A New Proof for the Existence of God

[Peter_Plato]

Look. If you have 1+1=3, what happens if you subtract 1 from both sides? You get 1=2. Now subtract 1 again from both sides and you have 0=1. You can’t have non-trivial mathematics with 0=1. Show me a mathematician that says that 0=1 can lead to non-trivial mathematics.

Not to trivialize the matter, nor the math, but if 0=1, then having 0 mathematicians who say that 0=1 can lead to non-trivial mathematics, that would be equal to having 1 mathematician who says it does.

It’s very simple really, in a trivial kind of way.

 

[Peter_Plato]

Good question. First we have to decide what subtraction means in our system. Subtracting usually means that you’re adding an inverse. All elements of S have inverses with respect to Oreo sums, so this is a well-defined notion.

No. Firstly, 2 doesn’t exist in our group. In fact, we shouldn’t expect to get 2 at all, since subtraction is just a special case of taking an Oreo sum, and S has already been shown to be closed under Oreo sums. So if you have an addition or subtraction problem in terms of 1 and 3, your answer will be either 1 or 3.

Here’s what happens: You wish to subtract 1, and the only sensible way to interpret this subtraction in our system is to say that we are adding (by Oreo summation) the inverse of 1 to both sides. By definition, the inverse of 1, -1, is the number such that 1+(-1)=0, where 0 is just the symbol for the identity element of the group. As you noted, 3 is the 0 of this group, so the equation is 1+(-1)=3. So which element of S plays this role for -1? According to the equations we already have, 1 is the inverse of 1 since 1+1=3.

So subtracting 1 from both sides amounts to adding 1 to both sides in this group. Indeed, 1+1+(-1)=3+(-1) can be rewritten by this argument as 1+1+1=3+1 and both sides have an Oreo sum of 1. So subtracting 1 from both sides poses no problems for our arithmetic.

It’s easier to accept this sort of thing once you appreciate the group in its own right rather than try to compare it to other groups or translate problems between differing groups.

This is about as coherent and convincing as using ambiguous terms to construct a logical argument. You must realize that you are merely playing with mathematical terms and have not shown your original contention to be true that is in any way germane to the discussion.

 

[Oreoracle]

This is about as coherent and convincing as using ambiguous terms to construct a logical argument.

This is the problem with philosophy forums; it’s a mixed bag. Some people are genuinely interested in learning and thinking about things in a new way. I think Tomdstone, in spite of perhaps being frustrated with me at this point, is such a person.

Then you have some people who whine anytime a discussion gets too in-depth. They’ll make a flippant remark and just when someone gets on the verge of proving them wrong, suddenly the tangent they’ve been on for pages now is unacceptable! These people don’t want to learn, they are just sore losers.

 

[Tomdstone]

Good question. First we have to decide what subtraction means in our system. Subtracting usually means that you’re adding an inverse. All elements of S have inverses with respect to Oreo sums, so this is a well-defined notion.

No. Firstly, 2 doesn’t exist in our group. In fact, we shouldn’t expect to get 2 at all, since subtraction is just a special case of taking an Oreo sum, and S has already been shown to be closed under Oreo sums. So if you have an addition or subtraction problem in terms of 1 and 3, your answer will be either 1 or 3.

Here’s what happens: You wish to subtract 1, and the only sensible way to interpret this subtraction in our system is to say that we are adding (by Oreo summation) the inverse of 1 to both sides. By definition, the inverse of 1, -1, is the number such that 1+(-1)=0, where 0 is just the symbol for the identity element of the group. As you noted, 3 is the 0 of this group, so the equation is 1+(-1)=3. So which element of S plays this role for -1? According to the equations we already have, 1 is the inverse of 1 since 1+1=3.

So subtracting 1 from both sides amounts to adding 1 to both sides in this group. Indeed, 1+1+(-1)=3+(-1) can be rewritten by this argument as 1+1+1=3+1 and both sides have an Oreo sum of 1. So subtracting 1 from both sides poses no problems for our arithmetic.

