Guy Threepwood
Mighty Pirate
(altogether) ohhh yes it is
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McBell
Admiral Obvious
False dichotomy.
M. J. Fernandes
Member
It may be worthwhile referring to the First Vatican Council in the statement on the provability of the existence of God which is very likely infallible from the point of view of the Catholic Faith. See here for the statement.
I have developed a proof of the existence of God but I am not sure whether there are any flaws in it. Perhaps you could have a look at it.
I started developing it when I could not understand how to assume the premise used in Aquinas' First-Cause proof stipulating that all things had a cause (I think some ppl here had the same problem).
It is shown below in a mathematical manner as well as in a prose form.
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Part 1 - Proof of the Existence of G-d
For every two things, there is a relationship of sorts, between the two things. For example, one can say that there is a relationship between two objects a million miles apart via space. The relationship is such that either both things depend on something 'outside' of themselves (in the prior example, the dependency would involve space, a separate thing) or one of the things is caused by the other. This relationship must exist, by virtue of their co-existence in the same universe. Something ties all things together - nothing is completely isolated. Take for example the colour red, and the song of a bird. It might seem as though there is no relationship between them. However, something makes the colour red not the song of a bird and the song of a bird not the colour red. This relationship involves distinguishing them into quite different existences. It is like a grand person sorting the two things into two different boxes representing different categories; the person then acts as part of a link (relationship) between the two things.
There cannot be two uncaused causes, since, as stated, for every two things, there is a relationship between the two things. An uncaused cause implies no dependency & a relationship would imply at least one dependency. Furthermore, there must be at least one uncaused cause because otherwise, we would have a universe of just dependencies on other things and this cannot exist. It cannot exist because the dependences would never be fulfilled; for every dependency, another dependency would need to be fulfilled. Therefore, there must be only one uncaused cause and we call this uncaused cause, G-d.
I have developed a proof of the existence of God but I am not sure whether there are any flaws in it. Perhaps you could have a look at it.
I started developing it when I could not understand how to assume the premise used in Aquinas' First-Cause proof stipulating that all things had a cause (I think some ppl here had the same problem).
It is shown below in a mathematical manner as well as in a prose form.
------------------------------------------------------------------------------------------------------------------------------------------
Part 1 - Proof of the Existence of G-d
For every two things, there is a relationship of sorts, between the two things. For example, one can say that there is a relationship between two objects a million miles apart via space. The relationship is such that either both things depend on something 'outside' of themselves (in the prior example, the dependency would involve space, a separate thing) or one of the things is caused by the other. This relationship must exist, by virtue of their co-existence in the same universe. Something ties all things together - nothing is completely isolated. Take for example the colour red, and the song of a bird. It might seem as though there is no relationship between them. However, something makes the colour red not the song of a bird and the song of a bird not the colour red. This relationship involves distinguishing them into quite different existences. It is like a grand person sorting the two things into two different boxes representing different categories; the person then acts as part of a link (relationship) between the two things.
There cannot be two uncaused causes, since, as stated, for every two things, there is a relationship between the two things. An uncaused cause implies no dependency & a relationship would imply at least one dependency. Furthermore, there must be at least one uncaused cause because otherwise, we would have a universe of just dependencies on other things and this cannot exist. It cannot exist because the dependences would never be fulfilled; for every dependency, another dependency would need to be fulfilled. Therefore, there must be only one uncaused cause and we call this uncaused cause, G-d.
McBell
Admiral Obvious
This is nothing but a long winded word salad.
First you must demonstrate an uncaused cause.
If you ever get around to doing so, we can move on to step two.
Ouroboros
Coincidentia oppositorum
What about pantheism? I don't see that in there.
M. J. Fernandes
Member
Catholics believe pantheism is wrong.
Referring back to the First Vatican Council, if you look at the chapter accessible here, you will see that at the time of the Council the Church taught that God created everything from nothing - this teaching has not changed. In fact, I believe this chapter is very likely considered to be infallible Catholic teaching.
Pantheism is incompatible with this belief.
M. J. Fernandes
Member
There may well be a better way to write this 'proof'. I have tried to demonstrate an uncaused cause & I hope there are no holes in this 'proof'.
If we take the example of two colours for example. Red and green are both independent but also dependent on something else or each other. They are related in some sense to each other. This means that unless one created the other, they are both caused in some manner of speaking (perhaps in a metaphysical way & not really in a temporal way), and neither of them is uncaused or in other words, God or a god.
This principle of comparing two things can be applied to any two things you can think of. This leads, I believe, to belief in there having to be only one uncaused cause.
If you can point out a particular problem or confusion, then perhaps I might be able to better address it.
Mark
Ouroboros
Coincidentia oppositorum
But the proof doesn't show either or. Pantheism would be the end conclusion as an alternative to theism. Besides, Catholicism is not the same as theism. Theism is belief in a generic monotheistic God, not the Bible version.
The proof doesn't prove Catholicism, and it has a hole somewhere since pantheism isn't proved or disproved. If you can't account for all outcomes, then there's a vague parameter somewhere in your material. We don't have to find it, we just know that there must be one since you can't account for all options.
But not with the proof.
