I am pretty surprised by the claim here that mathematics is created, rather than another one of those things that God is, in the transcendent sort of way that God can be said to be.
Could God have decided that 2 + 2 = 5? To me, that seems at least as incomprehensible as saying that God could have decided that cruelty was good.
That last comment was getting long, but I also wanted to address your idea that mathematics could be understood as one of those things that God just is. Now, I agree with this, at least to an extent. But I won't be getting to this idea until Part 3!
I definitely don't think that God could ever make 2+2=5. Likewise, God couldn't make a square circle—not because God isn't omnipotent, but rather because "square circle" is a meaningless phrase. I think the same is true of 2+2=5. But that doesn't mean that squareness or circleness are somehow ultimate or absolute metaphysical realities. (Of course, plenty of people might disagree here—certainly, I think the Pythagoreans would have.)
But notice that there is a logical sort of necessity to all kinds of expressions. For example, I cannot be both above and below the water. Either state is mutually exclusive to the other. But it would be odd, I think, to conclude from this that water, or "aboveness", or "belowness", or me myself, are somehow metaphysical necessities, just because this statement about me and my relationship to water is logically necessary.
2+2=4, and always must, not because 2, or 4, or "plus" are somehow metaphysically fundamental realities, but because the number 4 literally just *is* 2 added to itself once. That is what the terms mean. The equation is really more of an analytical statement, rather than some kind of true discovery. In this sense, mathematical expressions never tell us any new information, they simply express the same information in new ways. (One could more flippantly argue that they are really just tautologies, though I think that'd be going too far.) Of course, just because math may not be telling us new information in a strict, ultimate sense doesn't mean that it's not useful(!) Of course, math is super useful to us in all kinds of tasks. But this practical truth doesn't necessarily translate to a metaphysical one.
It's worth noting that philosophers have had a lot to say about this, and that indeed plenty of philosophers of math think that you can reduce all of mathematics to the terms one and zero, which are really abstract references to being and nonbeing. (I do know there are mathematicians who argue you also need the term infinity, but I share Hegel's suspicion of this conception of infinity.) Every other mathematical expression basically just relates these terms to themselves in new and subtle ways.
But this will rapidly draw us into a deeper discussion of the philosophy of mathematics, a field of which I have next to know useful knowledge. But as I mentioned in a comment above, there are all kinds of provocative perspectives on math. E.g., mathematical non-realism argues that mathematical terms are really only signs within human thought, and have no independent reality. If such a view is true, then of course any anxiety about the metaphysics of mathematics would probably disappear.
I am neither a mathematician not a philosopher so my thoughts might be underdeveloped, but if we accept, for example, that all mathematical statements and objects are just analytical statements and analytical objects relating 1 and 0 to themselves and each other, and 1 and 0 are really just abstract representations of being and non-being, then all mathematical truths are analytically equivalent to being itself, or the distinction between being and non-being.
That seems to be quite a different mode of existence than mine. A world without me is easy to imagine, and has existed before, and will exist again. A world without analytic truths about being seems much harder to imagine. Rather, analytic truths about being seem like they would be entailed in the possibility of being to begin with. Certainly Being is an accepted name of God, at least in the Christian tradition.
Maybe I've tricked myself by shuffling words here, but I have a very hard time thinking of mathematical truths and mathematical objects as anything less fundamental than the possibility of being and finite thought.
I think I am inclined to actually agree with both your first and third paragraphs above. It seems to me that you see them as mutually exclusive, but I don't think I do. That is to say: I think it may indeed be the case that, if being and consciousness exist (or at least if they exist more or less in the way we know them in this cosmos) then their existence will entail the mathematical truths we know. But I think this is actually precisely because those truths are really just a way of talking about being itself, and its relationship to non-being, abstractly and formally. But perhaps I have misunderstood one of your points?
As for God and Being: while it is true that many Christian theologians and philosophers would be comfortable saying that "God is Being" (or "God is being-itself"), I would want to interrogate this. I could agree with God's identity with being, but only *asymmetrically*. But I think that it is more accurate to say that God is *beyond* Being. (more on this in part 3!)
I intended for my first and third paragraphs to be equivalent: if mathematical truths are analytic statements about being and non-being, then they are at least as fundamental as the possibility of the kind of being and non-being they analyze.
And I think that is why I was surprised at the use of the word "create" to describe them. I tend to think the word "create" applies to the realm of empirical facts, rather than the (in my opinion) more fundamental realm of logical facts, and logical facts are "emanations" or some other word for a necessary expression of God's nature as ultimate Reality.
That's an interesting distinction. My guess is that different philosophers would come down differently on this issue. My own view is a more radical position vis-a-vis the creaturely/Creator relation, in which everything other than God Godself must be understood as in an asymmetrical relation with that absolute Whence which is beyond both being and consciousness. As I have said above, I plan to say more about this in Part 3.
Thanks so much for these comments; you've helped me hone my own views. I hope the conversation has been of benefit to you as well!
