Know Your Tools (and Their Limitations)
I noticed an interesting series of video interviews conducted by John Dehlin over at Mormon Stories about the psychology of religion with a man named Dr. James Nagel and felt obliged to throw in my $0.02. Sparks flew for a bit but it was all in good fun. I didn’t really disagree with a lot that was in the videos, but what I objected to was the implicit assertion that showing that there are psychological principles at work in religion somehow proves religion to be false. This is one of the first issues I dealt with at this blog, mostly because it’s an issue that comes up quite a bit when we talk about the psychology of religion.
Now I’ll be the first to admit that knowing these principles should at least cause people to think about the reasons why they do things, particularly the reasons why they are in the religion they are in. On the other hand, I have mentioned before that psychology is not equipped to judge truth claims about religions due to its methods and assumptions.
Psychology is a science. This means that it has inherited a certain epistemology, metaphysics, and method from the “hard sciences” and sticks with that. For instance, science as a whole is based on methodological naturalism – the belief that the natural world is all there is. So psychology could never really answer a question like, “Is there a soul?” because it already operates based on an a priori assumption that there isn’t. Perhaps you might ask, “How do we know naturalism is true?” This is a good question, but you couldn’t use current science to answer that question because science presupposes naturalism. You can’t use a yardstick to measure itself for accuracy. You need to turn to philosophy if you want to pick a new metaphysics to use. Maybe one day science will embrace a different metaphysics – I happen to be partial to Aristotelian formal and final causality myself. However, until that day, science will wear naturalistic goggles to view the world.
I actually don’t think that’s necessarily bad, as long as psychology makes more modest claims. For instance, if someone asks a psychologist whether prayer “works,” the psychologist could tell them how prayer makes a person feel, why people pray, what kinds of effects different prayers can have on mood, how people with different personalities pray, whether prayer reduces or increases anxiety or depression, etc. But psychology cannot say whether or not prayers actually reach the ears of a God or gods and whether that God or gods chooses to send down powers to heal a person. Knowing that the social aspect of going to church causes people to be healthier, and that sometimes the black and white thinking of religion can cause people to become extremists, doesn’t really say anything about whether God actually exists or not. That’s completely outside of the realm of science. Religions say that God created all of reality, which includes psychology, so presumably he could and would use psychology to help direct people to him and create social networks among his children. Or perhaps he didn’t and doesn’t exist. The point is, those are philosophical and theological questions, not scientific questions.
So if a person has a yardstick, and they are asked to measure how much something weighs, their only honest answer is to say, “I do not have the right tools to make that judgement. If you want to know how long something is – I’m all over that. But a yardstick is simply useless when it comes to weight. Go find a person with a scale.” Similarly, if psychology is equipped to only make quantifiable claims about material objects, then they need to refrain from trying to use that methodology in the realm of philosophy, ontology, metaphysics, etc. Certainly psychology has something to say to those disciplines but philosophers are a lot better at making claims about philosophical truths than psychologists.
This is why I don’t think that the psychology of religion “disproves” religion anymore than it “proves” religion. I think it sheds light on many quantifiable aspects of religious belief and behavior, and develops theories as to why that is. But that’s it.
http://valueofsaintliness.wordpress.com/2012/05/05/know-your-tools-and-their-limitations/#respond
“philosophers are a lot better at making claims about philosophical truths than psychologists.”
To my way of thinking a more accurate statement would be: philosophers are a lot better at making philosophical claims than psychologists.
It’s similar to avoiding the error of saying that science ‘proves’ or ‘has proven’ this or that.
I think it is more accurate to say that science ‘demonstrates’ or ‘has demonstrated’ that this or that ‘claim’ has valid merit (from a human being’s perspective).
Someone may say that I am being too semantically rigid because science has most definitely PROVEN that the earth is a round sphere and not a flat disk like most people used to claim.
I would still rather think in terms that science hasn’t proven or disproven anything, even that the earth is a sphere because the earth is what it is notwithstanding what science or religion or philosophy affirms. All that science has done is demonstrate what appears to be what a sphere and not a flat disk from a normal, regular, mortal human perspective. “What?!” you say, “That’s shooting way beyond the mark.”
Well, I am not ‘absolutely’ positive that the earth is a spherical rock ‘floating’ in ‘empty space’ in the sense that this IS the absolute TRUTH. When I die, I no longer will be a ‘mortal human being’ or anything what I ‘appear’ to be now. But let’s assume that there is life after life. What will I be, then, and where will I be — on a spherical rock floating in empty space? Maybe when I am in that state I will ‘see’ or ‘perceive’ the earth that I lived ‘on’ in a totally different way, and not just the earth, but even ‘time’ or ‘space time’ as well. Maybe in that dimension (a higher one?) the earth and empty space, up and down, solid matter, energy, light, etc, is altogether a lot different than what we ever could have imagined let alone still affirm that we had at one time ‘proven’ something to be ‘true’.
This is why I retain the rational belief that many aspects of religion (NOT all) are just as valid as many aspects of science (NOT all). We are mere mortal, ephemeral, presumably sentient beings made of crude matter with limited perceptual capacities. But I think there is a lot more ‘out there’ and about us than what we currently know, or think we (science) have ‘proven’.
So, Dehlin’s podcast is interesting and has some valid merit pertaining to certain aspects of how we think, group think or whatever, but I am with you, i.e., in no way does it prove or even adequately demonstrate religion(s) to be ‘false’. That’s very simplistic thinking.
