Atheism and the existence of peanut butter

[polymath257]

Computers are designed by us to mimic the operations we want. We use transistors to mimic nand gates and use those for more complicated operations. but there is nothing about computers, per se, that disallows designing them to operate via other systems of logic.

Given how useful these computers proved to be, by only using classical logic, do we really need a different system of logic?

Who knows what will be needed in the future? it is a valid area of study in any case.

But if you look through history, those 'laws of thought' have changed and been modified. 

I am not sure what you mean by "changed". Sure, one can pick axioms different from these laws of thought, but what use would it have? I think you already know that dropping one law of thought topples all our results in mathematics, all of them. Classical logic deals with propositions that are two-valued, they only have {true, false} as truth values. And two-valued propositions reflet our thinking very well. Any statement, when formulated properly, about an abstract object or a real phenomenon, can only be true or false.

Well, the development seen in Aristotle is very poor, failing to make distinctions between basic concepts (such as identity and logical equivalence). So when Boole came along to clarify things, there were changes that needed to be made.

Also, the rules for quantifiers (existence and universal) were not developed until quite recently.

Buddhist tradition has cases of four valued logic and three valued (true, false, neither) has a rather long tradition.

In a more modern take, the technique of forcing in set theory (which was used to show the independence of the axiom of choice) relies on a version of multivalued (even infinitely valued) logic.

Next, the whole point of paraconsistent logics is exactly that the 'explosion' phenomenon of classical logic (where one false statement implies everything), is avoided. i can give you some references if you are interested in looking at what this leads to, including some very interesting aspects of mathematics including how to deal with Russell's paradox.

There are of course more "controversial" axioms like the axiom of choice. Interestingly, many results require the AC, and dropping the AC renders many famous theorems in mathematics unprovable. Now imagine dropping the excluded middle...........

Look up intuitionist mathematics some time. A great deal of math can be done without excluded middle. And, yes, like math without AC (which, by the way is NOT an axiom of logic, but of set theory), such mathematics tend to be stilted and lack beauty. But don't forget the paradoxes produced by AC (like the Banach-Tarski paradox).

That said, some of the recent developments in set theory are based on looking at alternatives to AC and seeing how such alternatives apply to the more traditional math.

There are many more alternatives to the 'laws of thought' than you seem to think exist.

Logic alone is *very* limited. Topics such as causality are NOT part of logic, but are properly part of physics. They are ideas that need to be subject to testing and modification to see when and how they apply.

You use vague phrases like 'began to exist' and don't eve say *exactly* what they mean (does it mean there is a time when the thing does not exist?). Can time itself 'begin to exist'? What does it mean if it does?

Why does something 'beginning to exist' imply that it must be 'caused'? What does it mean to be 'caused' anyway?

I am not sure why many here keep bickering about the meaning of "began to exist". It simply means that it didn't exist at some point. And by "at some point", I mean at some point along the causal chain of all things that ever existed or exist or will exist in prior/current/future universe.[/quote]

And that is *precisely* what does NOT happen with the universe. There is no *point* along the causal chain where the universe does not exist: the chain itself impluies the existence of the universe.

I think it's perfectly clear what "began to exist" mean when we picture a causal chain, something that began to exist didn't exist when some prior cause of it did. A deity, as usually defined, is posited as the first element of this causal chain, but it continues to exist after the "appearance" of the universe/the beginning of time.

Actually, the connection between causality and time is one of the aspects here. I think it is clear that causality is dependent on time (an order of causal events). For the universe, the issue is *precisely* whether it is in a chain of causal events where it did not exist at some point.

My position is that whenever there was a 'point' in a 'causal chain', the universe existed.

With regads to causality, I am assuming here that the principle of causality holds, that anything that began to exist has a cause. If you allow for the possibility of something to just pop into existence, then I really don't think any argument can possibly be made.

Well, as above, it is far from clear that the universe 'began to exist' in the sense you have give: was there a *point* when the universe did not exist and was it in fact in a causal chain?

if so, where did that causal chain begin?

But, more specifically, causality is something that happens *within* the universe and *within* time. And no, not every event is caused. It is clear that many events at the quantum level cannot be said to be caused in any classical sense.

Except that it is possible to have an 'eternity' (infinite past) and have the interval between any two times be finite. So, at any time an eternity *has already passed*. There is no need to wait for an eternity to pass. It already has.

The basic mistake is thinking that there is a *starting point* after which an eternity much past. And that is NOT the case even if there is an infinite past.

Your example above only applies to potential infinities, not actual infinities like events in the real world. We already know potential infinities are possible. The set of natural numbers is evidently infinite and countable, and one can "get" to the number 13 for example without counting infinitely many numbers (which is what actual infinites kind of require).

What you're referring to as a "mistake" is the key reason why an eternal past is impossible. The words past and eternal are mutually exclusive, if something is eternal, it's improper to speak of its past, because it doesn't have a present.

Where is the contradiction? And no, thi sis NOT a difference between 'potential' and 'actual' infinities. I am talking about an *actual* infinite past. My example has an *actual* infinite past. Look at the set of *all* integers, both positive and negative. That is a countably infinite set and every element has infinitely many precursors. And yet, you still have 0 and 10 and -100.

You say "there is no need to wait for an eternity", are you sure you thought clearly about this statement? If an eternal past really exists, then the universe (not us) really waited for this eternity to get to where it is now, which is clearly impossible.

WRONG. You seem to think there is a start, then a wait until we get to the present. My point is that there may well have been no start. Any wait between events would be finite. At any point, an infinite past had already existed. That's what it means to not have a start.

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