Philosophy Now Forum

Immanuel Can wrote:Number 1, then. Let me reword it for you:

"Can mathematics be so parochial and partial that it would reveal its secrets only to people who know how to do mathematics, though many (presumably very good) people believe that 2+2=4, but others believe 45, or 63, or 1, 007.33, or ∏ ? If so, what a poor mathematics, and what an unjust, bigoted image we have created of it from the figments of our imagination."

I would not want to drive over a bridge built by an engineer who would make the above statement. What makes it more rational when its referent is changed from maths to the Supreme Being? For *assuming* (for the sake of argument) He is real, then He would be every bit as real as mathematical truths. We should expect there to be singular, precise answers to questions concerning Him, just as we would expect them in the case of other real things. And we would not think that the multiplicity of answers counts for anything against that, since in maths the infinite alternate answers are simply wrong. That's not bigotry, but simple common sense when applied to mathematics, so why should the same not be applied to God?

You'll have to explain your reasoning to me.

Immanuel Can wrote:The case of mathematics is a good one to illustrate a simple point about logic, because in maths we can verify that real answers exist with ease. In every other area of human knowledge, we have to settle for probability calculations: science produces very high probabilities, and random guessing produces low ones. So in other areas of knowledge we are never 100% sure in the way we can be in maths. Maths lets us check to see if we're right about the way we're thinking, because maths has verifiable right answers.

So what's the simple point about logic? It's that the presence of many answers does not imply there can be no correct answer. That is all I am drawing from maths here; no more, but also no less.

That simple principle is something we need to keep in mind in other areas of inquiry too. For example, we do not know how many fish there are in the sea: that does not mean that there are no fish in the sea, that there are infinite fish in the sea, that we could not (at least in theory) ever find out the true number, or that all guesses were equally close to right. Or consider that we do not know the size of the universe; does that mean the universe has no size? Surely not. Even if that size is infinite, then it's true that it is infinite, and every other number suggested is not correct.

If something is real, then true and false statements can be made about it. Aristotle realized this principle in his Law of Identity, a foundation of logic. It states simply that a thing "is what it is," meaning it exists or it doesn't: there are no half-way states of being. Like a light switch is always either on or off (or like pregnancy wherein there is no such thing as "a little bit pregant" -- either you are, or you aren't) "being" is a true dichotomy.

We need to keep this simple principle in mind when we come to *any* area of inquiry that has to do with something real (i.e. something "being"). If the question is, "Is God real," then the same rule will apply: He will, or He won't. There won't be any "He sort of exists," or "He exists for some people and not for others," because these terms change the meaning of "being" into something simply merely metaphorical, not what Aristotle means by "being." There will be true and false statements about Him, true and false suppositions about Him, though some estimations may be perhaps closer to true than others.

On the other hand, if there is no chance He is real, then what are we talking about? He has no quality of "being," then. In that case, true and false no longer apply because all statements containing the predicate "God" are false by nature. So then there is no answer because there is no truthful question to pose.

What I was pointing out to abepat was simply that his/her question incorrectly supposed that multiple answers proves no truth exists. Then, oddly enough, abepat got metaphorically "sympathetic" with God, then in the same sentence denied His existence. A question premised on such a flawed assumption and worded in such a self-contradictory and logic-contradicting way cannot be answered with an intelligible response. But the fault is in the question's wording, not in the concept of God per se.

I suspect that abepat was simply "sounding off" to get a reaction. Because in his/her better moments, he/she could surely frame a more precise question than he/she did.

Conclusion: We can ask about God, sure; but we have to use the basic laws of logic when we do, because if we don't we can't possibly make any progress, and we're bound to end up merely confused. Abepat needs to realize this simple principle: multiple answers do not imply that no answer exists. Maths proves it. I suggest, therefore, that we need to stick with it, even in reference to the "being" of God.

That's our starting point: logic works, even when the referent to our questions is "God," not "maths."

Immanuel Can wrote:The case of mathematics is a good one to illustrate a simple point about logic, because in maths we can verify that real answers exist with ease. In every other area of human knowledge, we have to settle for probability calculations: science produces very high probabilities, and random guessing produces low ones. So in other areas of knowledge we are never 100% sure in the way we can be in maths. Maths lets us check to see if we're right about the way we're thinking, because maths has verifiable right answers.

So what's the simple point about logic? It's that the presence of many answers does not imply there can be no correct answer. That is all I am drawing from maths here; no more, but also no less.

That simple principle is something we need to keep in mind in other areas of inquiry too. For example, we do not know how many fish there are in the sea: that does not mean that there are no fish in the sea, that there are infinite fish in the sea, that we could not (at least in theory) ever find out the true number, or that all guesses were equally close to right. Or consider that we do not know the size of the universe; does that mean the universe has no size? Surely not. Even if that size is infinite, then it's true that it is infinite, and every other number suggested is not correct.

