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  Pascal's Wager is the opportunity for a mathematician turned theologian to justify their view of cosmic order in the mathematical ways they've come to know.  What's the pay off if you're right and what's the pay off if you're wrong.  If the pay off for being right far outweighs that for being wrong, should we out of principle take the wager? Ask Laplace and we have a different framing.  Now probability has replaced the divine role so the aspect of choice has been eliminated.  Probability no longer informs a bet on divine order, divine order is a subsidiary part of probability.  Laplace's famous demon is not an impossible gambit on an all-controlling deity as popularly assumed, but a thesis that cosmic order can be predicated by sheer mathematical analysis.  Pascal's world still contains Christian state law, but Laplace's does not.  How do we culturally bind people without such moral institutions? It turns out fairly easily.  We don't need to ge

  From the Renaissance to the Enlightenment, Europeans are all about the geometric approach.  The approach from Euclid.  When Galileo says that the universe speaks in mathematics, he's thinking about geometry.  When Newton writes the Principia, he does so following a geometric method.  His fluxions, or calculus, would allow otherwise, but somehow it still seems proper to construct the concepts geometrically. Of course this is not really Euclid, but the European reimagining of Euclid.  And as algebras advance, so do new geometries.  Fast forward to the end of the 18th century.  Kant talks what we can know and what we can't.  A priori knowledge is innate, what we know before experience, what he also calls analytic.  Synthetic knowledge on the other hand comes from experience, what he calls a posteriori.  But mathematics and geometry are something different.  He calls them the synthetic a priori. Like a priori knowledge, math is constructed in the mind, like synthetic knowledge it

Early modern formalizations of what is retrospectively called scientific practice (then a natural philosophical one) centre around geometrical methods and their experimental power.  From Galileo to Descartes, Pascal, Newton and Leibniz, commitment to visual mathematical techniques are paramount in bringing to bear an effective accumulation of knowledge.  It is a literate rationalism, bodies in space that offer a protocol for mechanical reproduction.  Galileo's  language of the universe becomes a necessary part of knowledge gathering, of the experimental trials that he put its formal predictions to. Fast-forwarding from the anticipations of Leibniz to the work of Peirce, Carroll and Wittgenstein, geometric diagrams are infused with symbolic and algebraic universality that progresses with time.  The visual proof and model takes a formal role in the development of mathematical foundations; and reasoning, now in a more pragmatic vein, comprises what we ascribe to the new social role of