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Spinoza's Proof to Prop.X says

"An attribute is that which the intellect perceives of substance, as constituting its essence (Def. IV.) and, therefore, must be conceived through itself Def. III.)."

Following note there doesn't make it any clearer for me as it goes even more confusing!

Does he means by 'intellect' here a human, or is it meant God? And what is the exact meaning of 'constituting' here (constituens) as this word can have so many different meanings? And what must be conceived through itself, is it God (substance)(Def.III is about substance) or an attribute?

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    For "intellect", I think it is meant the human one.
    – Mauro ALLEGRANZA
    Dec 3, 2016 at 13:55
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    See Spinoza's Theory of Attributes : Extension is a divine attribute.
    – Mauro ALLEGRANZA
    Dec 3, 2016 at 14:01
  • Extension - so perhaps 'constituting' its essence' means 'make, create'? @MauroALLEGRANZA
    – Aili J.
    Dec 3, 2016 at 14:13
  • Can be useful to read Principia philosophiae cartesianae, Spinoza commentary on Descartes, Principia. You can find freely the 1905 English translation. See page 19 for the "classical" example of te triangle and the fact that "the sum of the angles is 180°" : this is part of the essence of the riangle.
    – Mauro ALLEGRANZA
    Dec 3, 2016 at 14:21
  • Similarly - for Descartes - God is "trustworthy" : he is perfectly true, i.e. this is part of God's essnce. These are example of attributes : we conceive a triangle with its three angles forming 180°; we cannot conceive the triangle and at the same time deny its "essential" characteristic of having... (all this before non-euclidean geometries).
    – Mauro ALLEGRANZA
    Dec 3, 2016 at 14:24

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I suggest you to use some modern commentary, like :

or :

For a more detailed study, see :

Substance is in itself; this means that a substance is self-subsistent: it depends on itself alone.

Thus, the concept of a substance (our conceiving it) is not formed from the concept of another thing. A substance requires nothing beyond itself to exist and to be understood.

With his definition of attribute ("what the intellect perceives of a substance, as constituting its essence") Spinoza does not adopt a "subjective" point of view; he means that attributes are the different ways in which a substance can be perceived. The intellect perceives a substance not as "pure" being but through one of its attributes.

An attribute is the substance itself, as perceived in a certain way.

See Curley, page 24, for the example regarding omniscience. Omniscience is not an attribute of God because it is not a "fundamental" property: it presuppose thought. An omniscient being must be thinking, but a thinking being must not be omniscient.

So omniscience [...] is only a mode of the thinking thing, rather than an attribute of substance.

We perceive being as either as physical bodies or as minds. We perceive substances as extended and as thinking.

According to Descartes, extension and thinking are the fundamental properties of substances.

For Spinoza, extension and thinking are not properties of a substance, but rather two different "ways" that a substance can be perceived.

Extension and thinking are two expressions of the essence of substance.

According to P.II, two substances having different attributes have nothing in common with one another: they are two separate beings that are perceived in two separate ways.

Thus, each substance exists independently of the other, and is conceived independently, of the other.

According to Descartes, there could be multiple substances of the same attribute (many distict bodies all endowed with extension).

For Spinoza, this is not possible (P.V): two substances sharing the same attribute exist and are perceived as the same thing. Two substances with the same "essential characteristic" cannot be distinguished; therefore they are the same thing. There cannot be multiple substances sharing the same attribute.

Thus, there cannot be multiple substances sharing the attribute "thinking" or multiple substances sharing the attribute "extension". Since there cannot be two or more substances of the same attribute, there can be only one thinking substance and one extended substance.

Since distinct substances (if any) have nothing in common (different attributes implies different essences) they cannot cause or produce one another. A substance must therefore be "cause of itself" (P.VI). This implies that:

its essence necessarily involves existence, or existence belongs to its nature (P.VII).

Substance may have more than one attribute: there may be two, three or more ways of perceiving what it is. A substance could have infinite attributes, infinite ways of express its being. But, according to D.VI, a substance of infinite attributes is God.

Assuming this simplified reading of Part I (titled : Concerning God) of Spinoza's Ethics, what is the meaning of :

Prop.X. Each particular attribute of the one substance must be conceived through itself.

Proof. An attribute is that which the intellect perceives of substance, as constituting its essence (D.IV), and, therefore, must be conceived through itself (D.III).

Spinoza is clearly alluding to Descrtes' metaphysics, with his dualism of mind (the thinking thing) and body (the extended thing).

We conceive thinking and extension as distinct and independent attributes; but from this - according to Spinoza - we cannot infer that they pertain to two different and independent substances.

In the Note Spinoza says :

It is, then, far from an absurdity to ascribe several attributes to one substance : for nothing in nature is more clear than that each and every entity must be conceived under some attribute, and that its reality or being is in proportion to the number of its attributes expressing necessity or eternity and infinity.

Consequently it is abundantly clear [???], that an absolutely infinite being must necessarily be defined as consisting in infinite attributes, each of which expresses a certain eternal and infinite essence.

Is this really consequence of the proof of P.X ?

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  • "...consequenter nihil etiam clarius quam quod ens absolute infinitum necessario sit definiendum (ut definitione 6 tradidimus) ens quod constat infinitis attributis quorum unumquodque æternam et infinitam certam essentiam exprimit. " Perhaps Spinoza just meant this Def VI acts here as a proof?...
    – Aili J.
    Dec 3, 2016 at 21:01

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