Well, that does not follow without additional premises.
Consider U = {a, b, c} so that a causes b, b causes c and c causes a. Premises are satisfied, yet you have D = {}. By the way, the fact that U is finite is not in the premises either. So, the inference that causal chains must be finite is an invalid conclusion.
So, you have to change the premises accordingly and postulate that U is finite and the causality relationships generate an acyclic graph. More specifically, a tree
where all elements have a common ancestor except the root. The question begging nature of this sort of reasoning should become apparent when you have repaired your syllogism.
But the real killer is: isn't U a concept that exist in reality? After all, U is a concept representing the set of all concepts that exist in reality. If it did not exist
in reality, then the concept of all concepts that exist in reality would not exist in reality, which is odd.
But if it exists in reality then it is a member of itself. That is, there is a u, belonging to U, so that u = U.
So, does u have a cause?
You might say that sets of things that exist in reality do not exist in reality. But when we talk of the existence of the Universe and who might have created
it, we make the assumption that the Universe, which is a set of things that exist in reality, exists in reality. So, to assign a different ontology to containers
of concepts that exist in reality, depending on what we want to prove, begs the question by deploying special pleading.
Ciao
- viole
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M. J. Fernandes
Member
I probably confused things by referring to Catholicism. Yes, the personal God of Catholicism is not the same as simply a generic monotheistic god.
Actually, pantheism is disproved by the proof because the proof demonstrates the existence of a first cause (distinct from all other caused things) whom we call God (at least I am hoping it proves that). Pantheism, as far as I am aware is incompatible with this. It is a different belief and both beliefs are mutually exclusive. If the proof is right, then pantheism is wrong.
Ouroboros
Coincidentia oppositorum
Then it's not useful to argue against pantheism.
No it doesn't.
A first cause fits with pantheism. Pantheism also fits with a final cause, and simultaneous cause, a no cause. The non-temporal and temporal in one entity, that fits pantheism, while theism does not. First cause does not fit Alpha and Omega, since it's the end. The First Cause argument only argues a first natural cause, not supernatural. And so on. Your proof has holes in it and doesn't prove a God that is anything. If you have to prove your God, then it's not God.
Also, Theistic God is outside and separate from this universe and us. The pantheistic God includes everything and is therefore a much larger and encompassing entity than the Theistic God. The Theistic God is smaller than the greatest. The greatest must include everything.
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M. J. Fernandes
Member
My belief is that such a situation cannot exist a bit like how you cannot have circular reasoning. You need a first cause to 'get everything started'. Mathematically, you might be able to express it, but that does not mean that it makes sense.
I believe the causal chains are finite simply because I do not believe that an infinite causal chain can exist. It may be possible, for example, to conceive in a mathematical sense an infinite distance between two points, but I think this can never exist in reality. The term 'infinite' seems to be more of a useful concept for modelling certain situations.
I believe we cannot pass through an infinite amount of time. In causal chains, I believe something similar happens (even if not in a temporal way - the cause must precede the effect.)
What you have written here has made me think.
I think that you probably do need to assign a different ontology to containers of concepts in a certain sense. Perhaps what is key is that you have written 'U is a concept representing the set of all concepts that exist in reality' (emphasis added). The set and the contents of the set are not the same.
Suppose we have a universe where only God existed. What would U be then? What would be the meaning of u belonging to U? The use of any kind of set theory relies on mathematical reasoning which in itself would seem to be something created (at least to a certain extent). A universe where only God existed would seem not to permit such extensive reasoning & so u belonging to U probably then does not make much sense.
Lowercase u seems to be more of a mathematical concept (or abstraction). Perhaps it is the difference between an apple and the thought of an apple. What caused the apple and what caused the thought of an apple? Are they different?
The truths of mathematics are true, but if you can't count in the first place, what use are they?
M. J. Fernandes
Member
Please give a definition of this supposed pantheistic god. Catholics define God as being the first cause, we use the name Yahweh ('I AM WHO AM'), etc. I cannot get my head round what you might mean by your pantheistic god.
Ouroboros
Coincidentia oppositorum
Therein lies the problem.
--edit
The first problem is that you feel that you have to prove God's existence. The second problem is that you feel that you have to use deduction to create a reductive god-image that only suggests that natural phenomenon begets natural phenomenon, and as such, you only have proved God to be part of nature.
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Perhaps the point of formal languages, such as symbolic/mathematical logic, abstract algebras, analysis, set theory, etc., is the removal of ambiguity. Everything is defined exactly. However, your "proof" uses the same variable "c" for two different things, you use the relation notation mRn but then define it as having two rules, one of which isn't a relation, and you actually indicate your proof is over before it ends (among other problems). Rather than presenting your argument in both mathematical language and "prose", it would be more helpful if your "mathematical manner" was consistent with...well, mathematics. Otherwise, what's the point of presenting the formal (mathematical) version of your argument?
M. J. Fernandes
Member
I do not see much of a problem with this. 'c' is a concept. D is a single-element subset of U.
Suppose you have an apple & an orange. I suppose in my thinking (in the 'proof'), that they are related at least by both being fruits. An apple is a concept, an orange is a concept, and so also there is a concept of fruit. This is an example of the first rule.
