Pascal’s Pensées, A Tour: I

PascalSince 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.)

Update Comments fixed.


The difference between the mathematical and the intuitive mind1.—In the one the principles are palpable, but removed from ordinary use; so that for want of habit it is difficult to turn one’s mind in that direction: but if one turns it thither ever so little, one sees the principles fully, and one must have a quite inaccurate mind who reasons wrongly from principles so plain that it is almost impossible they should escape notice.

But in the intuitive mind the principles are found in common use, and are before the eyes of everybody. One has only to look, and no effort is necessary; it is only a question of good eyesight, but it must be good, for the principles are so subtle and so numerous, that it is almost impossible but that some escape notice. Now the omission of one principle leads to error; thus one must have very clear sight to see all the principles, and in the next place an accurate mind not to draw false deductions from known principles.

All mathematicians would then be intuitive if they had clear sight, for they do not reason incorrectly from principles known to them; and intuitive minds would be mathematical if they could turn their eyes to the principles of mathematics to which they are unused.2

The reason, therefore, that some intuitive minds are not mathematical is that they cannot at all turn their attention to the principles of mathematics. But the reason that mathematicians are not intuitive is that they do not see what is before them, and that, accustomed to the exact and plain principles of mathematics, and not reasoning till they have well inspected and arranged their principles, they are lost in matters of intuition where the principles do not allow of such arrangement. They are scarcely seen; they are felt rather than seen; there is the greatest difficulty in making them felt by those[Pg 2] who do not of themselves perceive them. These principles are so fine and so numerous that a very delicate and very clear sense is needed to perceive them, and to judge rightly and justly when they are perceived, without for the most part being able to demonstrate them in order as in mathematics; because the principles are not known to us in the same way, and because it would be an endless matter to undertake it. We must see the matter at once, at one glance, and not by a process of reasoning, at least to a certain degree. And thus it is rare that mathematicians are intuitive, and that men of intuition are mathematicians, because mathematicians wish to treat matters of intuition mathematically, and make themselves ridiculous, wishing to begin with definitions and then with axioms, which is not the way to proceed in this kind of reasoning. Not that the mind does not do so, but it does it tacitly, naturally, and without technical rules; for the expression of it is beyond all men, and only a few can feel it.3

Intuitive minds, on the contrary, being thus accustomed to judge at a single glance, are so astonished when they are presented with propositions of which they understand nothing, and the way to which is through definitions and axioms so sterile, and which they are not accustomed to see thus in detail, that they are repelled and disheartened.

But dull minds are never either intuitive or mathematical.

Mathematicians who are only mathematicians have exact minds, provided all things are explained to them by means of definitions and axioms; otherwise they are inaccurate and insufferable, for they are only right when the principles are quite clear.

And men of intuition who are only intuitive cannot have the patience to reach to first principles of things speculative and conceptual, which they have never seen in the world, and which are altogether out of the common.4


1From Allan Bloom The Closing of the American Mind: How Higher Education Has Failed Democracy and Impoverished the Souls of Today’s Students (p. 52):

Every Frenchman is born, or at least early on becomes, Cartesian [the mathematician above] or Pascalian [the intuitive]…Descartes and Pascal represent a choice between reason and revelation, science and piety, the choice from which everything else follows…These great opponents whom no snythesis can unite—the opposition between bon sens and faith against all odds—set in motion a dualism…

It was, therefore, very French of Toucqueville to say that the Americans’ method of thought was Cartesian…

2The great fallacy is to suppose we can do with only one of these types (even inside one body). American and British thought plunges headlong into the mathematical—we are all Cartesians here. This isn’t a new observation. Tocqueville said “each American appeals to the individual exercise of his own understanding alone. America is therefore one of the countries in the world where philosophy is least studied, and where the precepts of Descartes are best applied…they follow his maxims because this very social condition naturally disposes their understanding to adopt them.”

