What kind of physical impossibilities can God create?

[Prodigal_Son]

You are being tiersome to me because you have not studied physics.

I don’t need to study physics to know that A=A. However, let us consider, for the sake of argument, your statement to be correct.

Assumed:

(x) ¬(A=A) (It is not the case that A=A)
Consequence: ¬(x=x)

This could be translated: The statement that the law of noncontradiction is wrong* is not equivalent to itself*. But if it is not equivalent to itself, then how can it be stated unambiguously? Denying the law of noncontradiction makes all language and science meaningless.

Here is the key, then: The laws of logic must be predicated in order to understand anything. Perhaps they are wrong and we cannot understand anything. But, in that case, science is just another one of the things we cannot understand.

The way that the physicist looks at electromagentic waves you know everything from the math. The math came about as the creative effort by physicists to describe their real observational experiences. The logic of the whole thing works very well. The logical theory conforms to the reality of observation bettter than the logic of any other science.

But how can they trust the math if they’re not sure if 5 is 5, at any given moment? Or are you suggesting that the law of noncontradiction applies in some cases but not all? If so, what are those cases?

Logic is not reality, its only language.

Can you explain to me how we can get at reality without language?

 

[Langdell]

Can you explain to me how we can get at reality without language?

The fact that language (and logic and math) enable us to get at reality does not mean that they are reality.

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[Prodigal_Son]

The fact that language (and logic and math) enable us to get at reality does not mean that they are reality.
.

I agree. However, there are two possible things being said there.

1. “Language is not reality” means “language cannot pertain to reality”. This commits us to complete skepticism.
2. “Language is not reality” means that “there is much more to reality than language”. This is what I take you to mean, and this is indisputably correct.

 

[geometer]

I don’t need to study physics to know that A=A.
Here is the key, then: The laws of logic must be predicated in order to understand anything. Perhaps they are wrong and we cannot understand anything. But, in that case, science is just another one of the things we cannot understand.

But how can they trust the math if they’re not sure if 5 is 5, at any given moment? Or are you suggesting that the law of noncontradiction applies in some cases but not all? If so, what are those cases?

Can you explain to me how we can get at reality without language?

Study paraconsistant logics. I am sure that will open a whole new world of conjecture for you.

Water has more than twenty observed physical properties. We know water is water by the observations of these properties. This is the reality of water. But there is no verifed logical theoretical description that explains these observations of the reality of water.

We have partial logics which explain some of the properties of water, but these can not explain all the rest of the properties.

Observation is primary knowledge of reality. All descriptions of reality and the rules for making those descriptions are after thoughts about the reality that we observe. They are not primary knowledge of reality. Logic does not make the reality. The primary knowledge of reality which comes from our observations is the only reality that we have.

We know for instance that a system of gates which in the general sense is based on classical deductive logic (boolean) will never be able to perform all of the tasks of pattern recognition that human vision accomplishes. These high level tasks of pattern recognition can be efficiently accomplished by highly interconnected feedback networks.

And the reality today is that we know that connection machines are able to do many recogniton tasks. Because this is what we can easily observe in the performance of connection machines.

There is no general logical theory that accounts for what they do. Classical logic is not expected to reveal anything about the reality of the processes within connection machines. Connection machines are well beyond the limits of classical logic.

What I try to say is that the world has moved well beyond classical logic. Classical logic is understandable, but understanding classical logic is not the same as understanding reality.

 

[Prodigal_Son]

Study paraconsistant logics. I am sure that will open a whole new world of conjecture for you.

I just did some reading on this, and it is indeed interesting. It seems to me largely pragmatic, however. The idea is this: classical logic says that from a contradiction, *any *conclusion is valid. That is, A & ¬A can be used to justify B.

But there are situations where we cannot falsify either A or not A, and yet we want to draw some conclusion which cannot be drawn by rejecting either. From the statement that we cannot discard either A or not-A and derive the desired conclusion, however, it does not follow that both A and not-A are true. They are both useful, but they are not both true.

We have partial logics which explain some of the properties of water, but these can not explain all the rest of the properties.

