First order logic, set theory and God

[Cod]

I'm learning lots of new words today.

I never knew you were Genoese, Cod.

Same here

[ignoramus]

but what caused their god to exist?

They have an excuse for that.  Everything needs a "cause" EXCEPT their particular fucking god fantasy.  That was always there.

Why do you think I consider all of them assholes?

Maybe God special pleaded himself into existence! Checkmate!

[Rahn127]

Ok, so now you have this argument. Let's test it and demonstrate that it's true.

Can you do that ?

[ignoramus]

^ The best they will always have is unfalsifiability of their claim.

(otherwise they wouldn't be wasting our time, they'd be busy parading their nobel prize)

[dr0n3]

The problem is that first order logic is a language. It is not a feature of reality but one method among many of describing reality. This means that it is not a perfect match for reality and any inferences based on this assumption will be wrong.

You could for example put forward an argument for the existence of your god using interpretive dance or an impressionist painting. Both would describe different aspects in more or less effective ways. But like with logic, it's just another language that is being used. For example first order logic rather than fuzzy logic.

For example your argument starts with flawed assumptions that have no equivalence in reality, namely that True and False exists and that causation is atomic. This is wrong and consequently so is the rest of your argument. Reality is not discrete, it is continuous and stochastic. saying that A causes B is short hand for saying that matter is gradually rearranged from one state to another over time because of energy flowing through it in accordance with the laws of Thermodynamics. This is a fundamental aspect of reality that is completely ignored because of the language you chose to use.

No, first-order logic isn't merely a language that one could lump together with interpretive dance or an impressionist painting. The comparison is completely absurd as dancing or painting fails to deal with semantic truths and syntactic provability, both of which deals with provability within a clearly defined postulated system of axioms.
The examples you've mentioned are in no way regarded as proof systems to which one can derive true/false propositions precisely because there is absolutely no deductive apparatus that could convey a true disclosure of an external reality.


Speaking of True and False, well those are semantic values (and not assumptions as you've mentioned) chosen to constitute a simple system that allows for abstract reasoning. The existence of those values can be explained by the rule of identity, such that we know that True is True and True is not False(and vice versa). That's it. As for the causational dynamics of two different phenomenon being either discrete, continuous or whatnot, that's a moot point. The law of causality is in no way trying to establish the description of a state over time between phenomenon but rather it is simply asserting that effect event has a cause. Point blank. Surely you understand that it was completely unnecessary to extrapolate the law in question into mathematical dynamics.
 

Since the first cause need not be a god, the proof is an example of ignoratio elenchi, at minimum.  It is not a proof of the existence of God.

There are other problems, but that is sufficient.  This is simply the basic first cause argument fleshed out with formalism.  Hardly worth even bringing up.

The point sailed over your head it seems. You'd have to provide some compelling and convincing arguments to support your position, instead of pointing out the fallacy that I'm allegedly guilty of.

It seems you're implying we can only understand what we can physically perceive. I'm pretty sure that many of our current mathematical concepts cannot be experienced by the senses.

Actually we can only understand what can be sensed or measured. There is zero reliable or reproducible evidence for the existence of a god.

Not true. Causality for instance, in the real sense of the term, cannot be known by the senses.

Below is a copy-paste of my own thread that was posted in another forum. I'm reposting it here in hopes to spark an intelligent discourse on what I believe to be the most refined proof of God's existence.

Here it goes.

[snip]

With that being said, I would be more than curious to see if anyone could spot a noticeable error in Hatcher's logical deduction

I'd spotted some big errors in this before I'd even finished reading.

Let us consider phenomenon H, the set of all humanity, which is a composite consisting of all humans alive.  Leaving aside the question of where the first humans come from, is H self-caused?

Well, certainly a significant cause of each human's existence is the existence of their parents, who are also in H, or at least were at one time.  In this sense, H seems to be self-caused, because every (present) component of H owes its existence to H itself.  This seems to put the lie to the principle of limitation.  The counterexample provided -- that cars do not produce their own steering wheels -- is an appeal to a particular system which does not maintain and reproduce itself, and does not cover systems that do exactly that.

For another example, whether or not we appeal to dualism, we might consider any given human being B to include the sum of all their constituent cells (and chemicals and so forth) in their present arrangement.  Yet no adult human contains all their original cells.  Each cell currently in our bodies arose from the mitosis of previous cells in the system.   Nor can we appeal to the causation of the chemicals making up those cells, because the atoms in our bodies are not the ones we were born with.

In both systems, each component of the system is caused by the existence of the system itself.