Hmm, yeah, perhaps we might be operating on slightly different definition of “proof,” though I acknowledge that, in hindsight, I shouldn’t have said it to avoid confusion. I was thinking more along the lines of philosophical “proof,” such as a metaphysical or logical proofs. And even the definition of the word “proof” is more in the realm of philosophy.
Hi Syphax,
Thanks for chiming in on the podcast. While I do not directly disagree with anything you say, there are a few things I think that are worth adding to your thoughts.
1) It was never my direct goal to “disprove” religion through psychology. It was merely my goal to show how social psychology explains many facets of religious beliefs through purely natural means. You are correct that this does not “disprove” religious claims in any purely philosophical sense, nor does psychology deal with metaphysics.
2) That being said, I think you are neglecting an important principle in epistemology. Namely, if you have no justifiable basis on which to believe X is true, then it is a perfectly justifiable position to conclude that X is false. Of course, this does not mean that X is absolutely False with a capital F. However, it is hardly a rational position to harp on someone simply because they operate under that assumption.
To give you an example, suppose I took the time to show to you how every piece of positive evidence for the existence of Bigfoot turned out to be a hoax. Does this philosophically disprove Bigfoot? Strictly speaking, no. Bigfoot might still be real. But then ask yourself if is it still a rational position to defend Bigfoot’s existence anyway. The answer is again no. In the absence of any positively compelling evidence for Bigfoot, the only justifiable conclusion is that Bigfoot is not real.
3) Are you aware of the philosophical concept of tentativism? For all your talk of metaphysics, you seem to be chasing some ultimate Truth with a capital T. The problem is that such a concept is, generally speaking, completely out of human reach when discussing the external world. This is why everything in science is tentative. We make no claims to any “absolute” proof of anything because nothing in all of human epistemology can ever hope to achieve such a thing! We therefore have to settle for justifiable conclusions based on limited information and subject to possible future revision. So although nothing in the psychology of religion strictly “disproves” God, you have to admit that it makes for a pretty strong case nonetheless. Simpy by removing the foundations on which God is built, we implicitly build the foundation for his nonexistence.
1) Agreed.
2) I don’t think that the social psychology aspects of religion are the only pieces of evidence for God’s existence (nor were they very good evidence to begin with). So if you throw those out, you still have all the philosophical evidence. Now I realize you feel that “every argument for God’s existence ever” from Plato to Aristotle to Aquinas to Swinburne to Craig is the result of cognitive bias, but naturally I think that anyone who truly understands those arguments cannot hand-wave them away quite so easily (even those who ultimately reject them).
3) “Truth” is out of human reach when discussing the external world only if naturalism is true. If any form of realism is true, then our mental representations of the world are accurate. So you’re just begging the question in favor of naturalism (again).
This isn’t my discussion, but I would like to comment, if I may.
“We therefore have to settle for justifiable conclusions based on limited information…Simply by removing the foundations on which God is built, we implicitly build the foundation for his nonexistence.” – James Nagel
By saying “implicitly” instead of ‘explicitly’ this comment may have some merit with regards to Dr. Nagel’s “limited information” or experiences. However, why is it that so-called ‘scientists’ (I don’t mean “so-called” in a pejorative way), i.e., those who assert to be, or in fact are “scientists”, think that a moniker denoting an occupation doing science means that their postulations are supposed to trump all. That’s absurd and any truly rational and reasonable person — scientist or otherwise, should know that. Scientists are still just people, although they are people knowledgeable of what they have studied. But, let’s be clear in that not all scientists are on equal footing with one another, nor are they always in agreement, even with colleagues within the same field of study. Hence, there are a great many scientists that affirm the extreme likelihood that there is a God. It’s what exactly ‘God’ is or who He/She/It is that’s scientifically untenable to determine with any certitude. But, to dismiss the mountains of reliable evidence based upon first hand metaphysical experiences that correlate across cultural differences affirming there is ‘something God-like’, is quite startling. And I am not referring to things on the same level of credibility as ‘alien abductions’.
The issue, it would seem, is that Dr. Nagel apparently hasn’t had any type of metaphysical experience (and I’m not referring to a “burning in the bosom” type) that has led him to think otherwise. Sure, it’s very convenient to be an ‘armchair critic’ and dogmatically exclaim in that particular drawl of the old “Ripley’s Believe It or Not” antagonist, “I DON”T believe it!”, but that isn’t rational posturing — it’s very narrow thinking.
I attended very carefully as to what he had to say in those five “Mormon Stories” podcasts, and a lot of the stuff, to be honest, wasn’t all that new to me. Nevertheless, I appreciated the re-visit because as time passed a lot of it had been relegated to some dusty and abandoned shelf in the back of my mind. And what was discussed *in their own right* were indeed valid studies, which produced statistically significant results. There is no question about *that*. But, in a certain way he was also begging the question. It’s like:
Actor A: “God doesn’t exist”
Actor B: “How do you know?”
Actor A: “Because scientists say so.”
Actor B: “Why should I believe scientists?”
Actor A: “Because scientists have done studies, and so there isn’t a God.”
This is almost on par with the opposite side of the argument:
“God must exist”
– “How do you know.”
“Because the Bible says so.”
– “Why should I believe the Bible?”
“Because the Bible was written by God.”
Also, I am not suggesting that there is a burden of proof fallacy being perpetrated, e.g., “You cannot prove God does not exist, so He does,” but rather more of a fallacy of composition (The numbers 1 and 3 are both odd. 1 and 3 are parts of 4. Therefore the number four is odd.). It cannot be inferred that just because the parts of a complex whole have (or lack) certain properties in which the whole that they are parts of, always or totally have those properties as well.