It’s easier to accept this sort of thing once you appreciate the group in its own right rather than try to compare it to other groups or translate problems between differing groups.

OK. In your supposedly non-trivial system of 1+1=3, can you tell us what would be the commutator subgroup of the fundamental homotopy group of the Klein bottle. Further, what would be the homology groups of the complex projective plane or even just the n-sphere or torus? How do you define the betti numbers in your system? How do they relate to the Euler characteristic? Also, in your non-trivial mathematical system of 1+1=3, what would the global Cauchy theorems look like? What would be the analogue of the Caratheodory-Osgood theorem in your system and what new and exciting non-trivial results in Galois theory do you expect to find in your system of 1+1=0, oops, I meant 1+1 = 3?
My guess is that you have nothing because the system 1+1=3 (which is really 1+1=0) is a trivial system which leads nowhere, thus confirming my belief that there are extremely few, if any, mathematicians who will assert that 1+1=0 is a non-trivial system.

 

[inocente]

There is no difference between empiricism and rationalism; Kant synthesised them. You seem to have a very large blind spot in Philosophy if you think those two are the only two competing systems, especially as they are apart of the exact same tradition.

It’s called realism and has a history of its own in philosophy.

Even the article Peter himself linked is nowhere near as black-and-white as you guys. I’ll let it speak for me. Here’s the opening paragraph:

*"The question of the nature and plausibility of realism arises with respect to a large number of subject matters, including ethics, aesthetics, causation, modality, science, mathematics, semantics, and the everyday world of macroscopic material objects and their properties. Although it would be possible to accept (or reject) realism across the board, it is more common for philosophers to be selectively realist or non-realist about various topics: thus it would be perfectly possible to be a realist about the everyday world of macroscopic objects and their properties, but a non-realist about aesthetic and moral value. In addition, it is misleading to think that there is a straightforward and clear-cut choice between being a realist and a non-realist about a particular subject matter. It is rather the case that one can be more-or-less realist about a particular subject matter. Also, there are many different forms that realism and non-realism can take.

The question of the nature and plausibility of realism is so controversial that no brief account of it will satisfy all those with a stake in the debates between realists and non-realists."*

 

[inocente]

The fact that scientific knowledge is provisional does not mean it is all wrong until we get it right, it simply means that we have some understanding, albeit incomplete, and are (hopefully) heading towards a more full and consistent understanding. Otherwise scientific knowledge is merely taking shots in the dark with no assurance that we are even close to the target. Is that what you mean by provisional? I hope not, but it won’t be the first time I’ve been made to scratch my head at one of your posts.

Admittedly, my puzzlement has been more along along the lines of you arguing, “If x, then y; therefore z.” Apparently, the provisional nature of knowledge implies (sort of) the provisional nature of logic, so, I guess, ANY conclusion is possible, if it is assumed that any conclusion is possible BECAUSE every conclusion is provisional.

I’m not sure what this has to do with the price of bread.

I am simply saying that science works by falsifying whereas logic works by proving, and it is a mistake to confuse the two.

It is a common mistake. It leads to false notions such as the universe as one big deterministic equation, or that reality is what we know and our laws dictate reality, or that all other forms of knowledge are merely handmaidens to science.

 

[Tomdstone]

I am simply saying that science works by falsifying whereas logic works by proving,…

An interesting comment, but is it an oversimplification? Science uses logic and observation. Logic needs something to work with in order to construct a syllogism, but if what your logical syllogism is working with is dubious, i.e. dubious premises, I don’t see how logic will get you anywhere.

 

[inocente]

Tomorrow, yes. However, what about 500 billion years from now? Will this physical law still hold then? Do physical laws hold at all times or do they differ from one point in time to another?

I wouldn’t say it’s a physical law that the Sun will rise tomorrow, as that’s not nearly general enough. Just after you read this, a fast moving object could hit the Earth and knock it completely off its orbit.

(Note to those of a nervous disposition: this is highly unlikely ).