If something is real, then true and false statements can be made about it. Aristotle realized this principle in his Law of Identity, a foundation of logic. It states simply that a thing "is what it is," meaning it exists or it doesn't: there are no half-way states of being. Like a light switch is always either on or off (or like pregnancy wherein there is no such thing as "a little bit pregant" -- either you are, or you aren't) "being" is a true dichotomy.

We need to keep this simple principle in mind when we come to *any* area of inquiry that has to do with something real (i.e. something "being"). If the question is, "Is God real," then the same rule will apply: He will, or He won't. There won't be any "He sort of exists," or "He exists for some people and not for others," because these terms change the meaning of "being" into something simply merely metaphorical, not what Aristotle means by "being." There will be true and false statements about Him, true and false suppositions about Him, though some estimations may be perhaps closer to true than others.

On the other hand, if there is no chance He is real, then what are we talking about? He has no quality of "being," then. In that case, true and false no longer apply because all statements containing the predicate "God" are false by nature. So then there is no answer because there is no truthful question to pose.

What I was pointing out to abepat was simply that his/her question incorrectly supposed that multiple answers proves no truth exists. Then, oddly enough, abepat got metaphorically "sympathetic" with God, then in the same sentence denied His existence. A question premised on such a flawed assumption and worded in such a self-contradictory and logic-contradicting way cannot be answered with an intelligible response. But the fault is in the question's wording, not in the concept of God per se.

I suspect that abepat was simply "sounding off" to get a reaction. Because in his/her better moments, he/she could surely frame a more precise question than he/she did.

Conclusion: We can ask about God, sure; but we have to use the basic laws of logic when we do, because if we don't we can't possibly make any progress, and we're bound to end up merely confused. Abepat needs to realize this simple principle: multiple answers do not imply that no answer exists. Maths proves it. I suggest, therefore, that we need to stick with it, even in reference to the "being" of God.

That's our starting point: logic works, even when the referent to our questions is "God," not "maths."

"some sort of God"

we just don't know.

Immanuel Can wrote:Hello, Ginko:

I wouldn't think that we should worry ourselves much with whether or not Stephen Hawking believes in God, nor if someone like Anthony Flew converted to Deism before his death. These men were once famous Atheists, it's true, and their change of perspective is surprising; but we're never really wise to follow merely because an admittedly impressive person leads; we need to examine the reasoning for ourselves, don't we? It it's good, it won't matter much who advances it; if it's not, it an impressive person won't make it good. It's only in an area in which the person in question is a specific expert that we should, perhaps take thought for his reputation, and while Hawking is a highly respected scientist and Flew was an equally respected philosopher, theology is outside of both of their specializations. Still, it's an interesting aside; thank you for pointing it out.

Bivalence isn't always a problem, Ginko. Some things are just bivalent, aren't they? I used the example of light switches or pregnancy. The question of whether something "is" or "is not," (i.e. the question of being) is the same. Something can't 1/2 be: it "is" or it "isn't".

The God question is actually not merely bivalent but actually a trichotomy. Three statements:

1) Atheism: No gods exist.
2) Monotheism: One God (only) exists.
3) Polytheism: More than one, or many gods exist.

Of these three, it is utterly impossible for more than one to be true. If 1) is true, then both 2) and 3) are false. Likewise, if 2) is true, then 3) and 1) are both false. But since these three conditions cover every possible scenario, the interesting thing is that one *has* to be true. The next interesting thing that's true, then is that whichever is right, the other two logically *must* be false statements -- meaning that whatever is true about the "being" of God, much of the World is for sure and for certain wrong. Now, we're still not saying yet which one it is, but that in itself is a death-blow to inclusivism on the "being" question, not from theology or skepticism, but from pure logic. Fascinating, I find.

Now let's take the "excluded middle" you suggest:

"some sort of God"

I note you put it in the singular, so you'd be backing statement 2) in that case. On the other hand, if you meant "gods" instead of "God," you'd be backing 3). I'm not sure which you'd prefer me to deal with, but I think you can see that nothing in that "middle" alternative is different from the three options above. The trichotomy still applies.

But what about your other possible "middle,"

we just don't know.

The trichotomy can help us with that one too. It might well be true that we do not know if we should back 1, 2), or 3). But our uncertainty says nothing at all about the truth of the matter. I have never seen Beijing: that does not mean that there is no Beijing. I have never experienced skydiving; that does not mean no one else has. My uncertainty says nothing at all about whether or not something exists; it's only a statement about my personal awareness. So again, If there is any kind of a God or gods at all, whatever their nature or whatever I may or may not know about them, then 1) is not true; if there is no God or gods then 2) and 3) are not true. If there is more than one of these beings, then 1) and 2) are definitely not true.

You can see the situation with clarity now, I'm sure. Any of the three you pick defeats the other two. And since they cover all possible alternatives that can be imputed to the question of "being" in specific, there is no possibility of an excluded middle here. Sure there is elsewhere, with other kinds of questions: but there's none in a true trichotomy, and the "existence of a Supreme Being" question is a true trichotomy, pure and simple.

If the term "God" throws you off, try 1) 2) and 3) using the referent "cat" or "football" instead. You'll see that it works exactly the same way.

