(Grampa sitting reading. Enter Ayla and Joshua.)


Grampa: Joshie! Oh, Ayla, this is a nice surprise.  

Joshua: Just "Josh", Grampa. My friends tease me enough already. If they heard you call me "Joshie", I'd never live it down. 

Grampa: Oh, alright. I'll try to remember. You'll always be Joshie to me. How's life? 

Ayla: One of his data-sorting programs just won a prize, Grampa. Isn't that great? He's being watched by Microsoft people, you know. 

G: I love how smart my grand ...I always say that, don't I? 

A: Yes. But there are lots of smart people in Computing Science. 

G: But they don't have me. What are you both smiling at? Anyway, what's up? 

J: Ayla was telling me about how you write off Logic and Math. In Computing Science, we're kind of attached to those old fields, you know. They're all the heritage that us geeks have. 

G: Oh, no. I don't write them off. I just see their connection to reality as always shifting and evolving. It's there -- the connection, I mean -- between Math and Chemistry, for example, or between Computing Science and Meteorology, but the concepts in the actual, practical fields keep getting revised as new data and observations come in. That means that new models of reality have to be created over and over every few years. But as far as whether the concepts in Logic and Math exist in some other way or dimension ...for me, that is nonsense. Daydreams. 

J: So the tools or techniques of Logic and Math aren't real? 

G: They're real in the sense that they do show up as patterns of brainwave activity. And the familiar moves in Logic are real in the sense that they're very useful for organizing memories in the human mind and then for enabling us to communicate ideas about our categories of sense data memories to other people, but they don't have some separate, independent existence in some alternative reality in the way that Plato or Descartes claim. 

J: Alright, I can accept that, but you have to admit that Logic and Math give human minds some great training. And they aren't just useful in Science, they're essential. A new field doesn't get to really be called a "science" until the people in the field can make statements about what they think they've learned in the field in logical statement form or some mathematical formula and then those statements can be tested. But the statements in proper logical format have to be put together first. 

G: Yes. Absolutely. 

J: And then the claims have to borne out by later by more observations and tests.  

G: All of that is true, Joshie. I mean, Josh.

J: And it's Logic that gives us the thinking techniques that make even the wording of the statements and then the testing of them ...possible. Makes it all happen. 

G: Yes. 

J: Well, that's good enough for me, I guess. I don't really need to persuade you of anything more. You agree that if all t's are b's and all b's are j's, then all t's are j's, for example. That basic syllogism is always true and always reliable. And Logic is useful even in everyday life. 

G: Absolutely. 

J: But you still have worries about Logic. Or proof in Math. Or our whole way of thinking. I mean other mathematicians and me. I hear it in your voice. 

G: "Caveats" would be the right word, I think. 

J: Why? 

G: Because people slip so easily from finding a thinking technique useful to calling it "true" ...and then giving it blind loyalty. Logic and the thinking techniques it teaches are useful and get us good, reliable results, but only under certain conditions. 

J: Like what conditions? 

G: Well, consider your little syllogism. 

A: You mean the one about "all t's are b's". 

G: Yes. 

J: It is absolutely reliable and valid. I'd bet my existence on it. 

G: Yes, but to cut to the chase, as they say, the problem is that is that in the real world, there are no t's or b's. 






J: Well, okay, but there are classes of real things that can be substituted in place of t's and b's. All whales are mammals, all mammals are vertebrates, therefore all whales are vertebrates. 

G: Which is valid reasoning leading to a true conclusion, but only for now. Once there were no whales, only some intermediate creatures that swam around in the primordial sea. Once there were no mammals either. And so on. Or at least the evidence in the fossil-bearing rocks says there weren't. Biology is built around what we think that evidence is telling us. The Theory of Evolution. And that theory makes order and sense of all of Biology. Which is useful. 

J: But then you're saying ...what? That there aren't really any whales? 

G: Not in any final, eternal sense. All of the categories in our heads that we put our sense data and memories of sense data into ...all of the word labels we make up to keep those categories in order so that they're easy to sort and talk about ...so we can just deal with daily life ...they're all made up by us. In the physical world, there are no trees and no whales and no ...well, you get my point. 

