Spinoza on Infinity

“The question of the infinite has universally been found to be very difficult, indeed, insoluble.”[1] Questions of the infinite are notoriously problematic because once one accepts that infinities exist, it seems one runs into contradictions. For instance, Spinoza provides an example; “if an infinite length is measured in feet, it will have to consist of an infinite number of feet; and if it is measured in inches, it will consist of an infinite number of inches. So one infinite number will be twelve times greater than another infinite number.”[2]

However, Spinoza, like all the other rationalists, cannot so easily part with the idea of the infinite. This is because the Infinite is an idea which is presented to the mind immediately, and is not an idea we arrive at by negating the finite, as the rationalists maintained. I just wrote a final term paper on defining rationalism in which I argued that Rationalism was best defined as: “the commitment to the reliability of one’s rational intuition as an indubitable means to discovering indubitable truths.” The infinite, they maintained, was an idea which was presented to the mind by intuition. This explains why the rationalists held on to the idea of the infinite with such tenacity.

Spinoza explains, therefore, that there are legitimate inferences to the infinite, and illegitimate ones. In a series of letters written from 1661-1665 to interlocutors of his he explained this in detail:

“The question of the infinite has universally been found to be very difficult, indeed, insoluble, through failure to distinguish between that which must be infinite by its very nature or by virtue of its definition, and that which is unlimited not by virtue of its essence but by virtue of its cause.”

“Then again, there is the failure to distinguish between that which is called infinite because it is unlimited, and that whose parts cannot be equated or explicated by any number, although we may know its maximum and minimum. Lastly, there is the failure to distinguish between that which we can apprehend only by intellect and not by imagination, and that which can also be apprehended by imagination. I repeat, if men had paid careful attention to these distinctions, they would never have found themselves overwhelmed by such a mountain of difficulties. They would clearly have understood what kind of infinite cannot be divided into, or possess any parts, and what kind can be so divided without contradiction. They would also have understood what kind of infinite can be considered, without contradiction, as greater than another infinite, and what kind cannot be so conceived. This will become clear from what I am about to say.”[1]

Therefore, interestingly, he concludes; “it is obvious from the above that Number, Time and Measure, being merely aids to the imagination, cannot be infinite”[1]

In considering this, I realized that Spinoza here may inadvertently be providing the means to create a stronger Kalam Cosmological argument then is available to us for those of us who suspect that Dr. Craig overstates when he denies the reality of any infinite whatever. Instead, perhaps we can use Spinoza’s suggestion here to demonstrate that the kind of infinity which a universe with backwards eternal duration would need is not a legitimate one. The argument could then be just as plausibly strong as Craigs, and it wouldn’t commit us to the dismissal of all infinites. Alexander Pruss does something similar here; I do note in passing that Pruss’ third stipulation, that an infinity of objects could simultaneously co-exist, is one I think Aquinas would not accept, as I pointed out here.

In any case, it is clear that anything which is merely an aid to the imagination cannot, for Spinoza, be an actually infinite thing. Moreover, something can rightly be said to be infinite only if it is infinite in virtue of its nature and/or definition. On the other hand, something can be wrongly said to be infinite if it is infinite by virtue of its cause. Spinoza explains, according to his philosophical system, that substance is that which is infinite by its essence, and Modes of substance (what the Scholastics called ‘substance’) are only infinite be-cause of Substance. However, that one could tease out from Spinoza directly a way to rehabilitate Kalam cosmological arguments seems improbable, for he says near the end of the letter:

“However, in passing, I should like it here to be observed that in my opinion our modern Peripatetics have quite misunderstood the proof whereby scholars of old sought to prove the existence of God. According to a certain Jew named Rabbi Chasdai, this proof runs as follows: “If there is granted an infinite series of causes, all things which are, are also caused. But nothing that is caused can exist necessarily by virtue of its own nature. Therefore, there is nothing in Nature to whose essence existence necessarily pertains. But this is absurd. Therefore the premise is absurd.” So the Force of the argument lies not in the impossibility of an actual infinite, or an infinite series of causes, but in the assumption that things which by their own nature do not necessarily exist are not determined by a thing that necessarily exists by its own nature.”[1]

[1] Spinoza, From the Letters to Oldenburg and to Meyer (1661-65),

[1] Spinoza, From the Letters to Oldenburg and to Meyer, p.139

[2] Spinoza, The Ethics, p.150


About tylerjourneaux

I am an aspiring Catholic theologian and philosopher, and I have a keen interest in apologetics. I am creating this blog both in order to practice and improve my writing and memory retention as I publish my thoughts, and in order to give evidence of my ability to understand and communicate thoughts on topics pertinent to Theology, Philosophy, philosophical theology, Catholic (Christian) Apologetics, philosophy of religion and textual criticism.
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