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Spinoza argues that no two substances can share attributes. This is the way I understand it: modes can be fully explained via attributes. So, if we had two substances with the same attributes, they would produce the same modes and therefore be indistinguishable? Therefore, by the Leibniz’s laws, they would be the same substance.

My question is the following: If we had two substances, A and B, with the attribute of extension, why can’t they have different modes? One substance may, for instance, have a chair as one of its modes, whilst the other lacks chairs: they’re both extended substances with differing modes – which would allow us to tell them apart. Unless, there is no room for contingency whatsoever, and any extended substance will have the exact same modes all the time.

In other words, for a given attribute, is there only ever one deterministic set of modes that can possibly be produced from it, and no contingency at all? If there is contingency, surely we can have substances of the same attributes, but differing modes in which we can use to tell them apart. We can have a million extended substances, and it would be the exact same outcome every time. If Spinoza's system really is as deterministic as this, it seems to be quite the claim.

Thanks

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  • There is only one substance: Prop. XIV. Besides God no substance can be granted or conceived. Commented Oct 28 at 14:43
  • And see Prop. XXIX. Nothing in the universe is contingent, but all things are conditioned to exist and operate in a particular manner by the necessity of the divine nature. Commented Oct 28 at 14:44
  • Your confusion seems to lie in your own attribution about modes from the second sentence onward and beware indefinite and infinite may coincide, and if there's something deterministic there must be uncertainty in the same way as there're both long and short extensions of the attribute of extension relatively speaking... Commented Oct 28 at 22:59

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In Ethics book 1, P29, Spinoza states that given an attribute, there is, according to him indeed only one deterministic set of modes. So, there is no room for any contingency (underlinings are mine, quoted from Spinoza Ethics/Project Gutenberg):

PROP. XXIX. Nothing in the universe is contingent, but all things are conditioned to exist and operate in a particular manner by the necessity of the divine nature.

Proof.—Whatsoever is, is in God (Prop. xv.). But God cannot be called a thing contingent. For (by Prop. xi.) he exists necessarily, and not contingently. Further, the modes of the divine nature follow therefrom necessarily, and not contingently (Prop. xvi.); and they thus follow, whether we consider the divine nature absolutely, or whether we consider it as in any way conditioned to act (Prop. xxvii.). Further, God is not only the cause of these modes, in so far as they simply exist (by Prop. xxiv, Coroll.), but also in so far as they are considered as conditioned for operating in a particular manner (Prop. xxvi.). If they be not conditioned by God (Prop. xxvi.), it is impossible, and not contingent, that they should condition themselves; contrariwise, if they be conditioned by God, it is impossible, and not contingent, that they should render themselves unconditioned. Wherefore all things are conditioned by the necessity of the divine nature, not only to exist, but also to exist and operate in a particular manner, and there is nothing that is contingent. Q.E.D.

Note.—Before going any further, I wish here to explain, what we should understand by nature viewed as active (natura naturans), and nature viewed as passive (natura naturata). I say to explain, or rather call attention to it, for I think that, from what has been said, it is sufficiently clear, that by nature viewed as active we should understand that which is in itself, and is conceived through itself, or those attributes of substance, which express eternal and infinite essence, in other words (Prop. xiv., Coroll. i., and Prop. xvii., Coroll. ii) God, in so far as he is considered as a free cause.

By nature viewed as passive I understand all that which follows from the necessity of the nature of God, or of any of the attributes of God, that is, all the modes of the attributes of God, in so far as they are considered as things which are in God, and which without God cannot exist or be conceived.

Modes only appear to be contingent in reference to human lack of knowledge. In the note to P33 Spinoza writes:

A thing is called necessary either in respect to its essence or in respect to its cause; for the existence of a thing necessarily follows, either from its essence and definition, or from a given efficient cause. For similar reasons a thing is said to be impossible; namely, inasmuch as its essence or definition involves a contradiction, or because no external cause is granted, which is conditioned to produce such an effect; but a thing can in no respect be called contingent, save in relation to the imperfection of our knowledge.

A thing of which we do not know whether the essence does or does not involve a contradiction, or of which, knowing that it does not involve a contradiction, we are still in doubt concerning the existence, because the order of causes escapes us,—such a thing, I say, cannot appear to us either necessary or impossible. Wherefore we call it contingent or possible.

So, also if you would use Leibniz' criteria to determine if there is only one substance, you'd have to conclude that there is only one substance -- according to Spinoza. In the beginning of the Ethics Spinoza gives his own proof:

PROP. XIV. Besides God no substance can be granted or conceived.

Proof.—As God is a being absolutely infinite, of whom no attribute that expresses the essence of substance can be denied (by Def. vi.), and he necessarily exists (by Prop. xi.); if any substance besides God were granted, it would have to be explained by some attribute of God, and thus two substances with the same attribute would exist, which (by Prop. v.) is absurd; therefore, besides God no substance can be granted, or, consequently, be conceived. If it could be conceived, it would necessarily have to be conceived as existent; but this (by the first part of this proof) is absurd. Therefore, besides God no substance can be granted or conceived. Q.E.D.

This assumption that there is more than one substance may of course be seen as less 'absurd' than Spinoza thought, and his proof may be seen as less water-tight than he believed it to be. Anyway, I think it's fair to say that in this view it basically makes no sense to even assume there could be two substances. (A bit similar, perhaps, to it making no sense to assume there are two distinct "worlds".)

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I'll start by copying the relevant passages:

1D4. By attribute, I understand that which the intellect perceives of substance, as if constituting its essence.

1D5. By mode, I understand the affections of substance, or that which is in another thing through which also it is conceived.

1P1. Substance is by nature prior to its affections.

Modes cannot be used to differentiate between substances because they are affections of, or follow from, the substance. To differentiate between substances, we must differentiate between them insofar as they are substances. Spinoza explains this in the demonstration of 1P5:

Demonstration. If there were two or more distinct substances, they must be distinguished one from the other by difference of attributes or difference of affections (1P4). If they are distinguished only by the difference of attributes, it will be granted that there is but one substance of the same attribute. But if they are distinguished by difference of affections, since substance is prior by nature to its affections (1P1), the affections therefore being placed on one side, and the substance being considered in itself, or, in other words (1D3,1Ax6), truly considered, it cannot be conceived as distinguished from another substance, that is to say (1P4), there cannot be two or more substances, but only one possessing the same nature or attribute.

So if two substances share an attribute of extension, then by the definition of attributes, they share the same essence. If they share the same essence, they are the same substance.

What you are trying to do by differentiating between them by their modes begs the question, because you are taking it for granted that there is one substance, A, with chairs; and another, B, without, and this is what makes them different. But Spinoza is asking for what reason we would regard your chairful substance and your chairless substance as different substances, if both are extended and therefore have the same essence. No reason obtains. The division has no basis in the modes, since modes follow entirely from substances.

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