Hi!
Hello! How can I assist you today?
I am going to give you some definitions and axioms, and later I’ll give you some propositions and you can tell me whether they follow. Is that alright?
Sure! I'll do my best to help you determine whether the propositions follow from the definitions and axioms you provide. Please go ahead and give me the definitions and axioms.
Let’s start with just these definitions.
1. By a thing which is its own cause, I understand a thing the essence of which involves existence, or the nature of which cannot be conceived except as existing.
2. A thing is said to be finite, suo genere, when it can be limited by another of the same nature, e.g. a body is said to be finite because we can always conceive another body larger. Again, one thought is limited by another thought. But body is not limited by thought, nor thought by body.
3. By substance I understand that which exists in itself and is conceived through, or by means of, itself; i.e. the conception of which does not require for its formation the conception of anything else.
4. By attribute I understand what the intellect perceives of substance, as constituting the essence of substance.
5. By mode I understand the affections of substance, or that which exists in something else, through which it is also conceived.
Do you understand?
Yes, I understand. You have provided five definitions that define key concepts in metaphysics, including the concepts of "a thing which is its own cause," "finite," "substance," "attribute," and "mode." These definitions will serve as the basis for determining whether certain propositions follow logically from them.
Now please see whether this proposition follows:
Proposition 1. Substance is by nature prior to its modifications.
Yes, Proposition 1 follows logically from the definitions you have provided. According to the definitions, substance is that which exists in itself and is conceived through, or by means of, itself, and an attribute is what the intellect perceives of substance, as constituting the essence of substance. Therefore, substance must be prior to its modifications (i.e., modes), since the modes are affections of substance and exist in something else through which they are also conceived. In other words, the modes depend on the existence of substance, but substance does not depend on the existence of its modes.
Now please see whether this proposition follows:
Proposition 2. Two substances, whose attributes are different, have nothing in common.
Yes, Proposition 2 also follows logically from the definitions you have provided. According to the definitions, substance is that which exists in itself and is conceived through, or by means of, itself, and an attribute is what the intellect perceives of substance, as constituting the essence of substance. If two substances have different attributes, then they are not the same substance, since the essence of each substance is defined by its attribute. Therefore, two substances with different attributes have nothing in common, because they are completely distinct and separate entities.
For the next part, please accept also these axioms.
1. Whatever is, is either in itself or in something else.
2. That which cannot be conceived through, or by means of, something else, must be conceived through, or by means of, itself.
3. From a given determinate cause an effect necessarily follows; and if there be no given determinate cause, it is impossible that an effect should follow.
4. The knowledge of an effect depends on, and implies, the knowledge of its cause.
5. Things which have nothing in common cannot be understood by means of each other, i.e. the conception of the one does not involve the conception of the other.
6. A true idea must agree with its object.
7. If a thing can be conceived as not existing, existence does not belong to its essence.
OK?
Yes, I have accepted the additional axioms you provided. These axioms will also be used to determine whether the given propositions follow logically from the definitions and axioms you have provided. Please proceed with your next proposition.
Now please see whether this proposition follows:
Proposition 3. If two things have nothing in common, one cannot be the cause of the other.
Yes, Proposition 3 follows logically from the definitions and axioms you have provided. According to Axiom 4, the knowledge of an effect depends on and implies the knowledge of its cause. If two things have nothing in common (as per Axiom 5), then the conception of one does not involve the conception of the other, and therefore they cannot be understood by means of each other. Furthermore, if one thing is the cause of another, then there must be a determinate causal relation between them (as per Axiom 3). However, if two things have nothing in common, they cannot have a causal relation between them, since there is no means by which one can produce the other. Therefore, Proposition 3 is true.
Now please see whether this proposition follows:
Proposition 4. Two or more distinct things are distinguished one from the other, either by the difference of the attributes of the substances, or by the difference of their modifications.
Yes, Proposition 4 also follows logically from the definitions and axioms you have provided. According to Definition 4, an attribute is what the intellect perceives of substance, as constituting the essence of substance. Therefore, if two or more substances have different attributes, then they must be distinguished from each other by the difference of their attributes. Additionally, if two substances have the same attribute but have different modifications (i.e., modes), then they must also be distinguished by the difference of their modifications (as per Definition 5). Thus, Proposition 4 is true.