Strict Cartesianism leads to scientism and the worship of rationality and reason as if these could live without intellection, what Pascal called intuition. No mathematician could even begin to think without intellection. Intuition, used in this special sense, is necessary and prior to logic, mathematics, and ratio. Axioms, for instance, are not provided by rationality. Pure rationality is always incomplete. I’ll have much more to say about this in the coming weeks.

3It is well to put it here the fallacy that says that because sometimes our intuitions fail us that they always do. Sometimes our mathematical reason also fails us, but nobody would claim that therefore all of mathematics should be tossed or is suspect (except radical skeptics; paradoxically, personages only found in Western universities).

4Relying only on one leads to rank pedantry, sterility, and blind alleys.


  1. Ken

    While drawing on medieval analyses, consider [some of] what those were then based upon: explains how the Bible is right & science is wrong that the Copernican Model of a rotating, orbiting Earth is a fact-less, observation-denying deception that is the keystone which is holding up all of modern man’s false “science” and “knowledge”. It’s time for the truth; here’s where to find it:

    Some background:

  2. Ken

    A reference not to be missed: The Warfare of Science with Theology in Christendom by White, Andrew Dickson. Transcribed by Cosma Rohilla Shalizi. New York: Appleton, 1896:

    Includes a large section on the Galileo Affair as well as stuff on geocentrism, flat-earthism, & creationism. It appears as if Shalizi has transcribed the entirety of this hundred-year-old work to hypertext. A truly excellent resource in the history of science. White founded Cornell University as the first explicitly secular university in the United States.

  3. john b


    Those are fascinating

  4. JohnB

    By-the-by, I meant fascination more in regards to “fixedearth”…

    I am one who believes in the ‘Caesar rule’

    Anyone who sees only the single side of the coin, I find tedious

  5. JohnB

    Which is of course the point of the post (paraphrasing note 4)

    Relying only on one (side of the coin) leads to rank pedantry, sterility, and blind alleys.

  6. Ken

    @ john b — “fascinating”

    It never ceases to amaze me how the Bible is stretched to align with this or that viewpoint…should be printed on thin latex, or Silly Putty. Somewhere I happened upon a website that was adamant the Earth was the center of the universe, had rebuttals to astronomy, the Apollo missions, etc., etc. including some enjoyable audio presentations. Couldn’t find it…but it’s fun, though for most not fun in the way intended by the authors.

    Silliness aside, what too often happens (including this blog, with regularity) is people naturally interpret & envision options based on contemporary perspectives — when reviewing medieval (or older) references one needs to understand their perspectives, which were very very different (things like parallel universes, matter/energy transitions, etc. were beyond their ability to imagine much less comprehend).

    When one properly comprehends what an ancient author perceived/what that author could not possibly have perceived, one comes to realize that modern interpretations/explanations cannot possibly be consistent with what the medieval author could have possibly meant–even though the “plain meaning” of the words is oh-so-clear, the underlying concepts & interpretations were originally very very different.

    Kind of like someone interpreting this scene, in English, that nobody today would interpret literally & contrary to the subtitles:


    ….do precisely the same thing–interpret the words literally–in a document that’s a hundred, or thousand-plus, years old and nobody bats an eyelash.

  7. Ken, you do understand that historians of science regard Dickson White’s work as notorious tosh and for good reasons.

  8. Ken

    RE: historians of science regard Dickson White’s work as notorious tosh and for good reasons

    Of course I recognized that, and the other references, are “BS” — that’s the whole point. Namely, this obvious nonsense exists & is founded on the same shaky foundation as things presumed factual [based on philosophical logical gymnastics]…and…that a sizeable proportion of that nonsense creeps into the justifications of areas taken for granted.

    Read the nonsense, tosh, BS…call it what you will to recognize it & not reproduce it.

    Closely related, in the religious discussions, have been numerous commentaries that express views, proffer explanations, etc. that have been and remain formally heretical per the authorities for the particular faith professed.

  9. Ken, I’m trying to understand what point you’re making. Is it that Holy Scripture should not be taken literally, that it’s totally worthless or ???