OK, but how is this supposed to convince me that something can both be and not be water? Why assume that there is a genuine contradiction involved? Why not just assume that we don’t yet know the truth of the matter?

Logic does not make the reality.

Agreed.

The primary knowledge of reality which comes from our observations is the only reality that we have.

And yet 2+2=4 is still true, whether or not it can be observed. Math and logic are contained within reality, and not simply as human creations.

What I try to say is that the world has moved well beyond classical logic. Classical logic is understandable, but understanding classical logic is not the same as understanding reality.

It is one building block to understanding reality. Without certain premises contained within classical logic, no understanding is possible.

Let’s go back to the light example. You have said that “light is a particle (P) and light is a wave (Q).” This does not defy noncontradiction. What you need to prove is that “light is a particle” (P) and “light is not a particle” (not-P).

Is it just a dogma of physics that something cannot be a particle and wave? What reasons do we have to believe this dogma?

Gee, Spock, I’m sorry. Looks like Geometer and I have started another thread.

 

[Langdell]

And yet 2+2=4 is still true, whether or not it can be observed. Math and logic are contained within reality, and not simply as human creations.

This is exactly the issue that What Is Mathematics, Really? deals with. I would highly recommmend that you try to get a copy. Juding from your writing here, I think you’d find it extremely interesting.

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[WinterWH]

You are being tiersome to me because you have not studied physics.

There is a wonderful study called electrodynamic physics which has two forms the classical study, and quantum electrodynamic physics, the modern form.

According to the classical theory light is simply a class of electromagnetic waves that propagate isotropically, along straight lines.

I believe the quantum electrodynamic theory covers photon progagations. I haven’t taken that course.

As electromagnetic waves electromagnetism is completely described by two variables an electric and a magnetic one.

The way that the physicist looks at electromagentic waves you know everything from the math. The math came about as the creative effort by physicists to describe their real observational experiences. The logic of the whole thing works very well. The logical theory conforms to the reality of observation bettter than the logic of any other science.

Science is always observing, and even in this field there are anomalies which the logic does not resolve. Because like anyone knows who studies physics and logic, the physics is the reality that you try to describe with the logic, not the other way around.

Logic is not reality, its only language.

Have you read about the incompleteness theorem? And, Whitehead’s finding that there is no universal set of axioms?

I think you take your axioms too seriously. Take a walk on the wild side, pray for a miracle or two…

Of possible interest related to electrodynamic theory:

home.comcast.net/~adring/

 

[Deacon_Ed_B]

Do you believe something as complex as the Trident Submarine, with over 1 billion parts could just happen out of nothing or would it have to be made?

Does no one care to discuss this post, #39 with me. A natural expansion, by human logic, leads me to the inevitable conclusion of God. Any takers?

 

[tonyrey]

Does no one care to discuss this post, #39 with me. A natural expansion, by human logic, leads me to the inevitable conclusion of God. Any takers?

I believe it would have to be made **out of nothing **by the Creator. If matter already existed it could be made by an immensely intelligent and powerful Being.

 

[WinterWH]

I just did some reading on this, and it is indeed interesting. It seems to me largely pragmatic, however. The idea is this: classical logic says that from a contradiction, *any *conclusion is valid. That is, A & ¬A can be used to justify B.

But there are situations where we cannot falsify either A or not A, and yet we want to draw some conclusion which cannot be drawn by rejecting either. From the statement that we cannot discard either A or not-A and derive the desired conclusion, however, it does not follow that both A and not-A are true. They are both useful, but they are not both true.

OK, but how is this supposed to convince me that something can both be and not be water? Why assume that there is a genuine contradiction involved? Why not just assume that we don’t yet know the truth of the matter?

Agreed.

And yet 2+2=4 is still true, whether or not it can be observed. Math and logic are contained within reality, and not simply as human creations.

It is one building block to understanding reality. Without certain premises contained within classical logic, no understanding is possible.

Let’s go back to the light example. You have said that “light is a particle (P) and light is a wave (Q).” This does not defy noncontradiction. What you need to prove is that “light is a particle” (P) and “light is not a particle” (not-P).

Is it just a dogma of physics that something cannot be a particle and wave? What reasons do we have to believe this dogma?