A plausible objection to this might be that the system is defined in part by its components, and that every time a new component is produced and introduced into the system (a new human for H or a new cell for B, it produces a new system caused, in part, by the existence of the old system, which no longer exists because it has been transformed into the new system.  In other words, we might say that Hx -> Hx+1 and that Bx -> Bx+1 ... though I would caution against assuming that either process is mathematically discrete.  I would also caution against assuming a first cause in all such systems, such as an index of 1 or 0 before which no system of the sequence could exist.  That might be so in the case of both examples that I provided, but as the car example (yet again) illustrates reasoning from one specific example to the general case is bad logic.

However, plausible though this objection might be, it is clearly not one that the provided proof is ready to employ.  If we transform V, the universe, to a sequence of universe-states Vx, Vx+1, and so on, or perhaps a continuum of non-discrete states, then the logic no longer works.  We would again encounter infinite regress, which you say the proof avoids and does not address.

Yet even were we to accept the entirety of this proof as correct... what sort of god would have been proven?  It would be a simple god, one with no components whatsoever.  Such a god could not have emotions, or thoughts, or memories, or desires, or a plan, or goals, or anything approaching what we would think of as a mind or the components thereof.  To call it a god at all is very much at ends with any god that a theist might be attempting to prove as well as anything a typical person might think of upon hearing the word "god".  The proof appeals to a definition of God, but you have not provided that definition and so it cannot be addressed here.  However, it is obvious that such a definition, if properly applied, is either far distant from or far too broad for any conventional notion of the word "god", and so should be referred to by a different word to avoid confusion.

As a third, related objection, how is this a proof of a god at all?  Suppose I were to say that G is not actually a god, but the sum total of all joules of physical energy in the universe.  Matter, motion, chemistry, et cetera are all basically energy arranged in different ways, and while energy might be transformed from one form to another, it does not appear to ever actually begin or cease to exist.  That would mean energy is either self-caused, which would make IT the unique self-caused phenomenon that God is supposed to be, or uncaused, which would undo the principle of sufficient reason and cause the whole logical house of cards to come crashing down.

Given how these problems quickly popped out to me, I'm sure there's a lot more wrong with this proof that an exhaustive survey would reveal.  However, I just woke up, and I don't feel like chasing down all the rabbit holes.

First and foremost, I would like to extend my appreciation for at least making the effort in forming a well thought-out argument.

As for the validity of your argument, it leaves a lot to be desired. Here's why:

Let E be the collection of all components of H, such that E∈H

A composite phenomenon, based on the principle of limitation, cannot be a self-caused phenomenon. That is one thing we should keep in mind.

Precisely because the whole H does not even exist (to be a cause of anything) until all of its components E exist. However, the premise that " every (present) component of H owes its existence to H itself" is not fallacious by any means, since nothing excludes that a phenomenon (in this case H) cannot contain within itself a cause E for its existence. The conclusion you draw from it however, is logically unsound. It's not because the cause E originates within H that H is therefore, self-caused. It simply means that H is other-caused by E. E being the cause of H for which it is part, certainly doesn't imply that H→H but instead E→H.

As a side note, the car example I provided was meant to illustrate a simple analogy and confirm my point, namely that a composite phenomenon cannot be its own cause without the logical error of the whole pre-existing its own parts.


Regarding your second objection, you've merely described the notion of total/complete causality from a transtemporal perspective. As you've perfectly described, it is not the sum of all constituent cells in their present arrangement that formed the human body, but rather a continuum of different cell cycles through mitosis, tissue growth, biochemical processes, and so forth, that gave rise to the formation of the human body. Yet this in no way undermined the logical reasoning behind Hatcher's proof.


As for the rest of your post, perhaps it must be clarified that Hatcher's proof was meant to provide a cut-and-dried deduction of the existence of a minimal concept (ie. a "universal uncaused cause") from a set of self-evident and empirically grounded axioms. While the proof doesn't tackle the fuller characterizations of God, there is at least little logical doubt that something akin to this minimalist understanding of a "God" is entirely believable and plausible as a distinct entity that has an existence, though perhaps little relation to what religious folks these days think of as a personal God.

[Belacqua]

from a transtemporal perspective

Although First Cause arguments come up on forums like this every few months, I despair of ever having people address the real argument.

For example, it's clear from earlier responses that everyone here is thinking of a temporal series of events leading back to a beginning in time. It doesn't seem to matter that this is not what the First Cause argument addresses. As far as I know the only temporal argument is the so-called Kalaam argument, and that is rejected by both Aristotelians and Thomists. 