I think Dr. Nagel is poisoning the well with questionable cause fallacy tactics, notwithstanding that causal reasoning can be difficult to grapple with since causation usually involves rather complex philosophical issues such as ‘religion’. Still, no one can conclude that one thing causes another simply because the two are associated in some cases.
I’m a ‘believer’ because I have been an ‘experiencer’ of some profound events in my life. And not just me alone in ‘my own head’, but one of them in particular with my wife present who confirmed the experience. And these events, which we refer to as ‘spiritual’ have moved me, enlightened me, comforted me, and in fact have shifted my ‘belief’ more towards ‘a knowledge’ that most assuredly some things can be attributed to some sort of *real as can be* ‘god factor’ pertinent to our existence. And this implication goes way beyond than just something about the ‘utility’ of religion as John Dehlin seemed to argue for.
We can’t empirically determine that God exists or doesn’t, nor can we even begin to comprehend what God is any more than ants crawling on the ground can comprehend what human beings are. And of course Dr. Nagel must know this. However, I believe we are closer to God and being able to know something about Him/Her/It than ants can or are to us. This is something that perhaps Dr. Nagel doesn’t realize.
‘Higher knowledge’ or ‘spiritual knowledge’ has two meanings. First, it’s a way of seeing, perceiving, and experiencing; second, it’s about what you see, perceive and experience. In this way we are able to move forward and beyond towards a whole new state of knowing — one that’s free from having to rely on narrow reference points. The result, then, is leaving a person open to aspects of *the reality of life* which are beyond the boundaries of what that person already knows. But saying, “I’ve got it!” when we have certain “Aha!” moments and then conclude that now we understand what it is really all about, leaves us with no other place to go from there.
I don’t have all, or probably any of the answers, but still, as someone once said, “If you are dead to things spiritual, you are only half alive.” I am thankful I have experienced the spiritual side of life — experienced God in some meaningful ways. It has made living out and living through some of the harsher experiences of my life a lot more tolerable, as well as leaving me to stand in awe and desirous for more defined ‘higher knowledge’.
Thanks for the comment, viking! Not that I don’t appreciate your commenting here, but you also ought to develop your ideas even further on your blog, which I’ve noticed you haven’t actually posted anything on yet. I’m sure there are people out there who would value what you say. Just a thought.
Once again, much of this discussion is above my head, but I’m reminded of something a professor said in a psychology class I attended (once) years ago: “there is power in conforming to the norms and mores of the society in which we live.” I don’t know about proof, but I do believe that many people mistake social acceptance due to their conformity for genuine spiritual experiences.
With regard to Point (2), you are correct that I cannot just “hand wave” all the philosophical arguments for God away. I’m merely stating that I have examined them all and found them to be lacking. We can go down this road in more detail eventually, but first I have to finish writing up my critiques. I was casually working on this anyway, now I just have an extra incentive to wrap it up.
For Point (3), can I ask how exactly naturalism and realism are at odds with each other? As far as I know, nothing about these two concepts is contradictory. Nothing about realism is at odds with tentativism or fallabilism, either. Where are you getting these ideas in your head?
One final point, what do you have against naturalism? Think about this for a moment. Suppose that there exists some physical realm somewhere “outside” of the natural world. That means, by definition, you cannot observe it or interact with it. So on what basis do you go around making positive claims about the nature of these worlds when their very nature prevents you from knowing anything about them?
Naturalism does not mean such worlds cannot exist. It merely states that you have no justification for pretending they exist or claiming knowledge about their properties. Why is this such a terribly uncomfortable concept to accept?
I don’t think naturalism is consistent with realism, because I have never seen a coherent naturalistic explanation of intentionality. Without intentionality, our mental models of the world are indeed not accurate representations of that world (as you pointed out), and therefore, give us no knowledge about the world at all. If we have no knowledge of the world, then we are not justified in making a claim that either naturalism or realism is true. Therefore naturalism is self-refuting.
The only thing I have against naturalism is that it’s simply not true. If Aristotelian metaphysics is true (and I think there are good reasons that it is), then there are immaterial aspects of the natural world itself. So there’s no “parallel universe” somewhere that we can’t detect, but rather, immaterial aspects of the world that we can detect simply by observing them. Qualia, numbers, universals, and form would be main candidates. I have not seen a coherent naturalistic explanation of these things either. So I believe I rightly oppose any scientist that naively pushes naturalism as the only reasonable conclusion of science when it positively refutes any truth-claims the scientist makes.
James,
You say, “if you have no justifiable basis on which to believe X is true, then it is a perfectly justifiable position to conclude that X is false.”
This seems problematic. I do know the point you are getting at, but I have always felt that this position leaves much to be desired. For instance, we believe that the universe is consistent, that it follows physical laws, and that our human minds are able to understand these physical laws. These are all assumptions. These are not things that can be proven, demonstrated, or that science has any say so in. These beliefs arose out of the Christian western world from the biblical principle that God created the earth by number, weight, and measure. All throughout the middle ages this belief was emphasized. And thus it is no surprise that the scientific revolution happened in the heart of Christendom and not in the Arab world, Oriental world, etc. These other cultures assumed other things like God intervening at every instance to make rain, storms, earth quakes etc. Some just completely lacked the belief that the universe was orderly and rational. This belief in the intelligibility and consistency of the world was an act of faith that was not rationally provable, yet we reap the benefits from that act of faith still today.
Now you could say that although we can’t demonstrate it to be true we are certainly justified for believing it because these assumptions have been so successful through science. It could be said that because we assume this to do science, and science produces real results (medicine, airplanes, etc.), that we know these assumptions are correct. However, this is still not an epistemologically sound basis. It doesn’t demonstrate that it is in fact true. It is only the results that one would expect to happen if the theory is true.