J: So the problem isn't with Logic or the techniques of Logic; the problem is that there are no t's or b's. 

G: Not in any eternal or perfectly reliable sense. 

J: Alright. I can accept that. 

A: You make life seem pretty scary, Grampa. We can't trust anything we think we know about life one hundred percent, ever. 

G: But then, in addition ...

A: Okay. I know where you're going next. Life is also interesting. Challenging. 

J: We just have to keep remembering that there aren't any whales. "Whale" is a temporarily useful term. That's all. Have I got that right? 

G: Yes. Useful when we want to talk to each other about living things and how they got here. 

A: Even terms like "atom" and "molecule" are only useful for now then. Is that what you're saying? 

G: Good examples. No one's ever seen an atom. "Atom" is just a made-up term for what we think is causing the clusters of data that we have observed in labs. But no one's ever seen an atom and no one ever will. 

J: Not even with the biggest electron microscopes. 

G: No. Even if an image of a very large atom could be produced by a very powerful electron microscope, that image would still be a machine-made image of something that might be down there in the sub-microscopic world. And then you'd still have to ask yourself how much you trusted the machine. Which I do, by the way. At the 99 % level. 

J: But what you're saying is true of even things that we see everyday. My eyes can be fooled. 

G: Yes. 

J: So you don't one hundred percent trust Logic, but you don't one hundred percent trust your senses either? 

G: That's right. Logic in its purest forms just tells us about Logic. About its subtle tricks and hidden corners. But when I am checking sense data against concepts that I've learned about the real world and the things in it, I must not forget that the very terms in my statements are gambles. I can't know ever that any of those terms is unshakable. I do admit that people have to have those terms or concepts just to stay sane. Let's not forget that either. If you experienced just raw sense data and had no way to sort it, you'd end up sitting catatonic in a hospital, staring and drooling. 

J: Plato thought that we should try to create terms that ...how did he put it? ...cut nature at the joints. But you're saying ...

G: Now you're following me. I'm saying nature has no joints. Things are constantly wavering and forming and dissolving into and out of each other all of the time. There isn't even a reliable dividing line between thinking and feeling. Or between living and non-living or between molecule and cell or judge and criminal or rights and duties. 

A: Or even between rational numbers and irrational ones? 

G: Well, now you're back into a pretty rigorous field, namely Math. But, no, there is no perfectly reliable way to separate rationals from irrationals. Those words are just naming concepts that, it turns out, don't always work perfectly. Mathematicians invented imaginary numbers to try to fix what the real number system couldn't talk about. And wild as they sound, imaginary numbers turn out to have uses in real science. But to get back to our point, thinking about thinking is a tricky business. When we talk about numbers, we're talking about thoughts and patterns of thoughts and then trying to communicate what we think about this kind of thinking to other people. 

J: But mathematicians do it all of the time. They talk about proofs and make complete sense to each other. 

G: And why do people, at least some people, bother to expend the energy to investigate or talk about such stuff? 

J: Alright. I see where you're going with that thought. We -- people like me -- get into Math because people who came before us found it to be useful. 

G: That's right. Ninety percent of what went on in Math departments for centuries was just mental exercise. But sometimes an equation could be formulated that seemed to fit some model of reality. Then the equation not only described what was being observed, it told people who understood it what they would observe if they tweaked some conditions in the real world. For a few people who worked on the border where Math merges with Science, those were beautiful moments. 

A: Sometimes scary, dangerous ones, too. Like when they figured out how to make atom bombs. 

G: Yes. You sound like Katy now. She'd have loved this talk. But, you're right. Math and Science can lead us to incredible power over nature. And we haven't handled that power very well so far. 

J: Yes, but that's not the fault of the scientists. 

G: We're on the brink of a whole other discussion again. I have to stop. I've just got time to make us some lunch, and then I have to go to the dentist. 

J: Once again, reality butts into our lovely talk. 

G: It always does, Josh. 

A: Can I crack some beers? 

G: Of course. 

J: Any dark ales? 

A: Of course. 

J: Now you're talking. No matter what your wild ideas, Grampa, you always have good beer.