Two Necessities

A square tablecloth spread on a rectangular table will hang from the table edges same as before if the cloth is rotated ninety degrees lying on the table. A rectangular cloth not square—a cloth made longer in one length, shorter in the other—will require two rotations of ninety degrees to hang from the table edges same as before. We can open our geometry books and find that such facts are aspects of the rotational isometries of quadrilaterals.

Facts of pure geometry can have explanatory value to us for some facts about table cloths. I should distinguish two sorts of necessities in pure geometries. One sort is the plain necessity of geometric facts, such as one-hundred-eighty degrees being the sum of the angles in any triangle in the Euclidean plane or such as any square’s diagonal being not of any integer-ratio to the length of its sides. The other sort is the necessity between if and then in the inferences one makes in proving such results. Continue reading


[This is an Addendum to my paper on Descartes/Rand in the current issue of Journal of Ayn Rand Studies.]

Kant argued against Descartes’ view that the existence of one’s mind is more immediately and more certainly known than the existence of one’s body.[1] Kant cast out Descartes’ view that the mind is a thinking substance.[2] Because Kant rejected also Descartes’ ontological proof for the existence of God,[3] Descartes’ first philosophy collapses. Metaphysical arguments to rational necessity of the existence of God or immortality of the soul are all cases of reason flapping its wings in a vacuum, by the lights of Kant. The Critique of Pure Reason (KrV) contains Kant’s case for a more limited scope for effective theoretical reason: stay within the bounds of possible sensory experience.

Kant accepted, as had Descartes and Aquinas before him, some notion that ‘I think’ entails ‘I am’. Then again, with Rand’s mature philosophy, acknowledgment that ‘Existence exists’ entails existence of one who acknowledges. For Kant, contra Descartes, ‘I think’ does not mean I think with a mental substance,[4] radically distinct from body; and thinking of my body and of bodies outside me is as certain as the circumstance that I think and that I exist as a thinking thing.[5] Kant had a role for ‘I think’ basic to his transcendental idealism, and such is not the role it had in the first philosophy of Descartes. Let me call Kant’s the “company-role” of ‘I think’.

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Which Eternity?

Rand held her axiom Existence exists to include that the universe as a whole “cannot be created or annihilated, that it cannot come into or go out of existence” (1973, 25).[1] One would naturally suppose Rand was thinking that immunity from creation or annihilation means the universe has existed an endless time in the past and will exist an endless time in the future. Plausible as that picture appears, might the axiom Existence exists not strictly entail the endless duration of Existence? Continue reading

Dewey and Boydstun on Pure Mathematics

In my paper on Dewey’s 1915 book on German philosophy and WWI, I had quoted a general epistemological viewpoint maintained by Dewey: There are in truth “no such things as pure ideas or pure reason. Every living thought represents a gesture made toward the world, an attitude taken to some practical situation in which we are implicated.”

Irfan questioned whether I thought that correct when it comes to mathematics.

“Maybe it’s true of some parts of mathematics, but is it true of all of mathematics? Do professors of mathematics, or even college math majors, go into mathematics because it represents ‘an attitude taken to some practical situation in which we are implicated’”? Irfan inclined to think Dewey’s general position either implausible or as involving a very odd conception of “practical situation in which we are implicated.” He rather thought that math-folk got on with it due to an enjoyment of math-thought and perhaps, contra Dewey, a desire to escape from practical concerns. In any event, “it’s hard to make out what Dewey is trying to say.”

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John Dewey, Philosophy, and the German Aggression

(This is a paper I wrote in 2013. It has accumulated about 1650 reads at Objectivism Online, where I posted it. I imagine readers come across it there by the link to it and other articles of mine in “About Me” in my Profile there. // Irfan saw the link to it I posted on FB today, a century after WWI Armistice, and thought it might find interested readers here. So here I’ll try to post it now.)


Dewey and Peikoff on Kant’s Responsibility

Part 1 – Transcendental Idealism v. Experimental Pragmatism

John Dewey delivered three lectures in February 1915 that were published later that year under the title German Philosophy and Politics (GPP). Dewey attempted in this work to trace the contribution of some abstract philosophical ideas to the currents of German thinking that had contributed to bringing the world to its present situation. The Great War had been on for seven months. Hundreds of thousands had died already. Eight and a half million would die, and twenty-one million would be wounded, by the end of the war. Continue reading