This reminds me of a scene from Monty Python and the Holy Grail. A peasant makes the claim “witches are made out of wood”. When someone asks him how does he know he responds, “because when they are thrown into the water they float just like wood floats”.
This is similar to the response that we are justified for believing in a rational, consistent, intelligible universe because believing it produces results. It is only the results that one would expect to happen if the theory is true. There is an epistemological gap between what is claimed and the reason for believing. There is no epistemological explanation for how, why, or even that it happens. So in this most important sense it seems that since we have no justifiable basis on which to believe X(consistent, intelligible universe, follows physical laws) is true. In the absence of any positive compelling evidence that X is true, the only justifiable conclusion is that X is not true. It is significant that this belief and others (like the idea of human rights) arose from an act of faith.
You said, “We make no claims to any “absolute” proof of anything because nothing in all of human epistemology can ever hope to achieve such a thing! We therefore have to settle for justifiable conclusions based on limited information and subject to possible future revision.”
To me this is a cop out because people of your philosophical persuasion are willing to base your life and beliefs on things which aren’t absolutely or certainly true, yet you won’t accept evidence for supernatural which isn’t absolutely certainly true. Also remember that we teach children in school both scientific and historical facts which may not be absolutely and certainly true. So it seems that for all practical purposes there is a tendency among people of your philosophical persuasion to demand such high standards of absolute certain evidence for things like God, yet you may be perfectly fine living your life based on uncertain unabsolute truths and you are willing to allow children to be taught uncertain unabsolute facts in schools. There seems to be a disconnect here.
James, you said that you found all the arguments for God’s existence to be lacking. I would like to hear your criticisms some of Aquinas’ arguments. Could you tell me where you think Aquinas’ arguments from motion(1st way) and final causality(5th way) are lacking?
Thanks for your comment, Blogger. And actually, I think Aquinas’ 1st and 5th ways are the most powerful for me. A lot of the other popular ones in modern discourse (Kalaam, Moral, Ontological) to me seem to be a lot more debatable.
Syphax,
Okay, I see what you are driving at. I’m not going to spend time discussing ideas like qualia or universals, but I am well-versed in mathematics. So for the sake of argument, I’m going to pick on your assertion that numbers possess some kind of special “otherness” that exists outside of the natural world and yet observable from within it.
To begin, I invite you to watch the following video:
It’s a great little mathematical discussion about why 0.999… = 1. The girl who makes the videos is a very bright mathematician who is great at explaining the essence of many tough ideas. In particular, pay close attention to what she says at 8:20.
“Mathematics is about making up rules and seeing what happens.”
Contrary to popular belief, mathematical “proofs” do not count as Truth with a capital T. Rather, mathematical proofs are only true by logical deduction based on pure definition alone. There is no more “truth” to the phrase “1+1=2″ than there is to the statement that “all bachelors are unmarried.” It is only true because we ultimately created definitions that made it true. If I were so inclined, I could devise an entirely consistent mathematical vector space wherein “elephant plus pickle equals blue,” and it would still be technically true. The only reason we use the mathematical number system that we use is because it works as a functional descriptor of physical things in our experience and observation.
A great example of this is to ask yourself what it means to have a dollar. Then subtract a dollar. Now subtract yet another dollar. What do you do when you subtract a dollar from zero dollars? Mathematically, you might try to invent a thing called “negatives” that allow the operation to occur. But what did you do physically? Maybe you invented a thing called “debt” and then assigned those negative thingies as a nifty set of rules for describing it. But it’s still all just made-up ideas in the end.
Now take the square-root of your negative dollar. What happens now? Maybe you invent a whole new set of numbers called “imaginary” to handle it. But what does it mean to have “one i” dollars? (think the imaginary unit, “i”). It means nothing. Or, if you feel so inclined, it means whatever you want it to mean. The only value is in how well you can make it work to describe things.
So when you talk about things like numbers, you are literally using MADE-UP RULES concocted by human beings. They do not exist in any physical sense, and all this talk about numbers existing as some sort of ethereal object is just plain wrong. Nothing in mathematics is “discovered.” The correct term is that everything in mathematics is “invented.”
I’m not exactly sure what you think you’re arguing against, because I’m not a Platonist, but just pointing out that mathematics is in our minds – or that we have to test it for consistency by applying it to the world – is not an argument against Platonism (or Aristotelianism). Those systems seek to explain why our mental conceptions can actually be applied to real life. Sure, we could invent a big system of consistent nonsense, but if that system of nonsense helped us launch a rocket to the moon (to use one of your examples), then we are left in a very tricky situation to explain why our “made up” mental conceptions that we just took to their “logical” conclusions (whatever “logic” is, since by your definition logic might just be a made-up system in our minds, too) actually help us navigate the actual, empirical physical world.
Even you admit that the “value” of mathematics is “how well you can make it work to describe things.” WHAT exactly ensures that our mental conceptions have anything to do with the world? Especially without intentionality?
Furthermore, I am wondering in what universe you think beings could have 7 objects in front of them and count them without the same exact concept of 7 that we have in this universe. They could call it “elephant” or “pickle,” but if it’s the same number of objects, then you’re arguing for the reality of abstract universal numbers, not against it.
“but just pointing out that mathematics is in our minds…”
No, that’s not what you said:
“So there’s no “parallel universe” somewhere that we can’t detect, but rather, immaterial aspects of the world that we can detect simply by observing them. Qualia, numbers, universals, and form would be main candidates.”
