How would you characterize yourself with regard to formality? Think of yourself as a down-to-earth, commonsense, level-the-road-by-seat-of-the-pants kind of person? Not too concerned about style, preferring “substance,” instead? And what about your perspectives? Are they formal or informal? Are they “this is what I think today, but, hey, who knows, I’m open to think differently” or “this is the result of a formal thinking process, math-like in its precision, irrefutable on the basis of logic, and founded on self-evident truths”?
And now the big question for the day: Are you after truth in your life or consistency?
You know that if you are a physicist or mathematician, you rely on formulas that build one-after-another on symbols you accept as valid representations of some reality. In physics, that reality is generally accepted as “physical reality.” In mathematics, it is the circular mathematic reality; the symbols are themselves a kind of reality, and they need not apply to any “thing.” You can count from 1 to 10 without any “thing” in mind. Math is the formal toolkit of physics, and we accept that F=ma, for example, because it seems undeniable in the world we deal with daily. We often do have some “thing” in mind when we use formal math to define “things” and their relationships (like moving with respect to some other “thing”—e.g., a background).
Of course, the toolkit of symbols also includes those “representations” that seem far removed from what we understand as meaningful representations of everyday reality. Maybe that’s why so many of us say, “Okay, I learned algebra, now what am I going to do with it as I face the daily challenges life throws at me?” What do you think Immanuel Kant was talking about when he said, “For to substitute the logical possibility of the concept (namely, that the concept does not contradict itself) for the transcendental possibility of things (namely, that an object corresponds to the concept) can deceive and leave satisfied only the simple-minded”?
No, he really wasn’t saying that formal mathematicians were “simple-minded,” but he was noting a relationship between what we know intuitively to be real and what we do to explain it to ourselves (and to others). Don’t most of us prefer consistency over “truth”? Don’t most of us consider consistency to be “truth”? Our way of formalizing our worldview relies on consistency, even though we often include contradictory representations that defy a common definition of truth.
My “formal” approach appears to be consistent to me, but yours doesn’t. I might not accept your symbolic representations, and the symbols themselves. As long as mine seem “consistent” and become intuitively tied to the reality that I accept, they are representations of “truth.” Your formalism, however, might differ from mine. You argue that you are formally consistent. I argue similarly. Both of us see our formal representations as products of a consistent approach to “things” and our intuitive understanding of them.
In our personal formalism, we equate consistency with truth.
Now, you’re going to ask, “What does all this mean?”
I’ll respond to your question with a question: “How can people compromise when they differ on the basis of the consistency of their arguments and not on the basis of “truth”?*
*I hesitate to make my response more specific because I prefer not to guide you to your own insight. However, since you are pressing me on the issue in this footnote, I’ll say, “Watch a political discussion on TV. Examine the positions of enemy states. Eavesdrop on couples entering divorce proceedings.”
And now the big question for the day: Are you after truth in your life or consistency?
You know that if you are a physicist or mathematician, you rely on formulas that build one-after-another on symbols you accept as valid representations of some reality. In physics, that reality is generally accepted as “physical reality.” In mathematics, it is the circular mathematic reality; the symbols are themselves a kind of reality, and they need not apply to any “thing.” You can count from 1 to 10 without any “thing” in mind. Math is the formal toolkit of physics, and we accept that F=ma, for example, because it seems undeniable in the world we deal with daily. We often do have some “thing” in mind when we use formal math to define “things” and their relationships (like moving with respect to some other “thing”—e.g., a background).
Of course, the toolkit of symbols also includes those “representations” that seem far removed from what we understand as meaningful representations of everyday reality. Maybe that’s why so many of us say, “Okay, I learned algebra, now what am I going to do with it as I face the daily challenges life throws at me?” What do you think Immanuel Kant was talking about when he said, “For to substitute the logical possibility of the concept (namely, that the concept does not contradict itself) for the transcendental possibility of things (namely, that an object corresponds to the concept) can deceive and leave satisfied only the simple-minded”?
No, he really wasn’t saying that formal mathematicians were “simple-minded,” but he was noting a relationship between what we know intuitively to be real and what we do to explain it to ourselves (and to others). Don’t most of us prefer consistency over “truth”? Don’t most of us consider consistency to be “truth”? Our way of formalizing our worldview relies on consistency, even though we often include contradictory representations that defy a common definition of truth.
My “formal” approach appears to be consistent to me, but yours doesn’t. I might not accept your symbolic representations, and the symbols themselves. As long as mine seem “consistent” and become intuitively tied to the reality that I accept, they are representations of “truth.” Your formalism, however, might differ from mine. You argue that you are formally consistent. I argue similarly. Both of us see our formal representations as products of a consistent approach to “things” and our intuitive understanding of them.
In our personal formalism, we equate consistency with truth.
Now, you’re going to ask, “What does all this mean?”
I’ll respond to your question with a question: “How can people compromise when they differ on the basis of the consistency of their arguments and not on the basis of “truth”?*
*I hesitate to make my response more specific because I prefer not to guide you to your own insight. However, since you are pressing me on the issue in this footnote, I’ll say, “Watch a political discussion on TV. Examine the positions of enemy states. Eavesdrop on couples entering divorce proceedings.”
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