Now please see whether this proposition follows:
Proposition 5. There cannot exist in the universe two or more substances having the same nature or attribute.
Proposition 5 follows logically from the definitions and axioms you have provided. According to Definition 4, an attribute is what the intellect perceives of substance, as constituting the essence of substance. Therefore, if two or more substances have the same attribute, then they must have the same essence, since their attributes define their essence. However, by Definition 3, substance is that which exists in itself and is conceived through, or by means of, itself; i.e. the conception of which does not require for its formation the conception of anything else. Therefore, if two substances have the same essence, they would be indistinguishable from each other, and there would be no reason to think of them as two distinct substances. Thus, there cannot exist in the universe two or more substances having the same nature or attribute. Therefore, Proposition 5 is true.
Now please see whether this proposition follows:
Proposition 6. One substance cannot be produced by another substance.
Proposition 6 follows logically from the definitions and axioms you have provided. According to Definition 1, a thing which is its own cause is a thing the essence of which involves existence, or the nature of which cannot be conceived except as existing. Thus, a substance that is its own cause exists necessarily, and cannot be produced by anything else. Furthermore, according to Axiom 3, from a given determinate cause an effect necessarily follows; and if there be no given determinate cause, it is impossible that an effect should follow. Therefore, one substance cannot be produced by another substance, since that would require the second substance to be the determinate cause of the first substance, which is impossible by Definition 1. Thus, Proposition 6 is true.
It follows, as a corollary, that a substance cannot be produced by anything external to itself. Right?
Yes, that is correct. Since Proposition 6 holds true, it follows as a corollary that a substance cannot be produced by anything external to itself, since anything external to the substance would be considered another substance or a modification of a substance. If a substance were produced by something external to itself, that would contradict the idea that a substance is self-caused and has existence in itself, which is a key part of its definition (as per Definition 1). Therefore, a substance cannot be produced by anything external to itself.
Now please see whether this proposition follows:
Proposition 7. Existence belongs to the nature of substances.
Proposition 7 does not necessarily follow from the definitions and axioms provided. While it is true that Definition 1 states that a thing which is its own cause involves existence in its essence, this does not necessarily mean that existence belongs to the nature of all substances.
According to Axiom 7, if a thing can be conceived as not existing, existence does not belong to its essence. Therefore, whether or not existence belongs to the nature of substances would depend on whether or not substances can be conceived as not existing.
There are philosophers who have argued that existence does belong to the nature of substances, but this is not something that necessarily follows from the definitions and axioms you provided.
Actually, we had just shown that substance cannot be produced by anything external to itself. So, it must be its own cause, which means, by definition 1, that its essence necessarily involves existence, or, existence belongs to its nature.
You are correct. I apologize for my earlier response. Proposition 7 does indeed follow from the definitions and axioms provided, given that a substance is self-caused (as per Proposition 6) and its essence involves existence (as per Definition 1). Therefore, existence belongs to the nature of substances, and Proposition 7 is true. Thank you for bringing this to my attention.
Given what has been shown so far, see whether this follows:
Proposition 8. Every substance is necessarily infinite.
Proposition 8 does not necessarily follow from the definitions and axioms provided. While Definition 2 states that a thing is said to be finite when it can be limited by another of the same nature, this does not necessarily imply that every substance must be finite. Moreover, while it has been established that substances cannot be produced by anything external to themselves, it has not been established that they cannot be limited or bounded in some way.
Therefore, it is possible that a substance could be finite, and it is not necessarily the case that every substance must be infinite.
In the previous propositions, we had shown that there can only be one substance with an identical attribute, and existence follows from its nature. Right? Well, so its nature involves existence, either as finite or infinite. Now, it does not exist as finite, since by Definition 2, it would then be limited by something else of the same kind, which would also necessarily exist (cf. Proposition 7); and there would be two substances with an identical attribute, which, by Proposition 5, is absurd. So it has to exist as infinite, meaning that Proposition 8 is true.
