Spinoza’s Style Of Argument In Ethics I

The Ethics are set out in geometrical form, an arrangement intended to parallel the canonical example of a rigorous structure of argument producing unquestionable results: the example being the geometry of Euclid. The structure is synthetic rather than analytic; Spinoza begins with definitions and axioms and then derives the consequences. Both definitions and axioms are intended to carry high levels of certainty. The axioms are supposed to be indubitably true, to reflect ‘common notions’. The definitions could in principle be regarded as less certain; they could be regarded as stipulated, with the remainder of the results being of the form that if the definitions are true, then the results are true. While this is possible, we can take it that Spinoza believes his definitions are also in fact truly reflective of reality.

However, there are immediate difficulties. We open with “by cause of itself, I understand that whose essence involves existence” . We must be careful here because it already involves a variant of the ontological argument. Essence is generally defined as a property without which something cannot exist. So the definition refers to something that cannot exist without existing, which in fact has either no referents or encompasses the whole universe and thus has no explanatory power. Spinoza will later employ this ontological argument, and so if we accept it here, we must accept his subsequent position.

The axioms also display varying levels of certainty. Axiom 1 has the form (A v ~A): “Each thing that exists exists either in itself or in something else” . This of course is certain as it stands, though we must take note of the dichotomy introduced and its subsequent use, which may be less certain. On the other hand, axiom 4 seems more questionable: “Knowledge of an effect depends on the knowledge of the cause” . This seems to confuse ontology and epistemology. Hume would argue that we never observe cause or effect, merely constant conjunction. Even when setting that aside, there are manifold examples of situations wherein we claim to have knowledge of an effect without knowing anything of its cause. A child can observe a ship sinking without knowing anything about metal fatigue. The same objection applies to definition 4. Spinoza’s rigid determinism is expressed in axiom 3: “From a given determinate cause there necessarily follows an effect”

Spinoza’s three major concepts are substance, attribute and mode. A substance is any self-sufficient entity that can be conceived solely through itself. An attribute is an essential property of a substance. A mode, or affection, is the opposite of a substance in that it can only exist as a way of being of something else, i.e. it cannot be understood through itself solely. Spinoza espouses monism in the physical realm at least, and in p5, he brings these concepts together to argue that there is only one substance: “There cannot exist in the universe two or more substances of the same […] attribute” .

The argument proceeds via the claim that substances could only be distinguished either by having different attributes or different modes. If the former is the case, Spinoza has made his point; if the latter, then Spinoza claims that a difference merely in mode is insufficient to make a distinction.

Bennett holds that Spinoza commits the modal fallacy in this p5: the claim is that Spinoza has invalidly argued from (Fx and possibly Fy) to possibly (Fx and Fy). The inference is indeed logically invalid from the following substitution: x = the first student in the room, y = the second student in the room, F = the property of being the oldest student in the room. Spinoza is supposed to have done this in the move from ‘two substances x and y differ only modally’ to ‘two substances x and y could become the same and thus really be one substance’. However, a more charitable interpretation here would allow that Spinoza is guilty not of an error but of a suppressed assumption, viz. that a substance can be in any mode and may move freely among them irrespective of whether any other putative substance is already ‘occupying’ that mode. While this should have been spelt out, it does not seem a fatal error.

In p7, Spinoza introduces his version of the ontological argument: “It belongs to the nature of substance to exist” . Spinoza must be using his own definition of ‘substance’. In the tradition, the term is often associated with Aristotle, who would not have understood the idea of a single substance. “That Aristotle accepted it as a consequence of the identity of a substance with its essence that an individual substance like Socrates or Callias was identical with his essence may be disputed.”

