Ethics 1 Proposition 8 states that "Every substance is necessarily infinite", but in Scholium 2 he states: "there exists only one substance of the same nature.

I'm confused by him saying "every" substance and then saying there exists "only one substance", those two contradict one another don't they?

In what way is substance infinite according to proposition 8?

  • It's no more contradictory than saying that a grain of sand is sand, as much as a beach is sand. Both are sand, yet in different ways. A drop of water is water, and a lake or ocean is also water. An individual person is human as much as a crowd of people is also human. The sun is a star, and a galaxy contains lots of stars. The universe contains all of the above, yet is infinite. – Bread May 1 '18 at 1:13
  • You are ignoring the notion of 'nature', the second half of the second assertion is disappearing. – user9166 May 1 '18 at 17:12


I see the problem : 'every' = 'all' or 'each' but neither term applies if there is only one. The Latin is : Omnis substantia est necessario infinita. On the surface it would have been better, more intelligible, if Spinoza had said something like 'Substance as such is infinite', which would be perfectly consistent with there being only one substance.

Something definitely needs explanation. There are two main possibilities :

1 Spinoza has simply made a logical mistake

2 Spinoza is moving from one sense of substance to another and P8 is caught in the transition.

It is perfectly possible that Spinoza simply has made a logical mistake but I prefer the second explanation, which I think more likely.


A plurality of substances was a perfectly standard idea in Aristotle. Very roughly a substance (ousia) was whatever qualities, quantities, and the other categories inhered in as their support. There could not, for instance, be a quality unless it was a quality of a substance; it could not exist on its own but needed to be a quality of something, namely a substance. Aristotle assumed that there were indefinitely many substances. Descartes held that there was ultimately and strictly only one substance, namely God, but granted de facto substance-status to mind and matter.

This is the working idea from which Spinoza starts. There was general agreement (though Locke had his difficulties) that substances exist. Hence he is ready to talk of 'two substances' in I. P2. But the assumption of a plurality of substances is only a concession to the standard way of talking. There is a pointer to his own view of the single substance in I.P5 but he is still working with the standard view in I. P8.

Then in Scholium [Note] 2 to I. P8 he reveals his hand, develops his own distinctive position : 'there exists only a unique substance of the same nature' (Spinoza, Ethics, tr. G.H.R. Parkinson, Cambridge : CUP, 2000, 80) - substantiae existentiam ... eiusdem naturae. So how do we get to this point ?

We need to go back to I.P7 : 'It belongs to the nature of substance to exist' (Parkinson, 78). Its existence follows from its nature, and that nature is to be self-dependent, self-contained; to be in Spinoza's language 'that which is in itself' (I, Def, 3 : quod in se est; Parkinson, 75). It cannot be self-dependent and self-contained if there is another substance which can act as an external cause or limitation. Hence 'there exists only a unique substance of the same nature'.

'Of the same nature' : an enigmatic little addendum. I think what he means is that a substance has or supports attributes. There is, Spinoza thinks, an infinity of attributes I. Prop. 11; Parkinson, 82) of which we are acquainted with only two, namely thought and extension (II, Axiom 5; Parkinson, 114). 'Of the same nature' means that there could not be two substances having or supporting the same attributes (attributes of the same nature), else one substance could act as an external cause or limitation in regard to the other in respect of those attributes. But since Spinoza's substance has an infinity of attributes, i.e. all the attributes there are, the existence of a second - any second - substance is impossible on pain of its acting an an external cause or limitation.

On the matter of substance's being infinite, I think infinity follows from the infinity of its attributes, and (more basically) from the one substance's nature as self-contained and unlimited by any other substance. This makes it all-inclusive, hence in one sense infinite.

It's no easy task to make full sense of Spinoza. I have simply offered the best I can.


Spinoza, Ethics, tr. G.H.R. Parkinson, Cambridge : CUP, 2000. See Introduction, 55-7.

Joel I. Friedman, 'An Overview of Spinoza's "Ethics"', Synthese, Vol. 37, No. 1, Spinoza in Modern Dress (Jan., 1978), pp. 67-106.

William Charlton, 'Spinoza's Monism', The Philosophical Review, Vol. 90, No. 4 (Oct., 1981), pp. 503-529.

Stuart Hampshire, Spinoza, London : Penguin, 2007.

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    I think this answer is great 👍🏽 – Joseph Weissman Apr 30 '18 at 15:17
  • Text amended (at end) to cover the infinity of substance. – Geoffrey Thomas Apr 30 '18 at 15:22
  • @Joseph Weissman. Comment very much appreciated. Thank you - Geoff – Geoffrey Thomas Apr 30 '18 at 15:24
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    Thanks for the answer. I came to the same conclusions you posted i.e. infinite refers to infinite attributes and Spinoza is updating the theory in real time. – Robert C May 1 '18 at 11:38
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    @Robert C. Good to get some agreement in philosophy ! All the best - Geoff – Geoffrey Thomas May 1 '18 at 12:05

Spinoza is new to me.

His starting place of the definition of substances is God, being the primary substance, which is infinite and singular.

As with all philosophical arguments you need to start from their assumed premise. I also find the assumption that a substance can be created, however you define such a thing, and then suggests it exists in that form infinitely. The fact it was created by definition means it had a point where it did not exist, so equally in the future can have a point where it no longer exists. So within this logic an infinite thing has no beginning and no end, and will always be so, while everything else is indeterminate, ie has the potential for infinity going forward, but is not guaranteed.

I would like to see an argument that disproves this proposition, but then I am new to such propositions.

The word substance, appears to mean the existence of everything has a substance to it. So it is as infinite as much as everything that exists, so one has already assumed substance to be infinite, as there are no boundaries to the definition as it includes all existence and anything one might discover as existing. Equally by using this concept you will only get the conclusion one substance exists, because by defining it on this basis, anything that could be called another substance is not by definition of what a substance is.


Every number can be used infinitely many times, yet there is only one number of each size. There is no logical problem here. The two statements are not really related.

The same way 'size' is an aspect of numbers that completely differentiates them, 'nature' is an aspect of substances that completely differentiates them. That has nothing to do with whether or not the substance can be used up or limited in the same way having different sizes has nothing to do with whether any given number can be 'used up' or 'worn out'.


You could consider this like a proof by contradiction. Assume there are multiple substances... If we can show in general that the idea of two substances must actually be inherently contradictory, we have proved the “unicity”, the unity or singularity of substance.

  • Or at least that some other hypothesis might hold; we’d also have to assume “there are one or several substances” – Joseph Weissman Apr 29 '18 at 16:33

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