That’s from George Polya, who was Professor Emeritus at Stanford and a mathematician who wrote the 1968 book I’m reading on math; ‘Mathematics and Plausible Reasoning, Volume II – Patterns of Plausible Inference’. The father of problem solving. I like the way he thinks.Â
Interesting stuff, opposite to Aristotle’s suggestion two thousand years ago that all reasoning conforms to certain patterns. Polya argues that there are practical limits to impersonal, universal and self sufficient reasoning.
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The basis for difference: your own background, judgement and intuition affects any outcome. ‘It cannot escape being provisional…. The direction is impersonal, the strength may be personal.’
Inferred = forgeddabout the genes already (which jibes with the new science of genetically identical bacteria wildly diverging and mutating). The relevancy of life and how one is formed by it, determines reasoning and style.Â
Polya: “…Demonstrative reasoning appears as ‘machinelike’, definite, final, while plausible reasoning appears as vague, provisional, specifically ‘human’. ….the ‘strength’ or the ‘weight’ of the conclusion may depend not only on clarified grounds such as those expressed in the premises, but also on unclarified, unexpressed grounds somewhere in the background of the person who draws the conclusion. A person has a background, a machine has not. Indeed, you can build a machine to draw demonstrative conclusions for you, but I think you can never build a machine that will draw plausible inferences.”
So maybe I’ll crack the math codes after all.
“My method to overcome a difficulty is to go around it.” G Polya          Â
UCTV is my current favorite TV channel. I always find interesting programming there, and last night on Conversations with History, Stanford Professor Lucy Shapiro, spoke about having come from an artist’s and musician’s sensibilities into the world of microbiology. It’s fascinating to listen to her trajectory. She found herself confident enough to try anything after having studied the fine arts. ‘Thinking differently is critical’.
Your post reminds me of a class in the 4th grade, when my teacher, Miss Arrington, described philosophic method. It’s the first time I remember anyone mentioning philosophy, and the occasion was not auspicious, as she, too, discussed Aristotle’s arguments against empiricism. She said Aristotle claimed that one could deduce how many teeth a horse must have without ever resorting to the horse’s mouth. I was shocked, and at that moment resolved to avoid philosophy in favor of empirical science. The decision was ironic given that I adopted philosophy as a career 12 years later, and eventually I came across the offending passage in Aristotle’s De Partibus Animalium. If only I’d listened to Miss Arrington–but that’s another story. I like your point that knowledge derives from context, and context derives from experience, and I think that it’s necessary to take both into consideration when defining knowledge. Yet it’s also important to consider the arguments for idealism, not the least of which is the way the cosmos hews so closely to mathematics. Aristotle’s arguments derive from his confrontation with the success of mathematics in describing the behavior of the physical phenomena. On consideration it is truly bizarre that high abstractions like geometric theorems, Fourier transforms or a host of other mathematical structures have application to observable phenomena. Like many philosophers I’m still on the horns of a dilemma between mathematical knowledge, which can advance as a pure act of rationality, and the many other kinds of knowledge which require investigation and experience.
Your post reminds me of a class in the 4th grade, when my teacher, Miss Arrington, described philosophic method. It’s the first time I remember anyone mentioning philosophy, and the occasion was not auspicious, as she, too, discussed Aristotle’s arguments against empiricism. She said Aristotle claimed that one could deduce how many teeth a horse must have without ever resorting to the horse’s mouth. I was shocked, and at that moment resolved to avoid philosophy in favor of empirical science. The decision was ironic given that I adopted philosophy as a career 12 years later, and eventually I came across the offending passage in Aristotle’s De Partibus Animalium. If only I’d listened to Miss Arrington–but that’s another story. I like your point that knowledge derives from context, and context derives from experience, and I think that it’s necessary to take both into consideration when defining knowledge. Yet it’s also important to consider the arguments for idealism, not the least of which is the way the cosmos hews so closely to mathematics. Aristotle’s arguments derive from his confrontation with the success of mathematics in describing the behavior of the physical phenomena. On consideration it is truly bizarre that high abstractions like geometric theorems, Fourier transforms or a host of other mathematical structures have application to observable phenomena. Like many philosophers I’m still on the horns of a dilemma between mathematical knowledge, which can advance as a pure act of rationality, and the many other kinds of knowledge which require investigation and experience.