  10. John B

    Ken said : …the religious discussions, have been numerous commentaries that express views, proffer explanations, etc. that have been and remain formally heretical per the authorities…

    The views expressed in this commentary are not necessarily…

    Yes, Ken, I am an heretic. I could be considered a skeptic BOTH climatologically speaking and theologically (especially in appealing to authority); however…
    I do believe in God
    I even believe in Jesus Christ and the Holy Spirit

    I grew up Roman Catholic (with all the trappings).I had a very brief tour of pre-Vatican II although the only thing I remember from Latin Mass was “Per ipsum, et cum ipso, et in ipso…”. Spent another ten thereafter.

    A long time ago, I tried not to believe. Tried to give up God.

    It didn’t take. ‘God’ wouldn’t stand for it.
    So I tried to approach ‘God’ intellectually. Tried to make him fit with me.
    Nope. God wouldn’t comply (Some might consider me an unarmed man, anyway – I have troubles getting through many of Briggs’ posts).

    Although I learned a lot about ‘God’, that wasn’t what He wanted.

    Eventually, watching others, I learned to love God (NOT necessarily how). In fact, it was easier watching them in their unguarded moments, rather than their guarded “I am a Christian – watch me worship” moments.

    I challenge myself almost daily, listening to “Christian” radio, “Catholic” radio (EWTN), whatever…

    I hear some of the words coming out of their mouths, and am dismayed; other times their “challenges” cause me to rethink and reinvestigate. Even where I am “dismayed”, it still forces me to “give a reason” even if only to myself.

    That’s my intellectual outlet that God still allows me, but I’ve got to keep up the whole heart and soul part. Part of that comes into play when I disagree with or am “dismayed” by the views of others. Those “two most important commandments” are pretty kick-ass.

    So dismayed by the fixedearth, I may very well investigate some more.

  11. Thanks, but I am waiting until it’s treated on this blog, as it is part of the pensees. Browsing through the translation, Pascal is far better reading material than Aquinas, who is very slow in his argumentation. Aquinas reads like Moby Dick, it takes 200 pages to set sail.

  12. Possibly Pascal’s most profound thought was that it was impossible to show from reason along that God exists (so much for Aquinas and Anselm):
    “If there is a God, He is infinitely incomprehensible, since having neither parts nor limits, He has no affinity to us. We are then incapable of knowing either what He is or if He is.”
    (Pensees, #233).
    So it is only by faith that we truly know His existence.

  13. @ Bob Kurland

    I know that it is a common belief that Pascal didn’t think that one could demonstrate God’s existence, but it is simply not true, and has only been perpetuated because people only take the time to read the Wager and surrounding thoughts from his Pensees. For instance, he says elsewhere:

    “Therefore I shall not undertake here to prove by natural reasons either the existence of God, or the Trinity, or the immortality of the soul, or anything of that nature; not only because I should not feel myself sufficiently able to find in nature arguments to convince hardened atheists, but also because such knowledge without Jesus Christ is useless and barren. Though a man should be convinced that numerical proportions are immaterial truths, eternal and dependent on a first truth, in which they subsist and which is called God, I should not think him far advanced towards his own salvation.”
    (Pensees, #556).

    If one further reads the context around this quote, it shows Pascal’s true position on this matter; reason can prove God’s existence, it’s just that Pascal does not think that it is a particularly useful dialectical tactic against hardened skeptics, since such an argument could only at best prove to them that there is an author of nature, and not that Jesus Christ is God.

    As for what you quoted, note that it comes from the famous Wager passage itself, which is presented as a dialog with a hypothetical agnostic. The statements that he gives there could easily be interpreted as just being concessions to the agnostic for the sake of argument, and not as representative of Pascal’s own view on the matter. And in fact, given the quote I have provided, I submit that this is in fact how we should understand him.

  14. RobR

    Ken, If the Universe is infinite, then the Earth is at the center, so is every other place.

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