Gee, Spock, I’m sorry. Looks like Geometer and I have started another thread.

… particle … wave … 2 … + … 2 … = … 4 …

humans are merely struggling to attempt to describe what is going on around them. not really sure. particle … vs… wave … maybe yes, maybe no, could be this, could be that, maybe not, i don’t know … what should I do to explain … sounds like comedian jackie mason’s routine.

we just don’t know.

i heard fr. groeschel say we don’t understand and can’t explain gravity.

it’s almost saturday. less calories or less filling.

 

[Prodigal_Son]

This is exactly the issue that What Is Mathematics, Really? deals with. I would highly recommmend that you try to get a copy. Juding from your writing here, I think you’d find it extremely interesting.

.

I’ve read the first chapter or so, and I do find the thesis very interesting. He suggests, in essence, that mathematics is a cultural object, and its truths are culturally defined truths. This could certainly be true, but so far I find Hersh’s arguments seem woefully inadequate. He assumes that something being a culturally constructed object excludes the possibility of its being another kind of object as well.

Consider: It is indisputable that theories of literature are culturally constructed, that they change over time and are influenced by the prevailing cultures. Does this mean that no theory of literature can make any statement of truth? Or, better yet, history: historians come up with various theories and interpretations of the past, which seek to explain *why *past events happened. These theories are subject to the historian’s culture and community, and so they are very much culturally constructed objects.

But does that mean that there is no *actual *object – no real historical event? Of course not. The goal of classical education is to align the culturally constructed object (the belief) with the actual object (the reality). It is a trend in modern education to claim that there is no actual object – this trend may be broadly termed postmodernism. If I follow Hersh’s argument so far, it is a postmodern theory of mathematics.

My own take: numbers are cultural objects, but they are not *only *cultural objects. *How *are they more than cultural objects? The theist can answer that they exist within the mind of God. This is, I admit, an awfully simple answer. But it must not be a dogma of philosophy that simple things cannot, nevertheless, be true.

Thanks for the book recommendation!

 

[Contarini]

Edwin – Is the orthodox Christian position that logic was created by God or was not created by God?

The latter. Logic is an expression of God’s nature.

If it’s the latter, would you be able to point me to any authority?

Well, to most Christians historically the fact has seemed so obvious that it’s not easy to find a succinct place where this is stated. Even the nominalists, who thought that God created *moral *laws and could perhaps have created them differently, didn’t think that God could do things that involved contradiction. The neo-orthodox theologians come closest to saying that logic is created by God, although I think that’s probably a simplistic misreading of their position. (They insist that we cannot know God by “human” logic.) Their position derives from Kierkegaard to a great extent. But Kierkegaard is clearly going against the mainstream of Christian tradition in this respect and knew himself to be so doing.

I’m not trying to be evasive, but the position is assumed by Christian theologians more than it’s explicitly stated. The best single example I can give is, I think, Aquinas’s discussion of God’s power (Summa Theologiae Part 1, Question 25, Article 3), where he defines God’s omnipotence as applying to everything that “does not imply a contradiction in terms.” In other words, the laws of logic are presupposed as the parameters within which God’s power operates. To understand Aquinas’s position more fully, you’d need to read at least his discussion of God’s immutability (Question 9), Knowledge (14), truth (16), and the eternal law (The First Part of the Second Part, Question 93). I use the Summa because it’s so easily accessible online and so central a text in the Christian intellectual tradition.

Among contemporary conservative/fundamental Protestants on the Internet, you find the same classical assumption for the most part, so I’m not quite sure where you and many other online atheists are getting the idea that Christians think the laws of logic are created. Perhaps you could enlighten me on this point?

One interesting example of fundamentalist adherence to the traditional view is the discussion of natural law at Answersingenesis.They do speak of the “laws of nature” being the result of God’s will, but if you look at what they say about the laws of mathematics and logic you find them affirming very clearly that *these *laws are reflections of God’s nature and could not be otherwise (in contrast, they argue, to the laws of physics). This isn’t a particularly profound or sophisticated discussion of the subject, but you find the same basic view upheld as in Aquinas.

