Since our walk through Summa Contra Gentiles is going so well, why not let’s do the same with Pascal’s sketchbook on what we can now call Thinking Thursdays. We’ll use the Dutton Edition, freely available at Project Gutenberg. (I’m removing that edition’s footnotes.)
There are different kinds of right understanding; some have right understanding in a certain order of things, and not in others, where they go astray. Some draw conclusions well from a few premises, and this displays an acute judgment.
Others draw conclusions well where there are many premises.
For example, the former easily learn hydrostatics, where the premises are few, but the conclusions are so fine that only the greatest acuteness can reach them.
And in spite of that these persons would perhaps not be great mathematicians, because mathematics contain a great number of premises, and there is perhaps a kind of intellect that can search with ease a few premises to the bottom, and cannot in the least penetrate those matters in which there are many premises.
There are then two kinds of intellect: the one able to penetrate acutely and deeply into the conclusions of given premises, and this is the precise intellect; the other able to comprehend a great number of premises without confusing them, and this is the mathematical intellect. The one has force and exactness, the other comprehension. Now the one quality can exist without the other; the intellect can be strong and narrow, and can also be comprehensive and weak.1
Those who are accustomed to judge by feeling do not understand the process of reasoning, for they would understand at first sight, and are not used to seek for principles. And others, on the contrary, who are accustomed to reason from principles, do not at all understand matters of feeling, seeking principles, and being unable to see at a glance.2
1A tacit premise here are the levels of intellectual ability. Einstein was famously considered by his peers to be less than an immaculate mathematician. But Einstein’s mathematical skills, relatively (get it? get it?) poor as they were, were orders of magnitude greater than, say, those of the homme moyen. I think what Pascal means is that in any of us one form of thinking dominates the other, and perhaps this isn’t by choice: he cannot be saying that each of us is either a great mathematician or a terrific inductionist.
The two manners of thinking reminds of the little science fiction I remember. Asimov’s men versus his robots, which he always had men call “logical, not reasonable.” Many see this as a goal. Peter Kreeft warns of the consequence: (in Socratic Logic, p. 35) “a new species of human mind has appeared: one that does not know the difference between a human mind and a computer”. Who would aspire to be a walking calculator?
2I prefer induction over intuition, inductive over intuitive, and so forth. Our culture with just suspicion looks down on “intuitionist” modes of thinking, for this is where “feelings” reign and charlatans of every stripe live. Robotics is promoted, philosophy maligned, or rather it is aligned to robotics. But our “feelings” are not Pascal’s “feelings.” Because we don’t keep this straight, we incorrectly condemn, or rather fail to reward, inductivist thinking. Deepak Chopra in an intuitionist; Einstein was an inductivist.
What Pascal shows is that there is a touch of truth to the academic “different ways of knowing” fraud. Some of us come at the truth at once, and some by formal rigorous calculation. Surely the path taken does not matter if one arrives at the proper destination?
Except the difficultly is that not all truths can be reached by calculation. Rigorous calculation proves this! Right, Gödel? Empiricism is circular and all mathematics, logic, and rationality must begin on inductivist grounds. Inductivist thinking is thus superior because it holds and discovers greater truths.
Quoting in Groarke p. 293): “‘Not to know of what things one may demand a demonstration, and of what things one may not’ is, for Aristotle, to lack education.” And (pp. 298-299): “If modern philosophers have generally focused on logic and deduction as the most authoritative source of knowledge, Thomas [Aquinas], following after Plotinous, considers intellectus or “understanding” to be a higher form of knowing.”
Intellection, or inductivism, is to know “through a species of immediate, instantaneous illumination.” It is to see the universal in the particular, to see the essence in an example. It is a gift.
On Thomas’ account, what we call reasoning [ratio] is, in fact, an inferior form of knowing. We do not immediately grasp the implications of the facts that we know. We are not intelligent enough for that! Because we lack intelligence, we must reason through a middle term [as in syllogisms]. Discovering the truth requires effort. We need an aid, a crutch. This is what logic provides. Because “of the dimness of the intellectual light in [our] souls,” we must reason things out, moving step by step from premise, to premise, to conclusion. We see part of the truth and use it to logically calculate another part of it. Although Thomas could be said to devote his whole theological and philosophical career to logical argument, he himself recognized that this form on insight is inferior.
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