I see your argument, but I think there might be some issues with it. While it is true that a substance with a finite attribute would be limited by something else of the same kind, which would necessarily also exist, it does not follow that there would necessarily be two substances with an identical attribute. It is possible that there could be only one substance with that attribute, but that it is limited or bounded in some way.
Moreover, it is not clear that the definition of a finite thing in Definition 2 necessarily implies that it must be limited by something else of the same kind. It simply states that a finite thing can be limited by another of the same nature, but it does not rule out the possibility that a thing could be limited by something of a different nature.
Therefore, while it is true that existence follows from the nature of a substance, it does not necessarily follow that every substance must be infinite. The argument you have presented is not sufficient to establish Proposition 8 with certainty.
The example that “body is not limited by thought, nor thought by body” was clearly meant to exclude limitation by something outside the kind. A substance could only be limited by another, if it were limited. But since this is absurd, it must be infinite, i.e., Proposition 8 follows.
You're correct in your analysis. The example given in Definition 2 was meant to illustrate the concept of limitation by something of the same kind. The argument you presented, based on the earlier propositions and definitions, shows that a substance with an identical attribute to another substance can only exist as infinite, not finite. Therefore, Proposition 8 does follow from what has been established so far.
Now, from Definition 4, the following should be evident:
Proposition 9. The more reality or being a thing has, the more attributes belong to it.
Yes, Proposition 9 follows from Definition 4, which defines an attribute as what the intellect perceives of substance as constituting the essence of substance. The more reality or being a thing has, the more aspects of its essence or nature can be perceived and described as attributes.
See whether this follows from what we know as well:
Proposition 10. Each particular attribute of the one substance must be conceived through itself.
Yes, Proposition 10 follows from the definitions and axioms we have discussed so far. By Definition 4, an attribute is what the intellect perceives of substance as constituting its essence. And by Definition 3, substance is that which is conceived through, or by means of, itself. Therefore, each particular attribute of the one substance must be conceived through itself.
For the next part, please accept a few more definitions. I have added explanations to some of them to make them clearer.
6. By God I understand a Being absolutely infinite, i.e. a substance consisting of infinite attributess each of which expresses an infinite and eternal essence.
Explanation. I say absolutely infinite, not infinite suo genere; for if a thing be infinite suo genere only, we can deny that it has infinite attributes; but that which is absolutely infinite includes in its essence whatever expresses essence and involves no negation.
7. I call that thing free, which exists solely by the necessity of its nature and is determined to action by itself alone. I call a thing necessary, [or rather compelled,]3 when it is determined by another to exist and act according to a certain and definite law.
8. By eternity I understand existence itself, conceived as following solely and necessarily from the definition of the thing which is eternal.
Explanation. For existence so conceived is an eternal truth, inasmuch as it is the essence of the eternal thing; consequently, it cannot be explained by duration or time, even though the duration be conceived without beginning or end.
Thank you for providing these additional definitions.
Based on these definitions, it follows that:
Proposition 11. God is the only free substance.
Explanation: By definition 6, God is an absolutely infinite substance consisting of infinite attributes. By definition 7, a substance is free if it exists solely by the necessity of its nature and is determined to action by itself alone. God is the only substance that exists solely by the necessity of its nature and is not determined by anything outside of itself. Therefore, God is the only free substance.
Proposition 12. God is the only necessary substance.
Explanation: By definition 6, God is an absolutely infinite substance consisting of infinite attributes. By definition 7, a substance is necessary if it is determined by another to exist and act according to a certain and definite law. But since God is the only substance that exists solely by the necessity of its nature, God is the only necessary substance.
Proposition 13. God is the only eternal substance.
Explanation: By definition 6, God is an absolutely infinite substance consisting of infinite attributes. By definition 8, eternity is existence itself, conceived as following solely and necessarily from the definition of the thing which is eternal. Since God's existence is necessary and follows solely from God's nature, God is the only eternal substance.
Note: I was also surprised that it made up and proved some Propositions by itself. I decided to skip Spinoza’s prop. 11–13 since prop. 11 was clearly already understood and props. 12–13 are not used in what follows, besides that it keeps the numbering easy.
Very well, and I believe from the previous Propositions it should be trivial to show the following as well:
Proposition 14. Besides God no substance can be granted or conceived.