But on your question, to me the most remarkable thing about the universe is it never breaks down. No matter what happens, even when galactic clusters collide, everything serenely continues. Nowhere do we see a rip in the fabric. So I don’t think the universe can be a machine, because machines break down. Whether that means the laws somehow evolved I don’t know.

 

[inocente]

An interesting comment, but is it an oversimplification? Science uses logic and observation. Logic needs something to work with in order to construct a syllogism, but if what your logical syllogism is working with is dubious, i.e. dubious premises, I don’t see how logic will get you anywhere.

No, I think the oversimplification is to confuse the two. There’s a difference between using logic to form a hypothesis, and using logic to test the hypothesis.

In science, empirical evidence, not logic, is the final arbiter. “It doesn’t matter how beautiful your theory is, it doesn’t matter how smart you are, if it doesn’t agree with experiment, it’s wrong”. (Richard Feynman)

 

[Peter_Plato]

I’m not sure what this has to do with the price of bread.

I am simply saying that science works by falsifying whereas logic works by proving, and it is a mistake to confuse the two.

It is a common mistake. It leads to false notions such as the universe as one big deterministic equation, or that reality is what we know and our laws dictate reality, or that all other forms of knowledge are merely handmaidens to science.

Funny, I thought science works by confirmation. Observation leads to hypothesis leads to experimenting to confirm the hypothesis by conclusion. The scientific method is a positive endeavor in that it leads to affirmations. If it was nothing but debunking false notions. science wouldn’t make progress in that no one would be making positive claims, only disproving them.

Again, your black OR white thinking shows its head. Only empirical OR rational, only about falsifying (science) or proving (logic,) but not both, right?

 

[Oreoracle]

OK. In your supposedly non-trivial system of 1+1=3, can you tell us what would be the commutator subgroup of the fundamental homotopy group of the Klein bottle. Further, what would be the homology groups of the complex projective plane or even just the n-sphere or torus? How do you define the betti numbers in your system? How do they relate to the Euler characteristic?

Firstly, my example is just an illustrative one. Obviously if a group in which 1+1=3 that has mildly interesting properties exists, then we could, with enough effort, construct one that’s more interesting. Secondly, there are many groups that don’t have interesting topological consequences. This doesn’t invalidate the study of those groups.

The question is not “can your group do what these groups can?” but rather “can your group do something more easily than other groups can?” For a non-group example, consider coordinate transformations. We could make polar coordinates look bad if we tried to use them to solve problems involving lines. But polar coordinates are meant for circles, not lines, so it’s not fair to compare them to Cartesian coordinates. Again, you have to appreciate the mathematical object in its own right.

 

[inocente]

Funny, I thought science works by confirmation. Observation leads to hypothesis leads to experimenting to confirm the hypothesis by conclusion. The scientific method is a positive endeavor in that it leads to affirmations. If it was nothing but debunking false notions. science wouldn’t make progress in that no one would be making positive claims, only disproving them.

No, that would be very sloppy. The experimenter would be led into ignoring data which disproves the hypothesis, and designing the experiment so that it couldn’t fail, while her colleagues wouldn’t critique the results for fear of being labeled negative.

The common approach is to try to disprove the null hypothesis, which is (to oversimplify) the opposite of the proposed hypothesis. For example, if your hypothesis was that the earth is flat, you would try to disprove the null hypothesis, which would be that the earth is spherical. The emphasis is on disproof.

*Again, your black OR white thinking shows its head. Only empirical OR rational, only about falsifying (science) or proving (logic,) but not both, right? *

The exact opposite. The religious zealot or idealist may crave certainty, but the rest of us realize that certainty is indicative of a closed mind.