In your own words, numbers constitute a distinct aspect of our world that we can “detect.” But as I just explained, numbers are inventions, not observations or detections. There is a huge difference. You did this because you are trying to argue that there exist things “outside” of the natural realm, even though we can observe them. The whole point is to show that, at least with your suggestion for numbers, that this is patently false. Numbers do not occupy some special place beyond the natural realm.
“I am wondering in what universe you think beings could have 7 objects in front of them and count them without the same exact concept of 7 that we have in this universe.”
How about THIS UNIVERSE? Consider a simple pizza. Now place a second pizza next to it. What if the second pizza is 1-inch smaller in diameter? Is it now “two” pizzas? Or is the second pizza something less than the “one” of the first pizza?
This is a perfect example of what you are asking. I can have “two objects” in front of me, yet still decide to call it something other than two. I might just call it “more pizza.” Or maybe I would call it “too much pizza.” Or 1.9 pizzas. It doesn’t matter. It’s only as useful as I need it to be.
Describe for me what it would mean to have “1+i” dollars in front of you. Or perhaps “7-2i” pizzas. There is no difference between whole numbers, natural numbers, integers, reals, and fully complex numbers, except in the things we decide to use them for. “Counting” is just a really handy tool for describe physical arrangements of stuff in front of us.
How about if a single crumb falls off of a pizza? Is it still “one” pizza? Yes? No? It depends on the utility of the description. If you just want to eat a pizza and don’t care, you still call it one pizza. If you are perhaps weighing the actual mass of the pizza, then you might decide to account for this loss of a crumb and call it 0.9999 pizzas.
Again, the point is: numbers are not some magical things that exist outside of the natural world. They are merely conceptual inventions used to describe stuff.
Listen, I’m by no means an expert in mathematics, but I’m wondering if you’re making an attempt to argue against mathematical realism or Platonism (or Aristotelian realism), of if you’re just trying to dismiss my argument by telling me that these concepts have been done away with in contemporary mathematics and you’re just cluing me in on that fact. If the former, then I wonder why you think what you said is really an argument against those positions? Because showing that there are multiple ways to measure things is not an argument against realism or Platonism. If the latter, then you must know that mathematical realism/Platonism are by no means dead in the mathematical world, and it can’t just be asserted in such an airy way that these concepts have been somehow abandoned or disproven in mathematics.
“If the former, then I wonder why you think what you said is really an argument against those positions?”
What part of “math is invented, not discovered,” fails to refute realism? This is the essence of the realism assertion, Syphax.
“If the latter, then you must know that mathematical realism/Platonism are by no means dead in the mathematical world,”
I will say this loud and clear:
Mathematical realism and mathematical platonism are dead, useless ideas. Those of us who actually apply mathematics in the real world have known this for decades (if not centuries). I am a personally very competent mathematician. I work every day with other competent mathematicians. I have explained in great detail that math is invented and not discovered. Every competent mathematician knows this. Math is nothing more than a glorified linguistic hammer which we use to rigorously formulate/solve problems. In fact, to be perfectly blunt, the only context where I have ever seen people try to argue the opposite is when non-mathematicians try to sound all smart and gee-whiz in their philosophical discussions about God and epistemology.
Then to what do you attribute this statement:
“It is a truth universally acknowledged that almost all mathematicians are Platonists, at least when they are actually doing mathematics rather than philosophizing about it. As Hardy said, “I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our ‘creations’, are simply the notes of our observations.” One might maintain that mathematicians can create new structures within mathematical reality just as engineers can create new structures within the physical world, but most of us have no trouble with the idea that there is such a reality and that our job consists of studying it. Moreover, we are all trained to believe that the universe that encompasses this reality consists of sets, and that every respectable mathematical object should possess a precise definition as a set.”
http://oz.berkeley.edu/~aldous/Blog/folland.pdf
James,
You seem to be arguing against a purely platonic conception of math and numbers. I do not believe that Syphax is arguing for some higher realm of reality where the platonic form of 5 exists right behind the platonic form of 6, which is right behind 7, etc. Rather, they are merely abstract truths that are neither material nor mental, but do in fact show themselves in nature. For example consider a man walking into a room and sees two desks. On one desk there are 8 marbles. On the other desk there are 9 marbles. What do YOU SAY is the difference between what is present on each desk? It is obvious that the difference is a difference in quantity, and quantity is measured by numerical sequence. We may have invented the shape of the number “7” and we may have given that the meaning of “that which is prior to 8, but after 5”, but if this were truly just a made up invented system then it wouldn’t be so easy to teach children to count and teach them math. These numbers correspond to truth and are not mere mental constructs that are being projected on reality from the mind. Prior to the existence of the first human mind these numbers and mathematical truths were in existence and after we all die they will still be around even without our minds. Furthermore, there are an infinite possibility of numbers but only a finite amount of matter. The number series is infinite, but our minds are finite and can only contain finite things. So given that there is a finite amount of matter and our minds can only contain a finite amount of concepts, this infinite number series must exist apart from matter and our minds.
Mathematic truths include geometric truths. Back before any human beings existed and it hadn’t been discovered that A^2 +B^2 = C^2, it was still true nonetheless. It was always true that the 3 angles of a triangle add up to = 180 degrees. But if what you say is true then this could not be true since this would just be a conceptual projection from the subjective human mind onto reality, an invented system. If all humans die tomorrow these facts will still be true and they will still be expressed in various ways throughout the world without themselves being empirically verifiable. These are facts about the world that we discover, not invented systems.