Edwin

 

[Contarini]

It wouldn’t surprise me if Christians before the later 19th century held logic to be uncreated, because that was before the invention (or discovery, if you prefer) of non-Euclidean geometry. Before then, most (all?) people thought logic and math were universal and unchanging “things” that simply had to obtain. But then mathematicians showed that geometries and logics other than the classic Euclidean and Aristotelian flavors could work. And then, in the 20th century, astronomers and others found that non-Euclidean geometry actually explained some phenomena better than Euclidean geometry did.

Nowadays, it’s much more plausible to see logic, geometry, and math as things that could be created and in fact probably were created (though I suspect that many thinkers would ascribe the creation to humans rather than God).

I’d be interested in knowing if any modern theologians have addressed this issue.

Barth would be an excellent example, I think. His affirmation of God’s utter transcendence and of the folly of attempting to extrapolate from our logic to God’s nature is in part a reflection of these cultural developments. (I find myself in a lot of tension these days between Barth and Aquinas. I’m still basically loyal to Aquinas but I find Barth’s position challenging and thought-provoking.)

I wonder if we are not speaking at cross purposes here. Does non-Euclidean logic violate the law of non-contradiction? I am not well-versed in the complex subject of modern philosophical logic, but I didn’t think that the eternal validity of basic logical principles such as non-contradiction was at stake. Am I wrong?

Edwin

 

[Prodigal_Son]

Logic is an expression of God’s nature.

I have never heard it put that way. But others will hear me put it that way in the future.

 

[geometer]

I have never heard it put that way. But others will hear me put it that way in the future.

Logic is a perfect case of highly specialized language, and like anything that is highly specialized it simply can not apply to everything.

Classical logic is bivalent. It demands that results be true or false. There are other logics.

Someone provided a link to a video that showed the traditional problem with this absurd insistence on bivalent truth.

Two philosophers observe squirels in a tree. Over time they see that one by one a squirel runs down the tree, then runs around the tree, then runs back up the tree.

So they both try to give their oppinion about squirels, that circumambulate trees. But they immediately enter into a disagreement.

One philosopher believes that when one of the squirels circumambulates the tree, he has circumambulated the tree, only.

The other philosopher believes that when the squirel has circumambulated the tree, he has also circumambulated the other squirels in the tree.

They never come to agreement, so they develop two philosophies, concerning squirels who circumabulate trees…

 

[Contarini]

Logic is a perfect case of highly specialized language, and like anything that is highly specialized it simply can not apply to everything

We may be speaking past each other. I don’t know the specialized language of technical logic very well, although I doubt that it’s really true that it doesn’t apply to everything (I presume that it’s simply a more precise and complex way of saying what the rest of us say in simpler and vaguer terms). But to stick to what I do know:

To what does the law of non-contradiction not apply?

And by the way, absolutely nothing about your example contradicts “bivalent truth.” There may be several ways of describing something without the same thing being both true and false.

Edwin

 

[Image_of_God]

The latter. Logic is an expression of God’s nature.

Well, to most Christians historically the fact has seemed so obvious that it’s not easy to find a succinct place where this is stated. Even the nominalists, who thought that God created *moral *laws and could perhaps have created them differently, didn’t think that God could do things that involved contradiction. The neo-orthodox theologians come closest to saying that logic is created by God, although I think that’s probably a simplistic misreading of their position. (They insist that we cannot know God by “human” logic.) Their position derives from Kierkegaard to a great extent. But Kierkegaard is clearly going against the mainstream of Christian tradition in this respect and knew himself to be so doing.

I’m not trying to be evasive, but the position is assumed by Christian theologians more than it’s explicitly stated. The best single example I can give is, I think, Aquinas’s discussion of God’s power (Summa Theologiae Part 1, Question 25, Article 3), where he defines God’s omnipotence as applying to everything that “does not imply a contradiction in terms.” In other words, the laws of logic are presupposed as the parameters within which God’s power operates. To understand Aquinas’s position more fully, you’d need to read at least his discussion of God’s immutability (Question 9), Knowledge (14), truth (16), and the eternal law (The First Part of the Second Part, Question 93). I use the Summa because it’s so easily accessible online and so central a text in the Christian intellectual tradition.

