First order logic, set theory and God

[dr0n3]

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.

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.

The validity of the principle is as clear as daylight - there is absolutely no way of rationally conceiving a counterargument to the notion that a composite can never be the cause of one of its own components. The logic is impeccable. The reason you're questioning it is because of the ambiguity of your previous example. Namely that, cells in a human body are continually dying out and being replaced by new cells through the process of mitosis. Yes, at first glance you might think it nullifies the principle in some way since one could consequently deduce that the whole (human body) has been the cause of one of its own parts (new cell).

Yet, upon careful analysis, the conclusion doesn't hold water.


First, we know that your example hinges on several time-parametered phenomena coming to being through a succession of stages( where a stage is the state of the phenomenon at a given instant of time), which of course logically presupposes a causal discrete-time system. Secondly, one must make a clear distinction that the new human body (the one that contains the new cell) is different than the (old) human body that manufactured the new cell.

In light of the above points, we can now suppose the old body H1 at time T1 and the new body H2 at time T2 where we understand that H2=H'+B, where H' is H1 however transformed in the process in producing the white cell B. Thus, the correct causality relation (logically and temporally) is then H1→B|B⊄H1 and not H2→B|B⊂H1.

As for your last argument, temporality is not necessary within the scope of Hatcher's proof. The notion of causality is first and foremost logical and relational.

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.

For sake of simplicity and because "god" is the more-or-less standard term for a "universal uncaused cause". Regardless, it's not as if nitpicking over terminology will render the substance of the original argument any less valid.

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

Exactly, which makes it inherently linked to reality through its connection to truth. In that sense, one could just as confidently say that physical laws are descriptions of the dynamic behavior of matter in space-time.

I'm sorry, but what is your point again? 

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

Mathematics is abstract, yet inherently grounded in reality. Guess what? Same goes for True and False. Consequently, this renders your argument completely false.

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.

What you fail to grasp is that the law of causality is not descriptive but rather relational. A hammer's existence is not contingent upon whether or not the cause of its existence has to be known to us. Rather, the hammer's existence is already necessitated by an external cause preceding it, whatever that cause may be. Just as it is necessary for number 4, for instance, to occur between the numbers 3 and 5.

But just for argument's sake, the answer to your question would simply be - the causal link of all phenomenon that has brought the necessary and suffi­cient conditions for the realization of the hammer. That's it. Causality is merely established by the interdependence and relation between the cause and the effect.

 

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.

No, I wouldn't have.  The existence of a fallacy indicates that your conclusion doesn't follow from the premises.  That's how logic works, dumbass.  I could have pointed out other errors, but there was no need to do so having established the one.  A point that apparently sailed over your head.

Are you really this stupid?

In all honesty, the impression one gets by reading your posts is akin to a douche on a futile endeavor of throwing around "fallacy" this and "fallacy" that, and not even understanding what they're talking about. Perhaps you should understand that you don't get the decisive edge in an argument by simply brandishing retardedly your "Fallacy" wand at every chance you get and cramming your goddamn post with an impressive-sounding Latin term. Ironically enough, you're just as guilty of committing the fallacy of supposing you can defeat an argument simply by appealing to a named fallacy. You fucking dunce.