While we do find support here for Spinoza’s line that a substance and its essence are identical, Aristotle clearly holds that there are multiple substances, as does Descartes. This would be a problem for Spinoza at this point, because then his version of the ontological argument would be open to the standard ‘floodgates’ objection, whereby if we can define a perfect dog or perfect island, then these must exist. It could be a neat inversion of the problem for Spinoza to claim that since he has used the ontological argument and this objection can be made when there are multiple substances, then there can be only one substance. There will also turn out to be a theological argument, because there cannot be more than one perfect being: the existence of one would impair the putative perfection of the other. Since Spinoza will later argue for the identity of the one substance, the universe and a perfect being, this line carries weight from his perspective.

Nevertheless, p5 and p7 are incompatible with a traditional definition of ‘substance’. Charlton considers various solutions to this, including Russell’s view that a substance is something self-causing – note the consistency of this with definition 1 and the fittingness that Spinoza should open his treatise with a reference, albeit disguised, to a perfect being. Also mentioned is Curley’s view that a substance is anything that is independent of everything else.

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It is held in p8 that “every substance is necessarily infinite” . Spinoza needs this because following his identification of the one substance with a perfect being, he will be open to a concern of Descartes that finitude is “unworthy of the divine nature” in Spinoza’s own later comment on the problem. The solution is that nothing external can act on the perfect being or limit it if it is infinite.

Spinoza aims to support his argument in p7 in p8s: “If anyone were to say, therefore, that he has a clear and distinct, that is true idea of substance and yet doubts whether such a substance exists, then that would be the same as if he were to say, if you please, that he has a true idea and yet is inclined to think that it may be false”.

Spinoza has adopted Descartes’ clear and distinct perception test of truth. The form of the argument is a reductio, because the consequent that someone could simultaneously consider a proposition to be false and true at the same time is clearly unappealing. But whether the antecedent entails the consequent seems open to question. It appears that Spinoza subscribes to a correspondence theory of truth, in that if a proposition is true then there is, following Aquinas, an adaequatio intellectus et rei, meaning that what is in the mind corresponds well or adequately to a real entity. Spinoza often speaks of adequate ideas later in his work.

So the current argument viewed in this light seems to say that if someone considers that they have a clear and distinct idea of substance, then that idea is true, which means it is adequate, which means that it must correspond to something existing in the world. Objections to this would include the point that the clarity and distinctness test may not actually be a valid guide to truth, and in fact Descartes needs the existence of a perfect being as a guarantor of that. This is fine for Descartes, but Spinoza does not have a perfect being who is personal; his perfect being is one infinite substance comprising all that there is, and taking no interest in humanity: such an entity would not seem likely to confer guarantees. Further, to what extent is it reasonable to claim that we can have a clear and distinct perception of infinity? Also a variant of the argument from illusion may be relevant here, in that we often have clear and distinct perceptions of false propositions that we must correct by reason.

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Later in this same section, Spinoza gives an interesting further demonstration by considering a universe comprising 20 men. Since he is determinist, each man must have a cause. But “the true definition of man does not involve the number 20” as may be appreciated from the fact that a different number could have been chosen. So the cause must be external, and “everything of whose nature several individuals can exist must necessarily have an external cause” . This is neat, because it reinforces Spinoza’s line on substance as being single and self-caused, and is a good example of his style of argument.

See Also:

Husserl’s Phenomenological Reduction: What Is It And Why Does Husserl Believe It To Be Necessary?

Does Nietzsche Favor Master Morality Over Slave Morality?

What Is “Theory Of Mind?”

Why Kids Are Robots


Spinoza, Ethics, Ed. and Tr. G H R Parkinson, Oxford University Press, 2000 (henceforward Ethics), p. 75, def. 1
Ethics, p. 77
J Bennett, A Study of Spinoza’s Ethics, Hackett Publishing Company, 1984
Ethics, p. 78
M. J. Woods, ‘Substance and Essence in Aristotle’, Proceedings of the Aristotelian Society, New Series, Vol. 75, (1974 – 1975), pp. 167-180
William Charlton, ‘Spinoza’s Monism’, The Philosophical Review, Vol. 90, No. 4 (Oct., 1981), pp. 503-529

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14 replies on “Spinoza’s Style Of Argument In Ethics I”