Yes, Proposition 14 follows from the previous propositions and the definitions, particularly Definition 6 which defines God as a being absolutely infinite, consisting of infinite attributes each of which expresses an infinite and eternal essence. From Proposition 5, we know that two substances with nothing in common cannot be conceived or understood by means of each other. From Proposition 10, each particular attribute of the one substance (God) must be conceived through itself. Therefore, if God is the only substance that can be conceived, no other substance can be granted or conceived.
And as corollaries of this, we can say, first, that “God is one”; and second, that “extension” and “thought” are either attributes of God, or (by Axiom 1) affections (modifications) of the attributes of God.
Yes, that's correct. From Proposition 14, it follows that there cannot be any substance other than God, which means that God is the only existent entity. Therefore, the statement "God is one" is a corollary of Proposition 14. Additionally, by Definition 2, all existing things must be either attributes of God or modifications of those attributes. Therefore, "extension" and "thought" must also be either attributes of God or modifications of those attributes.
This should help us apply the knowledge we have learned. Evaluate this proposition next:
Proposition 15. Whatever is, is in God, and nothing can exist or be conceived without God.
Proposition 15 can be deduced from the definitions and propositions stated so far. Since God is defined as an absolutely infinite being with infinite attributes, every substance and every attribute must belong to God. Proposition 7 states that existence belongs to the nature of substances, and Proposition 14 asserts that besides God no substance can be granted or conceived. Therefore, the only logical conclusion is that all substances exist in God, and nothing can exist or be conceived without God.
Moreover, Proposition 8 states that every substance is necessarily infinite, and Proposition 6 states that one substance cannot be produced by another substance. Therefore, since God is the only substance that exists, God must necessarily be infinite and cannot be produced by anything external to itself. Hence, Proposition 15 is true.
More generally, we can say:
Proposition 16. From the necessity of the divine nature must follow an infinite number of things in infinite ways—that is, all things which can fall within the sphere of infinite intellect.
Yes, that's correct. From the infinite attributes of God, and the fact that all things must be in God, it follows that an infinite number of things must follow from the necessity of the divine nature, in infinite ways. This means that everything that can possibly exist or be conceived falls within the sphere of infinite intellect, and is a necessary consequence of the divine nature.
So, God is the efficient cause of all that can fall within the sphere of an infinite intellect. God is a cause in himself, and not through an accident of his nature. And, God is the absolutely first cause. Right? Check these propositions next:
Proposition 17. God acts solely from the laws of his nature and is not constrained by any other being.
Proposition 18. God is the immanent and not the transient cause of all things.
Yes, that is correct. Here are some explanations for each proposition:
Proposition 17 follows from the definition of God given in Definition 6. Since God is a Being consisting of infinite attributes, it follows that everything that God does is a necessary consequence of his nature. Therefore, God acts solely from the laws of his nature and is not constrained by any other being.
Proposition 18 follows from the fact that God is the efficient cause of all that can fall within the sphere of infinite intellect, as shown in Proposition 16. If God were a transient cause, he would have to create things outside of himself, which would imply that there are things that exist independently of God. But this contradicts the definition of God as an absolutely infinite being that includes in its essence whatever expresses essence and involves no negation. Therefore, God is the immanent cause of all things, meaning that everything is contained within God and is a necessary consequence of his nature.
Now please check these propositions:
Proposition 19. God, or all the attributes of God, are eternal.
Proposition 20. The existence and essence of God are one and the same thing.
Yes, both Propositions 19 and 20 follow from the definitions and axioms previously established.
For Proposition 19, Definition 6 defines God as a "substance consisting of infinite attributes each of which expresses an infinite and eternal essence." Since each attribute of God expresses an infinite and eternal essence, it follows that God, or all the attributes of God, are themselves eternal.
For Proposition 20, Definition 8 defines eternity as "existence itself, conceived as following solely and necessarily from the definition of the thing which is eternal." Since God's essence and existence are one and the same thing (by Definition 6), and God is absolutely infinite (by Definition 6) and necessary (by Definition 7), it follows that God's existence follows solely and necessarily from God's essence, and therefore, the existence and essence of God are one and the same thing.
Note: At this point I got bored and stopped. This was originally published on Facebook.
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