Polytropy

The general question of this post is of the relation between

• Pascal’s thinking in the Pensées and
• the thinking of himself and his contemporaries about the physical and mathematical worlds.

The specific question is why Pascal juxtaposes Abraham and Gideon in two fragments of the Pensées.

A simple answer to the specific question is that

• God demands a sacrifice of each man, and
• the sacrifice is followed by a miracle.

For the general question, I have no clear answer. In the reading of the Pensées being documented on this blog, not till the eleventh week shall we reach Brunschvicg fragment number 1, which is Lafuma 512 and Sellier 670, headed Différence entre l’esprit de géométrie et l’esprit de finesse.

So far at least (Sellier 1–451, our first seven weeks), Pascal often grounds his comments in references to the Old Testament, the Apocrypha, or the New Testament. I fancy this blog reflects a similar impulse, for textual if not specifically Biblical grounding.

I wonder whether Pascal would say he searches the Bible for knowledge, in the way he has searched

• physical experience, for Pascal’s Law, which allows for the hydraulic press;
• geometrical intuition, for knowledge of such things as the conic sections, as reflected in Pascal’s Theorem.

I myself do not expect anything like theorems or physical laws to come from the Bible. However, that collection of scriptures is a repository for law of an earlier kind. It strikes me as unsatisfactory that Wikipedia currently makes no clear connection between

• “Law,” whereby

  Law is a system of rules created and enforced through social or governmental institutions to regulate behavior,

• “Law (principle),” whereby

  A law is a universal principle that describes the fundamental nature of something, the universal properties and the relationships between things, or a description that purports to explain these principles and relationships.

The relation between these two conceptions of law is investigated by Collingwood in The New Leviathan: Man, Society, Civilization, and Barbarism (1942). I investigated this book in five years of reading and blogging. Wikipedia defines law using words like rule and principle that are no more fundamental than law. I think it must be from our being subject to law, and knowing ourselves to be, that we derive the notion that the physical world is subject to law. Collingwood looks at how European civilization is based on Roman law; the relation to Jewish law should be investigated as well. I might think it must have been investigated, except that Collingwood’s own work seems not to be as well known as I might have expected it to be.

I turn to the specific question of this post.

All of Pascal’s Pensées are gathered on a single webpage, created by Philippe Misandeau. Searching the page for the name of Gédéon, I find it but twice, and then only in conjunction with Abraham, in Lafuma fragments 892 and 903, which are Sellier 446 and 450.

What is the connection between Abraham and Gideon? In the Pensées, Abraham himself is mentioned about twenty times, but not, I think, or not usually, with any particular personal detail.

At Les Pensées de Blaise Pascal, the rich scholarly website of Dominique Descotes and Gilles Proust, on the page of commentary on Sellier 446, Sellier is cited for the following remarks (which may be a direction quotation or a paraphrase; the translation is mine):

L’Abraham de Pascal n’est pas celui de la justification par la foi, cher à saint Paul. Pascal est muet, sur l’épisode de Sodome, sur la bigamie d’Abraham, sur les mensonges du patriarche à Pharaon et à Abimelech, et surtout sur le sacrifice d’Isaac. // The Abraham of Pascal is not he of justification by faith, dear to St Paul. Pascal is mute on the episode of Sodom, on the bigamy of Abraham, on the lies of the patriarch to Pharoah and Abimelech, and especially on the sacrifice of Isaac.

I am going to suggest that Pascal may not be entirely mute on the sacrifice.

On the same page of commentary, what is said about Gideon is based on Judges 6:36–40. Briefly, God says Gideon will save Israel from the Midianites, and Gideon asks for a sign of this, and God gives a sign:

36 And Gideon said unto God, If thou wilt save Israel by mine hand, as thou hast said,
37 Behold, I will put a fleece of wool in the floor; and if the dew be on the fleece only, and it be dry upon all the earth beside, then shall I know that thou wilt save Israel by mine hand, as thou hast said.
38 And it was so: for he rose up early on the morrow, and thrust the fleece together, and wringed the dew out of the fleece, a bowl full of water.
39 And Gideon said unto God, Let not thine anger be hot against me, and I will speak but this once: let me prove, I pray thee, but this once with the fleece; let it now be dry only upon the fleece, and upon all the ground let there be dew.
40 And God did so that night: for it was dry upon the fleece only, and there was dew on all the ground.

Is anybody then allowed to ask God for a sign before undertaking something difficult? Perhaps it depends on whether you think God is asking you to do it in the first place.

The story from Judges can be a sign for us readers: that Israel will be bedewed with the grace of God, when all other nations are lost in the desert of idolatry; but then the reverse will happen. This is talked about in La Bible de Port-Royal, or Bible de Sacy, on the last two of the many pages of commentary (they are pages 428–446) that follow Judges 6. I have just linked to a facsimile edition, not easy to read; Wikisource has the text of the Bible Sacy itself without the commentary, from an 1855 edition.

The Wikipedia article on Gideon suggests that, when an angel sits under a tree to talk to Gideon, as in Judges 6:11–2, this echoes how, when visitors come to Abraham, he feeds them under a tree, in Genesis 18:1–8. I’m afraid the analogy is out of place on Wikipedia, unless a known commentator can be cited for it.

On my personal blog, I can suggest an analogy that may be no tighter: that God asks both Abraham and Gideon for a sacrifice.

For no stated reason, God asks Abraham to sacrifice his son Isaac, in Genesis 22. Abraham is willing, but prevented, and then seemingly rewarded.

15 And the angel of the Lord called unto Abraham out of heaven the second time,
16 And said, By myself have I sworn, saith the Lord, for because thou hast done this thing, and hast not withheld thy son, thine only son:
17 That in blessing I will bless thee, and in multiplying I will multiply thy seed as the stars of the heaven, and as the sand which is upon the sea shore; and thy seed shall possess the gate of his enemies;
18 And in thy seed shall all the nations of the earth be blessed; because thou hast obeyed my voice.

We have seen that Gideon asks God for two signs with the fleece. Before that, he asked for an unspecified sign, and God told him to prepare a sacrifice. He did, of a kid and some cakes. Then the angel caused the offerings to be consumed by a fire that rose from a rock (Judges 6:17–24).

After that, God told Gideon to replace an altar to Baal with an altar to God, and to make sacrifice on that altar (Judges 6:25–32).

Are Abraham and Gideon then connected for Pascal because God asked each of them to make a sacrifice? All Pascal says directly about the pair as such is the following (but see the seventh reading for the whole of each fragment):

• (S 446, L 892) Abraham, Gédéon : signes au-dessus de la Révélation. Les Juifs s’aveuglaient en jugeant des miracles par l’Écriture.

• (S 450, L 903) Abraham, Gédéon. Confirmer la foi par miracles.

Apparently Havet thinks signes should be sont. The manuscript (pdf) is in a neater hand than Pascal’s and has something like siny here. In any case, the two personnages are somehow “above” revelation or scripture. Each one confirms his faith through a miracle:

• Abraham’s faith, or obedience, is rewarded by the miracle, so to speak, of getting to keep his son after all; but this faith needed the miraculous birth of Isaac in the first place, to a woman, Sarah, who was beyond menopause.

• Gideon’s faith needs a miracle before the man will go off to fight the Midianites.

That’s what I get, when I look for a law behind Pascal’s juxtaposition of the two names. I have no specific evidence that there is such a law. Neither, I would say, did Pascal have any evidence that there would be a law governing fluid pressure. Believing that there could be such a law, he found it. This will not always happen.