quantum theory, nor am i arguing that quantum theory is not successful. Entire Quantum theory does not fall apart if the world is not in deterministic. So I am failing to see your point.

No, it would fall down. It is absolutely basic to quantum theory that observables do not commute in general, i.e. AB - BA <>0, like in Heisenberg's famous commutation relations pq-qp = -i/2 h-bar (p: momentum; q:location).
As soon as you have that, indeterminacy sets in, because for each state there will be observables which do not have a sharp value in that state.


The success of a theory does not shift burden. I still have no burden in proving some things non existence.

Causality is not a thing, but a positive statement. Thus it carries the burden of proof.

Just like you will never have the burden in proving Gods non existence.

I am relatively ignorant in quantum mechanics and thankfully you have reinvigorated my desire improve that ignorance somewhat.

From what I understand the fact that Bell's inequality does not hold, does not demonstrate that the lack of a deterministic cause behind quantum phenomena. All it demonstrates is that Bell's inequality does not hold. It is theorized that there is no deterministic cause, but not demonstrated.

No. Bell's inequality is deduced from the assumption that there is a hidden variable (= deterministic) theory behind quantum mechanics. The inequality doesn't hold, thus the assumption is refuted, and quantum mechanics is basically indeterministic.

Regards, HRG.