Good question, though.

The next obvious question might better get to what may have suggested to you there might be an "excluded middle," so I'll just mention it without dealing with it. Once we've settled the question of whether or not *any* such Being or beings exist, then we might want to ask, "What sort of God or gods is it/are they?" Things that have real existence also have attributes that can be discussed. But the question of the Supreme Being's attributes is immaterial until we've decided against 1). At the moment, we may not have decided that, so I won't presume to go further.

So here we are: we're faced with the trichotomy: 1), 2) or 3), all mutually exclusive.

...However, I don't think it precludes us extending it into a three valued logical system that can include the undetermined along with true and false. I think I hinted in an earlier post of the role of quantum mechanics in this regard. I am suggesting an undetermined or a 'fuzziness' that we find in this field of study. Unfortunately quantum mechanics is counter intuitive and doesn't always follow sharp and well defined logic.

Immanuel Can wrote:

...However, I don't think it precludes us extending it into a three valued logical system that can include the undetermined along with true and false. I think I hinted in an earlier post of the role of quantum mechanics in this regard. I am suggesting an undetermined or a 'fuzziness' that we find in this field of study. Unfortunately quantum mechanics is counter intuitive and doesn't always follow sharp and well defined logic.

Quantum mechanics is also a field like Special Relativity (Einstein), which people hear something about and (incorrectly, I would suggest) think it has epistemological implications that specialists in the field would not feel comfortable asserting. Rumour has it that quantum physics implies uncertainty about truth -- but it doesn't. All it really suggests is that we have in hand some rather unusual physical phenomena that stand in need of better explanation that our received paradigm of physical laws allows. Whether such an explanation will be forthcoming is a matter of scientific faith, not present facts, of course; but all the same, there's no logic in moving from those physical phenomena to broad suppositions of the death of truth.

But let us suppose for a minute we were in a universe in which the basic laws of logic did not work -- in particular, one in which the laws of "being" and "non-being" were not laws at all. In such a place, items would pop into existence with no causes or reasons; and likewise, things would suddenly stop existing for no particular cause. Emus and aqua lungs, airmchairs and brick back houses and light fields -- all sorts of random items would just show up without a reason and disappear the same way. "Being" would have no stability.

Clearly, this is not the kind of universe in which we live: things begin from causes, and end for reasons. Things that exist do so in a stable and predictable way. If there is any sense in which the laws of being proposed by Aristotle are really in question, it would have to be on a level so microscopic that we would not be aware of it and would not affect life on the macro level -- in which case, my Aristotle's conclusions about existence and non-existence would still apply to the macro level. But as it is, we do not know that there is any such variance, even at the micro level, of course.

I think you'll find, in fact, that any universe in which the basic laws of logic did not work would be an unintelligible one. We do not appear to be in an unintelligible universe -- things like science work very nicely here. So I would be very conservative in my view of what is implied by quantum mechanics, until someone with both the scientific and epistemological training to produce evidence should appear on the scene. I certainly wouldn't jump to full faith in relativism based on popular interpretations of QM.

So I'm going to suggest that multivalence, which may apply to qualitative fields like Aesthetics, does not apply to matters of "being" and "non-being". I'm also going to suggest that we cannot abandon the basic precepts of logic. They're our only guides to things we currently do not know but wish to know; and they're fundamental to philosophy, science and reason -- which are our best friends in the search for knowledge.

However, I would disagree that quantum mechanics is a matter of faith.

Immanuel Can wrote:

However, I would disagree that quantum mechanics is a matter of faith.

No, no...I didn't say that. I said that whether or not we will ever find out that it is *not* random is, at the moment and given our current knowledge, something we would have to take on faith -- not that QM is a matter of faith. Sorry for the misunderstanding. I hope this clears it up.

The many worlds interpretation has a profound logical problem. If you go to my post on the brand new article by Joel Marks, you'll see what it is. I spell it out there. I don't find the multiverse hypothesis rational. I say why.

QM is a real thing, and part of current science -- no doubt about it -- at the same time, it's a new thing, and a thing that science itself currently understands only as a temporary theory about some observations of very bizarre swerving of particles in a vacuum. It's way, way to early to try to suggest it has any implications for philosophy; we don't even know our scientific theory is right yet.

I don't know if you know this, but recently the old belief that light is both a particle and a wave has been brought into serious doubt. (Relativists used to use that as an analogy for truth.) It turns out that Canadian scientists ( I believe at the Perimeter Institute) have found that taking very low-data readings may allow proper observation of light without "biasing" the observations. In a similar way, scientists working on QM are working in a highly speculative field right now, and they are fully aware that their current observations of apparent "randomness" in particles may turn out to be incorrect. In fact, they're not at all opposed to that happening; that's the great thing about science -- it doesn't mind correcting itself.

So again, I would draw no conclusions right now from QM. And even if the current theories somehow proved eventually to be the final fact about QM, there would still be a huge logical hole in saying, "Therefore the laws of being do not any longer apply." That just wouldn't follow, even then.