“I can live with doubt and uncertainty and not knowing. I think it is much more interesting to live not knowing than to have answers that might be wrong. If we will only allow that, as we progress, we remain unsure, we will leave opportunities for alternatives. We will not become enthusiastic for the fact, the knowledge, the absolute truth of the day, but remain always uncertain … In order to make progress, one must leave the door to the unknown ajar.” - Feynman

 

[Tomdstone]

The common approach is to try to disprove the null hypothesis, which is (to oversimplify) the opposite of the proposed hypothesis. For example, if your hypothesis was that the earth is flat, you would try to disprove the null hypothesis, which would be that the earth is spherical. The emphasis is on disproof.

Do they try to disprove the null hypothesis or simply show that the probability of the null hypothesis being true is less than some preassigned small amount? In any case, the null hypothesis in this case, for the theist would be that God does not exist, but the null hypothesis for the atheist would be that God does exist? So the null hypothesis would depend on your point of view. Taking it from the atheist point of view, then the atheist might say that the null hypothesis that God exists is disproven by the existence of evil which contradicts the all loving, and all powerful nature of God. But the theist might say that the null hypothesis that God does not exist is contradicted by the fact that we and everything around us exists at all, or that logic exists which is mentioned in the OP? The null hypothesis is usually associated with sampling, and I am not sure that sampling is appropriate in this situation.

 

[inocente]

Do they try to disprove the null hypothesis or simply show that the probability of the null hypothesis being true is less than some preassigned small amount?

I think the terminology is that a hypothesis is considered disproved when the results are statistically significant, i.e. beyond the probability of chance alone or sampling error.

In any case, the null hypothesis in this case, for the theist would be that God does not exist, but the null hypothesis for the atheist would be that God does exist? So the null hypothesis would depend on your point of view. Taking it from the atheist point of view, then the atheist might say that the null hypothesis that God exists is disproven by the existence of evil which contradicts the all loving, and all powerful nature of God. But the theist might say that the null hypothesis that God does not exist is contradicted by the fact that we and everything around us exists at all, or that logic exists which is mentioned in the OP? The null hypothesis is usually associated with sampling, and I am not sure that sampling is appropriate in this situation.

Argument alone doesn’t cut it in science though, so neither hypothesis is scientific since it makes no predictions which can be tested by the presence or absence of empirical evidence.

Why there is evil can’t be tested because it is subjective. One person’s freedom fighter is another’s terrorist, and anyway God could be as Isaiah describes him - “I form the light and create darkness, I bring prosperity and create disaster; I, the Lord, do all these things” (45:7).

Why-something-rather-than-nothing can’t be tested because we can’t make test tube universes (well, not yet at least, maybe one day, who knows) or step outside the universe.

 

[Bahman]

I am simply saying that science works by falsifying whereas logic works by proving, and it is a mistake to confuse the two.

No that is not correct. Science by definition is a set of consistent methods, so called framework, which try to explain what we measure. It is possible that a framework fails to explain a new measurement meaning that there exist an anomaly within the framework which could be resolvable withing a new framework but this doesn’t mean that science works by falsifying.

It is a common mistake. It leads to false notions such as the universe as one big deterministic equation, or that reality is what we know and our laws dictate reality, or that all other forms of knowledge are merely handmaidens to science.

The duty of science is to explain what is measurable. It is a correct approach to know the reality if we accept that objective reality, what we observe, is the only door to reality.

 

[Tomdstone]

Why there is evil can’t be tested because it is subjective.

Do you think that there might be disagreement about whether or not it is a good thing for a young child to be suffering continuously and painfully from a crippling incurable disease that is eating away at him?

 

[polytropos]

1. Logic exists everywhere in the universe.
2. Logic is thought.
3. Thought only comes from a mind.
   Therefore, a mind created the universe.

Premise #2 could use some explanation, so I’ll add the following:
Logic, in its various forms (including mathematics) has been something we discover, not something invented by man. It is not matter or energy. It does not require any dimensions in order to exist, and can exist outside the universe. What else is left for it to be, except thought?