Another interesting part of your comment is that you are falling into the pre-socratic problem of the “one and the many”. With the pizza example you are using universals and forms to argue against universals and forms. When you say things like “two pizzas” or 1.9 pizzas, or too much pizza, you are saying that the things they have in common is their pizza-ness. If pizza A and smaller pizza with a crumb fallen off B are both pizzas, then that which they have in common is their form. If there is no such thing as a form of pizza then they can’t in any sense both be called the same word “pizza”. You are regressing historically back to the metaphysical debates of Pythagoras and Hericlitus.
Also your example of the .9999 pizza etc. is in perfect conformity with Aristotelian metaphysics. You ask if a pizza with a crumb fallen off of it can still be considered a pizza. Or if there is a pizza and a second smaller pizza, can the smaller one still be called a pizza. A form can instantiate something even if not perfectly. In fact there are pretty much no perfect instances of objects perfectly conforming to their form for the reasons you brought up. Think back to triangles. There is never a “perfect triangle” drawn. There is always a squiggly line as one side or an angle that isn’t completely closed. However just because it is an imperfect instance of a triangle does NOT mean that is not a triangle.
At the risk of sounding crude, I would have to say that Gerald B. Folland is an idiot who needs to go back to high school algebra. He is also dead wrong in his assertion about everyone is a Platonist. As I said, I work with mathematicians all the time, and all of them would laugh at the very idea.
All of mathematics is literally built on nothing more than AXIOMATIC ASSERTIONS. This is plainly evident in even basic texts on algebra at the high-school level. The only requirement is that the resultant theory derived from the axioms should be consistent and perhaps someday serve as a useful description of reality.
This is why the result of division by zero is called “undefined,” and not “undiscovered.” You are free to define some object “X” such that “X = 1/0,” but you have to show that it does something consistent with all the other rules of algebra. Otherwise, no one wants to hear it.
Now to be fair, it is very tempting to want to think of mathematical theory as something “discovered.” It is maybe even useful to describe it in such a fashion. But it is still wrong, and everyone knows it. Discovering a mathematical theory makes just as much sense as “discovering hopscotch.” You don’t discover the rules for a game. You create them and see what happens.
But you’re left to still explain why these made up rules bear any resemblance to the external world.
Here is a thought problem:
Start with a rock. How many rocks do you see? Obviously the answer is one.
Crack the rock in half. How many rocks do you see now? The answer is now two, right?
Or is it? Physically speaking, the two chunks of rock already existed in the original rock. So why did I not call it two rocks to begin with?
Obviously that would not work because I could just as easily claim that there are 7, 24, or 8 billion rocks already existing in the original rock. So calling the original rock something other than “one rock” would not lead to a unique result. Yet clearly, that original rock was already two rocks to begin with.
1 = 2 ?
How about this… maybe I want to say that I now have “two halves” or a rock. Does that work? Perhaps, but then where did my original “one rock” come from? Simple. It fell off of a bigger rock, which fell from a boulder, which fell from a rock face, which formed on a mountain… So really, that original “one rock” was actually 1/2 of a prior rock, which was 1/100 of an even bigger rock, and so on.
1 = 1/2 ?
Okay, how about this? I need hard heavy things to throw into a lake because it is fun. So I grab a rock and skip it on the lake and call it “one rock.” Then I grab another rock and break it in half. Now I have “two rocks” because I have two things to throw into the lake. 1 = 1 and 2 = 2. Everything is consistent.
Now I need ballast to measure weight with. So I pick up a rock and weight it. It is 100 grams. I break it in half and weigh the two halves together. It is still 100 grams. Great. Everything is consistent again when the two pieces equal the whole.
Do you not see what is happening here? Numbers are just logical conclusions derived from axiomatic definitions that ultimately serve as linguistic descriptions for things. The only “correct” interpretation for the rock is the one that I need it to be. If I am throwing things in the lake, then the two pieces are two rocks. If I need to raise the water level in jar, then the two rocks are actually two halves of a whole. There is absolutely no such thing as a literal, self-contained “number” that magically exists in its own little world.
So when you ask why these rules bear any resemblance to the external world, the answer is simply because the world has patterns. All we did was invent rules that try and match the patterns we observe.
But if the patterns we observe are real, and the descriptions we use are constrained by the patterns we observe, then realism could still obtain. You’re just pushing “realness” from the numbers to the patterns, and then using numbers as symbols for the patterns. And either the numbers express the same thing as the patterns (in which case they are redundant, and realism still obtains), or they express some new truth in which case they actually don’t describe the world. The Platonist or realist would just say that all the different ways you could describe the rock are simply real descriptions of the rock, depending on what form (universal) you’re paying attention to. I don’t know why anything that you said changes realism or Platonism.
Also, all your unequal examples aren’t really making a point other than one thing can be described in several ways, all correct. Nobody argues that 1 could equal 2 when describing a rock in exactly the same way. We could describe the rock as 1 rock or 2 smaller rocks, but that seems like a trivial point that doesn’t affect realism at all.
Furthermore, to highlight even more your lack of understanding here, you seem to be completely ignoring the point that “Blogger” was making above. If we take your example of the rock, if you’re arguing that 1 rock and the two half-rocks it could be broken into have something in common (rock-ness), which seems to be the point you were making when you said 1 = 2, then you’re using a universal (rock-ness) to argue against universals. I don’t know what to make of that exactly.
Please define Platonism for me, because I don’t think it means what you think it means. So I will explain my understanding.