I am pretty surprised by the claim here that mathematics is created, rather than another one of those things that God is, in the transcendent sort of way that God can be said to be.
Could God have decided that 2 + 2 = 5? To me, that seems at least as incomprehensible as saying that God could have decided that cruelty was good.
That last comment was getting long, but I also wanted to address your idea that mathematics could be understood as one of those things that God just is. Now, I agree with this, at least to an extent. But I won't be getting to this idea until Part 3!
I definitely don't think that God could ever make 2+2=5. Likewise, God couldn't make a square circle—not because God isn't omnipotent, but rather because "square circle" is a meaningless phrase. I think the same is true of 2+2=5. But that doesn't mean that squareness or circleness are somehow ultimate or absolute metaphysical realities. (Of course, plenty of people might disagree here—certainly, I think the Pythagoreans would have.)
But notice that there is a logical sort of necessity to all kinds of expressions. For example, I cannot be both above and below the water. Either state is mutually exclusive to the other. But it would be odd, I think, to conclude from this that water, or "aboveness", or "belowness", or me myself, are somehow metaphysical necessities, just because this statement about me and my relationship to water is logically necessary.
2+2=4, and always must, not because 2, or 4, or "plus" are somehow metaphysically fundamental realities, but because the number 4 literally just *is* 2 added to itself once. That is what the terms mean. The equation is really more of an analytical statement, rather than some kind of true discovery. In this sense, mathematical expressions never tell us any new information, they simply express the same information in new ways. (One could more flippantly argue that they are really just tautologies, though I think that'd be going too far.) Of course, just because math may not be telling us new information in a strict, ultimate sense doesn't mean that it's not useful(!) Of course, math is super useful to us in all kinds of tasks. But this practical truth doesn't necessarily translate to a metaphysical one.
It's worth noting that philosophers have had a lot to say about this, and that indeed plenty of philosophers of math think that you can reduce all of mathematics to the terms one and zero, which are really abstract references to being and nonbeing. (I do know there are mathematicians who argue you also need the term infinity, but I share Hegel's suspicion of this conception of infinity.) Every other mathematical expression basically just relates these terms to themselves in new and subtle ways.
But this will rapidly draw us into a deeper discussion of the philosophy of mathematics, a field of which I have next to know useful knowledge. But as I mentioned in a comment above, there are all kinds of provocative perspectives on math. E.g., mathematical non-realism argues that mathematical terms are really only signs within human thought, and have no independent reality. If such a view is true, then of course any anxiety about the metaphysics of mathematics would probably disappear.
I am neither a mathematician not a philosopher so my thoughts might be underdeveloped, but if we accept, for example, that all mathematical statements and objects are just analytical statements and analytical objects relating 1 and 0 to themselves and each other, and 1 and 0 are really just abstract representations of being and non-being, then all mathematical truths are analytically equivalent to being itself, or the distinction between being and non-being.
That seems to be quite a different mode of existence than mine. A world without me is easy to imagine, and has existed before, and will exist again. A world without analytic truths about being seems much harder to imagine. Rather, analytic truths about being seem like they would be entailed in the possibility of being to begin with. Certainly Being is an accepted name of God, at least in the Christian tradition.
Maybe I've tricked myself by shuffling words here, but I have a very hard time thinking of mathematical truths and mathematical objects as anything less fundamental than the possibility of being and finite thought.
I think I am inclined to actually agree with both your first and third paragraphs above. It seems to me that you see them as mutually exclusive, but I don't think I do. That is to say: I think it may indeed be the case that, if being and consciousness exist (or at least if they exist more or less in the way we know them in this cosmos) then their existence will entail the mathematical truths we know. But I think this is actually precisely because those truths are really just a way of talking about being itself, and its relationship to non-being, abstractly and formally. But perhaps I have misunderstood one of your points?
As for God and Being: while it is true that many Christian theologians and philosophers would be comfortable saying that "God is Being" (or "God is being-itself"), I would want to interrogate this. I could agree with God's identity with being, but only *asymmetrically*. But I think that it is more accurate to say that God is *beyond* Being. (more on this in part 3!)
I intended for my first and third paragraphs to be equivalent: if mathematical truths are analytic statements about being and non-being, then they are at least as fundamental as the possibility of the kind of being and non-being they analyze.
And I think that is why I was surprised at the use of the word "create" to describe them. I tend to think the word "create" applies to the realm of empirical facts, rather than the (in my opinion) more fundamental realm of logical facts, and logical facts are "emanations" or some other word for a necessary expression of God's nature as ultimate Reality.
That's an interesting distinction. My guess is that different philosophers would come down differently on this issue. My own view is a more radical position vis-a-vis the creaturely/Creator relation, in which everything other than God Godself must be understood as in an asymmetrical relation with that absolute Whence which is beyond both being and consciousness. As I have said above, I plan to say more about this in Part 3.
Thanks so much for these comments; you've helped me hone my own views. I hope the conversation has been of benefit to you as well!
Yes, I look forward to future entries in the series, particularly the oft-foretold part 3.
Looking forward to reading more 🌟