Very much enjoyed your capable analysis of the logic employed by Spinoza in Part 1. And up to a point it made me quite nervous, especially since my second pamplet is in-progress and the working title is : A Discussion and Interpolation of Part 1 of the “Ethics’. Luckily I got hold of myself and recognized in your work the same misconstrued interpretation of Spinoza’s axioms, definitions and propositions. Applying an external analytic tool like the laws of logic seems a practicle and reasonable response to Baruch’s logical frame which he’s draped around the meaning of the term God, and your conclusions and a number of other variants on the problems he seems to have caused himself are clearly well intended but unfortunately miss the mark.
Studying Spinoza is not and academic exercise where matching his analysis to a preformed logical framework will net the meaning behind his words.
Studying Spinoza is rather a case where each axiom, definition and proposition must be considered singularly and on its own terms and as to what meaning can be derived from his insistence that his philosophy grasps the meaning of the objects in nature, not how well they compare to synthetic analysis.
It all begins with one human mind as the take off point. As this individual contemplates the vastness and enormity of all of nature he begins to intuitively sense an order and arrangement which while eschewing purpose, contains all the possible occurrences which reach to such an infinite amount interms of number and variety and whose chemical composition all involves a relational and measurably proportional bearing on each and every object reaching from the thinkers body to the stars and in fact all of the universe. This can only be one substance which reveals itself in an uncountable infinitude of attributes, each unique and yet commingled in their attribution to the one substance.
The individual can find the proof of this inside his own body which houses two different and distinct modalities which we term the body and the mind.Objects in nature are not the same as ideas nor vice versa but in an intuitively recognizable way they are the same thing. The individual thinker clearly sees that he nor anything else in the realm of these two attributes discernable to him is its own cause and following an inescapable logic back to its source, intuitively recognizes god as the one and only source capable of producing everything imaginable,all at once; without purpose but with a causality that clearly and adequately reflects an eternal thinking nature which has caused all of these necessary and connected arrangements to perpetuate one to the next in a neverending chain of causes that will continue and reperpetuate themselves forever.
Finally the thinker comes to the recognition that in the human evolutionary process observable with the aid of science and technology that we, as humans represent the leading edge of one of these infinite possibilities. We may not indeed ‘make it’ and may not reach the furthest extent of our potential to extend this one edge of this infinite possibilty to which we belong, but our ‘conatus’ will ensure that we give our best shot to extend this human endeavor as far as we possibly can.
Charles M. Saunders
Thank you again for your ontological wakeup call for me!

Thank you for the positive comments. Please see below for some points in response.

I wouldn’t worry too much about finding someone working on a similar area to yourself! This happens a lot, but my view is that the philosophical phase space, if you like, is very fine-grained. There are arguments and positions that appear prima facie to be very similar, but on closer inspection it turns out that they have very different consequences. You can benefit from the similar approaches nevertheless.

You are definitely right when you say that trying to jam an external logical framework on to Spinoza will not work. Indeed, trying to retrofit anything on to any philosopher without express evidence in a primary text is a risk. However, are we sure that the logical framework is external here? After all, Spinoza has presented his work here in the form of sets of axioms modeled on Euclid, so he clearly means us to take his work as being deductive or syllogistic in form.

Again, I agree with your next point that we have to look at each axiom individually, but surely we also have to take them together. If for example he equivocated between terms in different axioms, so that x in one axiom did not have the same meaning as x in another axiom, he would not be able to reach any syllogistic conclusions. Also, committing the modal fallacy is a definite error in all logical systems, and so we can only get him off that hook by showing he avoids it, not by saying it is permitted to him because he can employ a logic that allows it. (I think…otherwise one would need a logic that did permit it, which might not be possible, and then to show that was what he was using, which is also very difficult.)

I was interested in your paragraph beginning “It all begins…” because it showed links between Spinoza and Nietzsche. In particular, it looks a bit like Nietzsche’s Doctrine of Eternal Recurrence. I have often read that such links exist but until now I have not really seen where they might be.