It's hard to point out that the causal chain in question is essential, logical, and simultaneous. So the question is better posed as something like "what exists in order that people may exist?" or "what is it that holds people in existence?" The answer is then something like "the earth and its atmosphere." And again, "what exists in order that the earth and its atmosphere exist?" And pretty soon we're down to atoms and their parts, and then the fundamental laws of nature. That's where science stops, because it says that the fundamental laws of nature just are, with no further cause. 

As far as I can tell, it was alchemist, Bible critic, and physicist Isaac Newton who changed metaphysics so as to allow this sort of "it just is" argument -- a brute fact -- to end the causal chain. First Cause arguments wish to ask what holds these brute facts in existence as well. 

As for the rest of your post, perhaps it must be clarified that Hatcher's proof was meant to provide a cut-and-dried deduction of the existence of a minimal concept (ie. a "universal uncaused cause") from a set of self-evident and empirically grounded axioms. While the proof doesn't tackle the fuller characterizations of God, there is at least little logical doubt that something akin to this minimalist understanding of a "God" is entirely believable and plausible as a distinct entity that has an existence, though perhaps little relation to what religious folks these days think of as a personal God.

Likewise, many people object to First Cause arguments because such arguments don't prove that the God of the Bible has the characteristics which (they assume) he is supposed to have. But as you rightly point out, First Cause arguments only attempt to demonstrate a first cause, and anything more than that demands different arguments. 

I really don't know why people who have been posting on atheist sites for years haven't learned this yet.

[Reltzik]

A composite phenomenon, based on the principle of limitation, cannot be a self-caused phenomenon. That is one thing we should keep in mind.

Yes, but I am questioning the principle of self-limitation's validity as an axiom.

As for the rest of your post, perhaps it must be clarified that Hatcher's proof was meant to provide a cut-and-dried deduction of the existence of a minimal concept (ie. a "universal uncaused cause") from a set of self-evident and empirically grounded axioms. While the proof doesn't tackle the fuller characterizations of God, there is at least little logical doubt that something akin to this minimalist understanding of a "God" is entirely believable and plausible as a distinct entity that has an existence, though perhaps little relation to what religious folks these days think of as a personal God.

Yes, but why call it god? It's so divorced from both the common conception and most philosophical conceptions that the choice of term can only engender confusion. This is an equivocation land mine just waiting for someone to trigger it.

To field one more objection to the proof, it does not handle a scenario of cyclical time, perhaps from Big Bang/Crunch cycles. Here you can have A causing B which turns around to cause A, with a sequence of causes regressing into the (repeated) past ad infinitum.

[Pat Mustard]

I never knew you were Genoese, Cod.

Same here

Well why else would you proudly fly the flag of the republic of Genoa?

[I_am_not_mafia]

No, first-order logic isn't merely a language that one could lump together with interpretive dance or an impressionist painting. The comparison is completely absurd as dancing or painting fails to deal with semantic truths and syntactic provability, both of which deals with provability within a clearly defined postulated system of axioms.

My point is though that first order logic is still nothing more than a way of describing reality.


The examples you've mentioned are in no way regarded as proof systems to which one can derive true/false propositions precisely because there is absolutely no deductive apparatus that could convey a true disclosure of an external reality.

Speaking of True and False, well those are semantic values (and not assumptions as you've mentioned) chosen to constitute a simple system that allows for abstract reasoning. The existence of those values can be explained by the rule of identity, such that we know that True is True and True is not False(and vice versa). That's it.

Exactly. True and False are abstractions. They do not exist in nature.

As for the causational dynamics of two different phenomenon being either discrete, continuous or whatnot, that's a moot point.

Rubbish. It's extremely important.

What causes a hammer to exist for example? When someone connects a handle to a head? When a wood is reshaped to create the handle? When metal is melted down and shaped into a head? When a tree is cut down? When ore is mined from the Earth? When a tree is grown? When a planet is formed? What is the single cause of a hammer? There isn't one. All we have is energy flowing through and reshaping matter in accordance of the laws of Thermodynamics. Your abstraction of True, False and causation miss all that because they are abstractions.

Natural scientists see the laws of Thermodynamics work throughout the entirety of reality and make use of them in practice. The same cannot be said about the 'law' of Causation. This is a philosophical principle which has little practical use. No engineer builds a bridge for example using the 'law' of Causation. Nor does it have much explanatory power because it says nothing about why the cause happens.

[Cod]

Same here

Well why else would you proudly fly the flag of the republic of Genoa?

Bugger me! You learn something new every day.