Part of Platonism is the idea that abstract objects (like numbers) can possess an unique form of existence unto themselves, correct? This is the essence of the whole “Theory of Forms” buried underneath Platonism. It is also why you brought them up in the first place. You wanted to show that there exist things “outside” of the natural world, yet somehow perceptible do us. Yet now I see you admitting that numbers are just descriptors, which obviously have no existence outside of whatever we decide them to be. So I fail to see how you can have it both ways. Descriptions of your sensory experience are NOT distinct entities unto themselves, Syphax. They are linguistic tools that we use to make sense of our sensory experience.
In response to Blogger,
“These numbers correspond to truth and are not mere mental constructs that are being projected on reality from the mind.”
Except that’s exactly what numbers are: a “mental construct” that is being projected onto reality. The mere fact that I can describe a rock as being both 1 and 2 is exactly this point. It is a sensory perception that I attempt to encapsulate through a linguistic description. When you try to attribute ultimate “truth” to numbers, you may as well try to attribute an ultimate “truth” to a game of hopscotch. Again, the essence of math is all about making up rules and seeing what happens.
When you talk about nebulous gibberish like “rockness,” you are attempting to formulate a linguistic description of the external world. That world, by definition, is the natural world that we can interact with. Abstract objects like “numbers” are just words you use to try and form a coherent understanding of that natural world. But again, those number-thingies do NOT have an existence unto themselves.
“Prior to the existence of the first human mind these numbers and mathematical truths were in existence and after we all die they will still be around even without our minds.”
On what do you base this assertion? If numbers have this special property unto themselves, then explain to me what it means to have “-1″ pizzas in front of me. Or perhaps “1-i” pizzas. Mathematically speaking, they are all “numbers,” so why can’t I have an imaginary quantity of pizzas in front of me?
The answer is simple: Because no one has yet to define a useful convention for what complex-value pizzas should represent. That is it. That is the only reason. This is why complex numbers work so well at describing sinusoidal signals. It’s a nice set of rules that encapsulates information and keeps everything nice and consistent. So if you can think of nice rule set for complex-value pizzas, then great. But that does not mean it always existed in its own little realm of magical abstract wonder. It means you, as a thinking agent, concocted an arbitrary set of rules and then incorporated them into your linguistic description of natural observations.
Nothing about any of this supports the idea that anything can hold its own unique existence outside of the natural world.
The fact that you keep retreating to words like “idiot,” “nebulous gibberish,” and “magical abstract wonder,” while ignoring basic realist points about universals (and accusing me of not understanding what Platonism even is) makes me wonder if I’m using my time wisely in this conversation. It would, however, explain perfectly to everyone reading right here why you think you’ve so easily dispatched “every argument for God’s existence in history.” I’m a graduate student and a parent and don’t have the time to go over Metaphysics 101, so I’m going to make this my final comment in this discussion. I’ll leave it to the readers to decide whether you or I don’t know what Platonism is.
The Platonist principle that we’re going over is the reality of universals, which includes numbers (and the relationships between them, including imaginary numbers and negative numbers), “rockness,” “pizzaness,” “humanity,” “electron-ness,” “redness” (qualia), “wetness,” etc. You seem to be arguing some form of conceptualism (that these abstractions only exist in our minds), and I’m arguing for realism (of which Aristotle and Plato both advanced forms of), but I’m telling you that if you want to argue for conceptualism you have to explain how mental concepts are arbitrary fictions that are used to DESCRIBE REALITY (and communicate that reality intelligibly to others) without grounding them in anything that is real. I just don’t know how to do that. Every time you constrain one of your mental fictions by trying to map it to the external world, you’re showing that the “fictions” you’re using aren’t actually arbitrary at all but must directly hone in on real things, relationships, or situations to be useful. If so, then (as I said above, let’s try it one more time and hope it sinks in) your fictions are either redundant (why not just refer to the objective realities directly instead of giving it a symbolic term that means exactly the same thing?) or not grounded in reality at all (in which case why expect them to be any more useful than The Lord of the Rings or any other work of complete fantasy?). If mathematical truths are fictions but still must be constrained by logic to “work” in the real world (or in your words, they can serve as accurate “linguistic descriptions of natural observations”), then you’re just pushing the “realness” back a step to either logic or the natural observations themselves and you’re in the same predicament, except with logic or abstract “laws of nature” instead of mathematics. Why expect our logic to conform to reality? Even if we revised our mathematics or logic to more accurately describe reality, what ensures that we’re even succeeding? How do we know our logic “more” or “less” accurately describes reality without using logic itself? At some point there needs to be some grounding in something that is REAL or we are stuck in an infinite regress or painful circularity of fictions – and that grounding (the ability to say that our thoughts, logic, math, pragmatism, etc. really are conformed accurately to real objects or relationships in the world) is called realism. Pointing out that -1 pizzas is invisible doesn’t prove anything against realism, because -1 is still a coherent relationship that can be applied to real objects in certain situations. Since we can use it in our equations and apply them to real life situations with success, it proves that -1 describes a real relationship between things, even if it itself invisible. And that’s realism. You can call it “magical” or “nebulous” if you want, but that’s your deal, not Plato’s or Aristotle’s or mine.
You also completely missed my point about the 1 = 2 scenario. I’ll repeat again (because apparently I’m some kind of masochist with infinite time). You are saying that 1 rock can be described in two ways – as 1 rock, or as 2 smaller rocks. I agree. That’s because it’s coherent to say 1 = 2 when both sides of the equation are talking about the rock in different ways. The first 1 describes a real aspect of the rock (its complete quantity) and the second describes another real aspect of the rock (the fact that, when conceptually divided, you can consider it to be 2 smaller rocks). No Platonist would argue here, because they would just say that the rock “participates” in the (real, universal) number 1 in one way and it “participates” in the (real, universal) number 2 in the second way, and we recognize these realities directly with our minds (which are equipped with intentionality that allows them to directly observe reality and abstract away its real universal properties).