Among contemporary conservative/fundamental Protestants on the Internet, you find the same classical assumption for the most part, so I’m not quite sure where you and many other online atheists are getting the idea that Christians think the laws of logic are created. Perhaps you could enlighten me on this point?

One interesting example of fundamentalist adherence to the traditional view is the discussion of natural law at Answersingenesis.They do speak of the “laws of nature” being the result of God’s will, but if you look at what they say about the laws of mathematics and logic you find them affirming very clearly that *these *laws are reflections of God’s nature and could not be otherwise (in contrast, they argue, to the laws of physics). This isn’t a particularly profound or sophisticated discussion of the subject, but you find the same basic view upheld as in Aquinas.

Edwin

You speak high and complex truths, with such clarity and simplicity. You surely have been given a gift.

 

[geometer]

We may be speaking past each other. I don’t know the specialized language of technical logic very well, although I doubt that it’s really true that it doesn’t apply to everything (I presume that it’s simply a more precise and complex way of saying what the rest of us say in simpler and vaguer terms). But to stick to what I do know:

To what does the law of non-contradiction not apply?

Set theory. The logic of set theory follows a set of axioms, and it all works very nicely. People who study set theory come to believe that they really do understand useful things about sets.

However, a very basic question which can be asked about sets, does not seem to have an answer.

Does the set of all sets contain a copy of itself?

If it does not contain a copy of itself, it is not the set of all sets.

If it does contain a copy of itself, it has become a new set, which does not contain a copy of itself.

 

[Langdell]

I’ve read the first chapter or so, and I do find the thesis very interesting. He suggests, in essence, that mathematics is a cultural object, and its truths are culturally defined truths. This could certainly be true, but so far I find Hersh’s arguments seem woefully inadequate. He assumes that something being a culturally constructed object excludes the possibility of its being another kind of object as well.

Consider: It is indisputable that theories of literature are culturally constructed, that they change over time and are influenced by the prevailing cultures. Does this mean that no theory of literature can make any statement of truth? Or, better yet, history: historians come up with various theories and interpretations of the past, which seek to explain *why *past events happened. These theories are subject to the historian’s culture and community, and so they are very much culturally constructed objects.

But does that mean that there is no *actual *object – no real historical event? Of course not. The goal of classical education is to align the culturally constructed object (the belief) with the actual object (the reality). It is a trend in modern education to claim that there is no actual object – this trend may be broadly termed postmodernism. If I follow Hersh’s argument so far, it is a postmodern theory of mathematics.

My own take: numbers are cultural objects, but they are not *only *cultural objects. *How *are they more than cultural objects? The theist can answer that they exist within the mind of God. This is, I admit, an awfully simple answer. But it must not be a dogma of philosophy that simple things cannot, nevertheless, be true.

Thanks for the book recommendation!

I’m very glad you find it interesting. The first few chapters were, for me, the most enjoyable.

The question of whether, and how closely, math presents a true picture of reality seems to be of great significance to philosophy of science. As you point out, even if math is man-made, that doesn’t mean it can’t reflect some deeper reality in the universe.

My own tentative view is that God gave us the ability to devise math and logic, and possibly also nudged us along the way to devise them so that we could better understand His creation. However, I am reluctant to associate God too closely with math and logic (of any sort), because I think it paints us into the corner of needing to defend this or that mathematical or logical approach as an aspect of our faith. It strikes me as similar to the problem creationists face, in refusing to accept the weight of evidence for evolution because they have linked the literal truth of Genesis to the existence of God.

.

 

[geometer]

It strikes me as similar to the problem creationists face, in refusing to accept the weight of evidence for evolution because they have linked the literal truth of Genesis to the existence of God.

.

Some of us on this earth have real evidence that God creates, because some of us have been recreated by God. Jesus called everyone to this very same experience, of being sent.

So, I believe that I have evidence, that I was recreated, in that I do exist, and when I was taken up from the earth, I failed to exist.

You will find that evolution has very weak support from the hard sciences, and itself is not a hard science because of this.

Creationism needs to be directly observed, as evolution should be directly observed.

Now which one do you think you will directly observe first?