The second rule describes the case of cause (a concept) and effect (another concept). I consider this to be a causality relationship (perhaps in metaphysics).
Am I making mistakes with this thinking?
I do not see this. Please point out exactly what you mean.
It is true that it could be better written. However, I think it still makes sense, and it might be for other people to rewrite the 'proof'. I simply want to try to get the ideas across.
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You define the set U to consist of all elements c where c is defined as “a concept that exists in reality”. From that point onward, any use of “c” refers to this definition and this definition only, or should. That is how we avoid ambiguities. Also, subsets are defined using ⊆. Finally, you’re really saying that “D” isn’t a subset but an element of U. In other words, something like d ∈ U | d is uncaused. What you really want, though, is to have a precise relationship with symbols and propositions, operations, etc,. such that your proof contains no words. That’s why what you really want is the use of predicate logic s.t. you can define the predicate Dx to be “x is uncaused” and or the predicate Cx to be “x is a concept”. That way you can form WFFs like ∀x( [Dx v Cx] & ∀y(Dy→x=y)) or “for all x either x is uncaused or x is caused and for all y if y is uncaused than y is the same as x”. This means that everything is either caused except one thing: any argument that D takes.
I understand the motivation, and I sympathize. The problem is that there are ways to define such similarities, equivalences, and/or subsets in mathematics, and defining the same symbol or even using it in two different ways (at least in the same proof) is not allowed. That’s why it can be so tedious to say things in predicate logic like “there is only one Pope”, because you can’t use numbers so you have to define predicates like Px= “x is the Pope” and then define that for any/all x such that x is the Pope, then for all y such that y is the Pope, x is y”. This is a very roundabout and confusing way to say something as simple as “there’s only one Pope”, but again mathematics (including formal logic) is all about precision.
The problem is that you can’t have two rules for a relation aRb. The reason for the format is partly to indicate that (just the way the format for piecewise functions is special to allow a function to have more than one rule; even here, though, there is still one and only one assignment or mapping for any input in the function’s domain).
We really haven’t gotten to that point yet, as currently your proof can’t show anything because of certain notational problems (which is pretty common, even among those used to writing proofs if they aren’t use to a particular notational system and especially if they aren’t use to a particular algebraic structure or analytic language/system).
Sorry, I just thought it was a typo. Those three dots that form a triangle in your last line? They should go to the right of the last statement in a proof. They indicate the proof is over and what follows is not part of it.
In that case I would avoid the mathematical form altogether. For those who can read it, it is confusing to try to understand what you are saying.
Alternatively, if you need a refresher on set theory, formal logic, etc., there are free resources:
Sets, Relations, Functions
Proofs and Concepts: the fundamentals of abstract mathematics
A Problem Course in Mathematical Logic
Basic Concepts of Mathematics
M. J. Fernandes
Member
There appear to be mistakes in your remarks about the proof (such as the use of the subset symbol, the single-element subset not being a set, 'c' being defined). I do not need to form the proof using predicate logic and I think it is fine to use any informal style. However, I am grateful for your feedback. I would be happy to rewrite the proof in other ways, in more formal ways, but a mathematician should probably still easily be able to understand it.
Please examine the substance of the proof.
I wish you the best of intentions.
Ouroboros
Coincidentia oppositorum
Sorry to butt in here... but, you were attempting to use formal logic to make a proof. Wouldn't predicates be a very important part of such an attempt? It's like quoting the Bible without using the Bible to quote from, methinks. Also, formal logic means that you don't use informal style, doesn't it? They're at odds with each other. Formal v informal. Can you explain yourself a bit more about this, because it seems like you're contradicting yourself here?
The substance of the proof, at a cursory glance at it, seems to have a lot of holes. Not much of a substance to a sieve. If it's a swiss cheese, then sure, but the holes don't taste anything. They're still missing.
That’s certainly possible. However, I find it somewhat improbable that after years and years of working with such formal systems and the dozens of relevant textbooks and hundreds of relevant studies that your usage is somehow the norm despite these and despite the fact that you do not cite, quote from, or otherwise refer to any mathematical, logical, or similar text at all, while I provided you with several.
Sure. However, you didn’t just present an informal argument you deliberately and painstakingly took the time to (try to) imitate mathematical proofs. While admirable, this serves only to confuse. It is the use of systems in which proofs and similar derivations are possible despite the fact that the axioms required for said proofs do not exist.
As you say, you need not use predicate logic. Nor do you need to use an idiomatic mathematical argument. It would be better for us all if you either stated your argument purely in natural language or ensured that the mathematical representation made sense (I don’t mean that your argument didn’t; I merely refer to the its notational expression).
This has been done. The greatest logician who ever live presented a proof of God. However, we are none of us Gödel,, and in order to understand an argument it is helpful (at least for me) to see it clearly laid out in a logical fashion.
I have. As it exists, it asserts much, proves nothing, and (while the first “proof” is just a claim not an argument) the second “proof consists of multiple claims that must be accepted without cause in order to justify a conclusion which doesn’t really follow from the premises.
Many thanks, and I do so likewise.