So just saying that mathematics is made up in our minds is not an argument against realism, because realism just says that, instead of creating fictions in our minds that vaguely may describe reality somehow, our minds are simply grasping real universals. Either way, numbers, logic, mathematics, universals, etc. would appear in our minds – it’s just that on realism we should expect them to be accurate descriptions of nature while on conceptualism we have no real reason to. On realism, the process of “mapping” those universals onto reality is just honing in on a more accurate conception of what is real, while on conceptualism we have no reason to think that our mental fictions could be usefully mapped onto reality at all.
I have a hard time understanding how any scientist could deny universals and still try to form an intelligible picture of the world. You’re an electrical engineer – why do all the electrons you come across “magically” have the same properties, if they’re not sharing in some kind of real universal essence? Coincidence? Because you “project” that nature onto them with your mind? Why are any of the particles in the universe similar at all – why aren’t they like snowflakes, where every one has a different, arbitrary set of properties? Because the nature of an electron is constrained by its form, which is a universal for all electrons. Now a Platonist and an Aristotelian might argue about whether this form is in a “third realm” of abstractions or if it is an immaterial form that inheres to prime matter (respectively), but they would both tell you that the form is nevertheless real, it is not in itself material, and it is directly grasped by our minds, which is my original point that there are non-material things in the universe that are directly grasped by our minds.
Furthermore the conceptualist (or non-Aristotelian anyway) is still left with the impossible task of explaining how there are no universals anywhere in the universe, and yet they can appear in the chunk of meat that is our brains. This is just special pleading. If they don’t exist, they can’t exist in our brains any more than they do in a rock, a pizza, or a nebula. Our brains are just neurons with electro-chemical charges, without intentionality, final causality, teleology, etc.
Now if you really want to learn more about the form of realism I favor, here are some sources:
http://www.newdualism.org/papers/D.Oderberg/HylemorphicDualism2.htm
Aquinas (A Beginner’s Guide)
http://plato.stanford.edu/entries/aquinas/#ComPhyObj
Also – I appreciate the discussion. It’s been fun.
Syphax-
I’m taking a bit of a risk here because this is an old thread so I hope you’ll see it. I’ve read this post and comment thread as well as the one over on Mormon Stories which spawned it. I would really like to understand more about your point of view in part because I tend to agree with James (though I feel like he is missing some things too). Unfortunately, I’m not a philosopher or a psychologist. All of my philosophy knowledge is from cursory readings of Wikipedia pages. On psychology I’m a bit better as I’ve taken a couple courses, and read a fair number of books on the topic. So I feel like I can hold my own a little better on psychology. As a sidenote, if you haven’t read “The Righteous Mind” by Jonathan Haidt, I personally think that is the best explanation of psychology of religion that I’ve seen yet and I think it addresses some of your concerns. I am, however, an engineer (several different varieties) so I know a lot of math, but not a lot about the philosophy of math (though again I tend to agree with James that it is an invention).
Anyway, the real point of this comment is to ask you if you would be interested in preparing a few posts describing your viewpoint but in more easily understandable terms. Aristotelian empiricism means something to me, but my understanding of it is not real good. Same goes for all the other philosophy words you use here. I’d really like to understand more of what you mean but even with using Wikipedia to try and understand all the terms you use doesn’t really give me any intuitive feel for it. Let me know and I’ll read your posts.
As a final thought, let me say that although I think James goes a bit far, as you say, in concluding the falsity of religion based on understanding the psychology behind it, I similarly think you go a bit far in dismissing it. I’m somewhat of an expert in information theory (Bayesian inference) and although logically inductive reasoning is faulty, in terms of probability there is “information” contained in observations. So I think our understanding of the psychology of religion DOES say something about the likelihood of the truth claims of many religions but does not disprove the claims by any means.
If you want a better sense of my philosophy-psychology perspective you should look at my other blog: Aristotle’s Revenge (http://aristotlesrevenge.wordpress.com/). That’s where I primarily blog about philosophy and Aristotelian psychology. Hopefully there’s enough information there to get you started.
I have actually built my graduate thesis on Haidt’s work, so I am reasonably familiar with his research (though I haven’t read his popular books, just his research articles). I would say that Haidt’s morality makes sense to explain most of religion if humans don’t have an intellect (in the Thomistic sense). In other words, we can look to something like Haidt’s research if we want to know why we have certain “gut reactions” in moral judgments but we can look to someone like Kohlberg if you want to know how we REASON about morality. If reasoning is an immaterial process (as Aristotle and Aquinas and many other philosophers have taught) and it maps to real structures in the universe, then we have grounds to suppose that our reasoning alone is not subject to the psychological principles that James was trying to use. So as far as your last comment, I would agree with you if there were no independent arguments for the truthfulness of religion. In other words, if all we had were the social benefits of religion, the evolutionary adaptiveness of it, cognitive dissonance, etc., then I would say that this tells us something about the truthfulness of religion. However, there are deductive and inductive arguments for the existence of God and the truthfulness of various religions that are independent of those psychological reasons. I think some of those arguments do succeed, in my mind, and even if they don’t, taken together they make a strong collective case to accept religion as “not so easily dismissed.” Specifically Aquinas’ Five Ways and the various Cosmological Arguments are, for me, the strongest.
Sorry if this isn’t very complete, I must go to class in just a few minutes.
I’m definitely jealous! In another life I’m gonna be a psychologist.