I think the problem with your final theistic argument, suggesting we need to find an initial cause of what we observe, is that it does not in fact have any explanatory power, because it posits an uncaused deity. You are as it were sweeping the problem of causation under the carpet, and we need to know what caused the carpet to be there.

Best regards,


Thanks. My objection to applying a synthetic analysis to Spinoza’s Part 1 still holds. You are insisting that Spinoza’s meaning is distorted by its refusal to conform to an arbitrarily devised mathematical structure called logic. That indicates a backwards form of thinking where you’re asking Baruch’s philosophy to satisfy the artificial constraints of an external process.
What I intended by asking to think solely about Spinoza’s meaning is that analysts always seemed to be more interested in abstractions based on generalizations rather than on content and meaning.
Very much appreciate your intelligent writing.
Once my pamphlet is completed l’ll forward you a copy.

Thank you.

Well, I still take issue with whether the logical framework is *external* or not. Surely, if he starts from axioms and then makes deductions from them, he is intending that system to be a valid logic which we may use in understanding him. It would be a rather more Nietzschean trick to use a system like that without endorsing it!

Please do send me the pamphlet when it is ready.

Also might I suggest you take a look at articles around:

— that blog contains a lot of good insights into Spinoza.



Greetings Sir,
By external abstract system being appled to Part 1, the idea is that Spinoza did not intemd his use of logic to be applied in a comparative context. His intention was for his system to be understood as stand alone and consistent only within its own inherent logic. It simply does not compare to anything else in the extant.
His take on the ontological argument stands non-pareil and solves the ancient puzzle once and for all. My pamphlet #2 will detail this.
An idea might be for you to read Pamphlet #1:
Letters to No one in Particular
A Discussion and Illustration of Spinoza’s ‘Fragment’.
It is available for free on certain days of the month on Kindle and in paparback at Amazon. It may also be free on something called the Amazon Library. If you would take some of your valuable time to read it (121 pages), you would catch my drift. Would enjoy your feedback.
Meanwhile I remain,
Yours Faithfully,
Charles M. Saunders

Greetings Sir,
Spinoza’s intention with his use of a logical framework was so that it would adequately demonstrate the consistentcy of his philosophy. It is not meant to be compared to anything else. Once his solution to the Ontological proof of god’s existence becomes clear, the remainder of the Ethics can come to life.
Since that is the subject matter of Pamphlet 2, which will not get to you for a while, it might interest you to read Pamphlet 1.
It is available on Kindle free of charge through a program called Kindle Select and through the Amazon Lending Library worldwide. Title:
Letters to No one in Particular
A Discussion and Ilustration of Spinoza’s ‘Fragment’ or “On the Improvement of the Understanding”
Would enjoy your feedback, so, until then,
I remain,
Yours Faithfully,
Charles M. Saunders

OK, so I think I see what you are getting at. Your idea is that there is a logic which is internal to The Ethics but which we should not try to apply elsewhere. Am I right to think that that is your position? If that is right, do you think that the logic is valid only in a restricted domain?

Can you expand a bit on what you mean by a `solution to the Ontological proof’? Normally, we would say that a problem has a solution, while a proof is offered or demonstrated.

Unfortunately I am not a member of any of those electronic programmes! Things are still a bit 19th Century here.



You can send it to me at the dept.:

Department of Philosophy
University College London
Gower Street
London, WC1E 6BT



Greetings Kind Sir,
All’s been quiet which means it must be time for an additive. Hope your studies are going well.