I do not think (1) is true. It would be false to say that the number 7 exists everywhere in the universe. There are a couple senses in which the number 7 could be said to exist, either as an intentional object (which exists in the mind of a thinker, not everywhere) or as an abstract object which is non-spacial and therefore not everywhere. (One might label such objects in this latter category as “universals.” But in this case, I don’t think it would be warranted to say that a universal exists everywhere in the sense required. And one would of course have to specify one’s theory of universals; most Thomists, for example, believe that we cognize abstract objects like 7 as intentional objects, but genuine universals like the form of a cat exist “in” the simple mind of God. God is omnipresent–but this fully fleshed out theory of universals requires that we already know God to exist, so the argument in those terms would be circular.)

I think (2) will not work either. You are likening logic to mathematics. But again, the number 7 is not thought. So why would logic be?

Another additional issue depends on what “logic” is. The propositional calculus? First-order predicate logic? Second-order predicate logic? Modal logic? What is the status of Brouwer’s axiom? Logic is objectively grounded, which is to say that the principle of non-contradiction is not violated, valid rules of inference preserve truth, etc. But logic is in other respects somewhat perpsectival. One chooses a system with some axioms that one needs. But when one doesn’t need them, using a weaker system is fine. Certain rules can be eliminated in favor of others, or vice versa, so that which ones we actually include is inessential. Mounting an argument like this is kind of tough because there are a lot of knotty issues.

Your argument is not valid, either. Even if logic is omnipresent and requires a mind, it wouldn’t be the case that the universe is created by God, for logic could be omnipresent without logic being all there is in the universe. It would leave the other parts of the universe unaccounted for.

Some idealist philosophers (ie. Berkeley) have made arguments somewhat suggestive of this, in taking all objects to be ideas. If I see a tree, then the tree-image is an idea that I am aware of. When I look away, there is no tree-image. So perhaps one could say that the tree doesn’t exist. This is a rather counterintuitive result, opposing all of the inductive evidence we have that the world persists apart from our perceiving of it. So one might believe that there is a Great Thinker who perceives all of the ideas (ie. tree-imagers) while we aren’t looking at them. (This faces a number of issues, though. On top of the problems with idealism in general, it does not show God’s uniqueness. Also if things are ideas/perceptions, then there seems to be little reason for your perception of a tree and my perception of a tree to be the same perception. But likewise there seems to be little reason to think that your perception of the tree is the same as God’s perception of the tree, given idealism. So the original problem doesn’t seem to be solved.)

 

[inocente]

Do you think that there might be disagreement about whether or not it is a good thing for a young child to be suffering continuously and painfully from a crippling incurable disease that is eating away at him?

That would be perverse, but people argue all the time over which is the greater evil. Start a thread and you’ll find some who argue that his death should be assisted to stop his suffering and others who argue it shouldn’t because it is categorically wrong to kill innocents.

For evil to be objective there would need to be an absolute scale by which it can be measured. Is Hitler more or less evil than Stalin? Again, people disagree.

 

[inocente]

No that is not correct. Science by definition is a set of consistent methods, so called framework, which try to explain what we measure. It is possible that a framework fails to explain a new measurement meaning that there exist an anomaly within the framework which could be resolvable withing a new framework but this doesn’t mean that science works by falsifying.

I don’t really understand your point. I’m simply saying that there’s a world of difference between a logical proof and what science does. Otherwise no scientist would ever get her hands dirty with experiments, everything could be proved on paper. Take away experiment and there would be no difference between science and armchair philosophy.

The duty of science is to explain what is measurable. It is a correct approach to know the reality if we accept that objective reality, what we observe, is the only door to reality.

I’m a big fan of a line in the General Scholium, which I think is the moment when modern science is born, where Newton refuses pointblank to play Descartes’ game of wanting to explain absolutely everything measurable at the expense of experiment:

“I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not frame hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy.”

(Where “hypothesis” doesn’t mean quite what it does today of course.)

 

[Tomdstone]

For evil to be objective there would need to be an absolute scale by which it can be measured.

I don’t see that. Why is there a need for an absolute scale? Alzheimer’s disease is objectively present in many people to a greater or lesser degree, but AFAIK there is no absolute scale to measure its progress.