Prop.1- Substance is by nature prior to its modifications. [Page-1]
Proof- This is clear from definitions 3 and 5. [Page-2]
[Note- To use the non-existent to explain what actually exists will appear, at first glance, to be an awkward if not contradictory formulation. There is a very solid reason for this and it lies in the now common and widespread restrictions placed on any possibility of using conjecture to point to or to encapsulate something real. [The source of this restriction is the ‘law of non-contradiction’ which states that any given statement is either true or false. With a little careful consideration this ‘law’ can be seen as a completely artificial and arbitrary construct.]
Spinoza’s juxtaposition of non-existent and existent objects entails what is commonly referred to as, ‘thinking outside the box.’ Philosophy adamantly disavows the value in imaginative presentation.
Throughout the history of Philosophy any thinker who attempted to use this methodology was eventually ridiculed and their work summarily dismissed as either mysticism or the dreaded ontology. Ultimately, the art and practice of philosophy boxed itself into a corner along with the present day empiricist science.
Apparently the mainstream believes that it borders on the criminally insane to write about something that humans cannot know directly, but must somehow intuit, from an ‘angle’, so to speak.
Those who find fault with attempting to posit the unknown as a category of existence do not realize the impossibility of their insistence that humans somehow have at their disposal all the knowledge available though sense perception.
This is in fact saying that ‘Even what we do not yet know, we already know’, all this thanks to their reduction of possible knowledge only to that which falls under the rubric of logical positivism and the behavioral/psychological superstitions.
It must be an extremely comfortable position to occupy when the search for as yet unknown truth can be accessed by using a virtually preordained true hypothesis which needs only to be confirmed through observation of data and dispassionate objectivity. This point is extremely worthy of note.]
For our work together we will insist on following Baruch’s lead. To have any hope of ever coming to any form of adequate understanding of god, the indirect, reflexive method will prove invaluable.

Capsule- Substance and its modifications

Everything which we have so far learned in science about the extended universe tends toward standing in support of Spinoza’s concept of the one substance which constitutes and is the cause of everything.
Beginning with the weirdly named ‘big bang’; all objects in the known universe emanated from one source. This source originated in an unimaginably huge detonation which exploded from its compressed state, and transformed into all of the matter and the dark matter which taken together account for all that is visible and measureable: galaxies, constellations, solar systems, planets and people.
Each of these objects, considered individually, is comprised in some measure of concatenations of elements in the atomic table, e.g. birth of stars, hydrogen gas; air we breathe and water we drink, hydrogen, etc.
As mentioned previously, the chemical composition of gaseous matter present during the birth of stars and molecular structure of the cause of life forms on earth represents a proportional relationship among molecular elements formed under pressure from fission and fusion.
The ‘big bang’ and the subsequent matter which forms the elemental structure of heavenly bodies and all life forms comprise the modifications of substance so named by Spinoza.
Long before it would have been conceived of as possible Baruch intuited one self-caused substance which could not be conceived of as other than existent and further that its essence must further be understood as comprising a state of being.
This ‘ontos’ encapsulates at the functional level the twin attributes of extension and thought: breathing, thinking, procreation; and the creation, destruction and re-constitution of every element in the universe.
The ingestion and digestion process of taking in the nourishment which substantiates human life and allows for us to then contemplate all of these wonders can also be said to be, in terms of physics, a replication of the working functions of black holes in deep space.
These deep space objects are being observed by cosmologists even as we speak, in their never ending process of virtually ingesting and as far as we can tell digesting entire galaxies, constellations and it is purported even the ‘dark matter’ which is interspersed among all of these objects.
To extend this analogy further of interconnectedness and the unity of all universal activity we might ask ourselves, why did Einstein and all those who have followed him in the field of theoretical physics and mathematics pine for a ‘unified field theory’?
Was he a mystic or some type of dreamer? Or might there be some foundational construct which can be understood to be responsible for and the single cause of these individual and apparently discrete areas within the rubric of scientific theory and practice?
The answer is twofold: no he was not a mystic or a dreamer, he was a scientist. Assuming that at some point; electro-magnetism, physics, chemistry and celestial mechanics will conjoin into one consistent and interconnected field is not whimsy. It is the only logical conclusion to be drawn from all of the evidence so far gathered.
Second, Einstein’s intuition of a ‘unified field’ extended to the limits of its logical conclusion, tailors itself into Baruch’s uncanny recognition of the interconnectedness, of the infinity and of the self-caused essence of substance.
If the enormity of the size of the known universe can be captured and reflected upon by the individual human mind, one thought and understanding emerges and remains inescapable.

This thought is not ephemeral or phantasmagorical; it lies in the formation and presence in the human mind of the concept which takes the form of an adequate idea; the idea of god.
Because every adequate idea exists only through its correlation to reality, the adequate idea of substance which can be achieved by the human mind is the most significant feature within the entire “Ethics”. Something real must exist in nature for it to become reflected as an idea in one person.
This is the form of ‘self-evident’ truth. It needs no external prop or evidence for support.
The ability of a finite modality to encapsulate god’s essence within its individuality in the form of an idea is the only proof requisite for the existence of god. Spinoza said this; …“the finite demonstrates clearly the existence of the infinite”.
There are those who will still doubt this ontological proof and even mock its conclusion as futile, even puerile. The fact of the matter remains that this marks Baruch’s finest contribution to humanity; the existence of the individual human mind and its reality as a piece of god’s eternal nature and infinite potential lies at the core of the relevance and magnificence of the “Ethica in Ordine Geometrico Demonstrata”.
It is ours for the having. The time and strenuous mental energy which must be exerted to accomplish this understanding, when it comes to each of us, will hit like the proverbial ‘ton of bricks’. But it will feel most welcome indeed.
Spinoza called this feeling “Amor Dei Intellectus”. We can simply refer to it as god.
End Capsule

P.S. This is a roughed out, as yet, excerpt form my next book,
An Interpolation and Discussion of the “Ethics” Part1- Concerning God

All the Best,
Charles Milton Saunders

Dear Charles,

Apologies for the long delay. The book came out, the thesis is being finalized and I also got a paper accepted by Mind and Language, so it is about the busiest I have ever been. Thank you for your “additive” on which I make some comments below.

1). I think you might find Sartre interesting, particularly the areas where he uses the non-existent to say something about the existent; the former does something like “form the boundary” of the latter.

2). You might restrict your complaint that philosophy disavows imaginative presentation to “analytic philosophy”. Other areas, such as phenomenology or Nietzsche, especially in the original, are highly imaginative. (Of course, because of this some analytic types have therefore denied that they are philosophy, but that does not happen very often these days.)

3). Taking on the law of non-contradiction is a big deal! You will have to say more about this, either here or elsewhere. Quantum mechanics will probably help. Or Quine. Maybe both: Quine mechanics…

4). Re: your sentence beginning “Those who find fault…”, do you mean exactly what you have written or do you mean the similar “those who insist that we only have have information available through sense perception”? That I think is a plausible and widely-held position — when one adds to it theoretical knowledge, which is also sensory in some sense in origin. I don’t think anyone claims that humans can have access to all knowledge, through sense perception or otherwise. So challenging that position would look a bit like a straw man unless you can quote someone espousing the position you rightly say is questionable.

5). The physics in the second part looks about right. One element you might add in is something like “explanatory power” combined with simplicity. We see an explanation, in science and elsewhere, as superior based on these two figures of merit. If a candidate explanation explains a lot but has few moving parts, that is a better explanation than another candidate which does not explain as much but has the same number of moving parts. Similarly, if two explanations explain the same amount, the simpler one is preferred. You will note that this picture does not allow one to choose rationally between two explanations, one of which explains a lot but has many moving parts and one which explains less but is simpler. Anyway, this sort of motivation is behind the search for Unified Field Theories: they are simpler and explain a lot. Also, it’s worked before: viz. electricity and magnetism became electromagnetism, then there was electroweak unification, etc. I wouldn’t call this a “logical conclusion” as you do however; it is more like an extrapolation into the future of past trends.

6). My overall comment is that you need to do more unpacking to show the links between what Spinoza says, what he means, and how this fits into the physics. For example, when you say “Spinoza said this, “the finite demonstrates clearly the existence of the infinite” “, you need to give us much much more detail on what he is arguing for and how he does it.



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