Spinoza’s Ethics · the whole geometry

Trace a proof
back to its first principles.

Every proposition in the Ethics rests on earlier ones, and those on earlier ones still, down to 99 definitions, axioms and postulates. The Ethics reader shows one step at a time. This page follows every step: 365 items and 1,222 citations, as one graph.

Choose an item

Load-bearing

The foundations
that carry the most.

Counted through every chain, not just direct citations: how many of the 365 items would lose a premise if this one were taken away.

  1. E1d3By substance, I mean that which is in itself, and is conceived through itself: in other words, that of which a…294 items
  2. E1d1By that which is self, caused, I mean that of which the essence involves existence, or that of which the nature…290 items
  3. E1a1Everything which exists, exists either in itself or in something else.290 items
  4. E1a4The knowledge of an effect depends on and involves the knowledge of a cause.289 items
  5. E1a5Things which have nothing in common cannot be understood, the one by means of the other; the conception of one…287 items
  6. E1d6By God, I mean a being absolutely infinite, that is, a substance consisting in infinite attributes, of which ea…283 items
  7. E1d4By attribute, I mean that which the intellect perceives as constituting the essence of substance.282 items
  8. E1d2A thing is called finite after its kind, when it can be limited by another thing of the same nature; for insta…277 items
  9. E1d5By mode, I mean the modifications[1] of substance, or that which exists in, and is conceived through, somethin…273 items
  10. E2d1By body I mean a mode which expresses in a certain determinate manner the essence of God, in so far as he is c…256 items

The deepest proofs

The longest roads
from axiom to conclusion.

Steps in the longest unbroken chain of citations back to a first principle.

  1. E5p19He, who loves God, cannot endeavour that God should love him in return.50 steps
  2. E5p17God is without passions, neither is he affected by any emotion of pleasure or pain.49 steps
  3. E5p39He, who possesses a body capable of the greatest number of activities, possesses a mind whereof the greatest p…49 steps
  4. E5p16This love towards God must hold the chief place in the mind.48 steps
  5. E5p20This love towards God cannot be stained by the emotion of envy or jealousy: contrariwise, it is the more foste…48 steps
  6. E4p73The man, who is guided by reason, is more free in a State, where he lives under a general system of law, than …47 steps
  7. E5p10So long as we are not assailed by emotions contrary to our nature, we have the power of arranging and associat…47 steps
  8. E5p15He who clearly and distinctly understands himself and his emotions loves God, and so much the more in proporti…47 steps
  9. E4p46He, who lives under the guidance of reason, endeavours, as far as possible, to render back love, or kindness, …46 steps
  10. E4p51Approval is not repugnant to reason, but can agree therewith and arise therefrom.46 steps

One chain, written out

The last proposition,
39 steps down.

“Blessedness is not the reward of virtue, but virtue itself.” Here is the longest chain beneath it, each item citing the next.

  1. E5p42 Blessedness is not the reward of virtue, but virtue itself; neither do we rejoice therein, because we control our lusts, but, contrariwise, because we rejoice t
  2. E5p38 In proportion as the mind understands more things by the second and third kind of knowledge, it is less subject to those emotions which are evil, and stands in
  3. E5p37 There is nothing in nature, which is contrary to this intellectual love, or which can take it away.
  4. E5p33 The intellectual love of God, which arises from the third kind of knowledge, is eternal.
  5. E5p32 Whatsoever we understand by the third kind of knowledge, we take delight in, and our delight is accompanied by the idea of God as cause.
  6. E5p27 From this third kind of knowledge arises the highest possible mental acquiescence.
  7. E5p25 The highest endeavour of the mind, and the highest virtue is to understand things by the third kind of knowledge.
  8. E4p28 The mind's highest good is the knowledge of God, and the mind's highest virtue is to know God.
  9. E4p27 We know nothing to be certainly good or evil, save such things as really conduce to understanding, or such as are able to hinder us from understanding.
  10. E4p26 Whatsoever we endeavour in obedience to reason is nothing further than to understand; neither does the mind, in so far as it makes use of reason, judge anything
  11. E4p25 No one wishes to preserve his being for the sake of anything else.
  12. E4p22 No virtue can be conceived as prior to this endeavour to preserve one's own being.
  13. E3p7 The endeavour, wherewith everything endeavours to persist in its own being, is nothing else but the actual essence of the thing in question.
  14. E3p6 Everything, in so far as it is in itself, endeavours to persist in its own being.
  15. E3p5 Things are naturally contrary, that is, cannot exist in the same object, in so far as one is capable of destroying the other.
  16. E3p4 Nothing can be destroyed, except by a cause external to itself.
  17. E3p1 Our mind is in certain cases active, and in certain cases passive. In so far as it has adequate ideas it is necessarily active, and in so far as it has inadequa
  18. E2p40 Whatsoever ideas in the mind follow from ideas which are therein adequate, are also themselves adequate.
  19. E2p29 The idea of the idea of each modification of the human body does not involve an adequate knowledge of the human mind.
  20. E2p23 The mind does not know itself, except in so far as it perceives the ideas of the modifications of the body.
  21. E2p22 The human mind perceives not only the modifications of the body, but also the ideas of such modifications.
  22. E2p21 This idea of the mind is united to the mind in the same way as the mind is united to the body.
  23. E2p12 Whatsoever comes to pass in the object of the idea, which constitutes the human mind, must be perceived by the human mind, or there will necessarily be an idea
  24. E2p11 The first element, which constitutes the actual being of the human mind, is the idea of some particular thing actually existing.
  25. E2p10 The being of substance does not appertain to the essence of man, in other words, substance does not constitute the actual being[2] of man.
  26. E2p9 The idea of an individual thing actually existing is caused by God, not in so far as he is infinite, but in so far as he is considered as affected by another id
  27. E2p3 In God there is necessarily the idea not only of his essence, but also of all things which necessarily follow from his essence.
  28. E1p32 Will cannot be called a free cause, but only a necessary cause.
  29. E1p28 Every individual thing, or everything which is finite and has a conditioned existence, cannot exist or be conditioned to act, unless it be conditioned for exist
  30. E1p26 A thing which is conditioned to act in a particular manner, has necessarily been thus conditioned by God; and that which has not been conditioned by God cannot
  31. E1p25 God is the efficient cause not only of the existence of things, but also of their essence.
  32. E1p15 Whatsoever is, is in God, and without God nothing can be, or be conceived.
  33. E1p12 No attribute of substance can be conceived from which it would follow that substance can be divided.
  34. E1p8 Every substance is necessarily infinite.
  35. E1p7 Existence belongs to the nature of substances.
  36. E1p6 One substance cannot be produced by another substance.
  37. E1p5 There cannot exist in the universe two or more substances having the same nature or attribute.
  38. E1p1 Substance is by nature prior to its modifications.
  39. E1d3 By substance, I mean that which is in itself, and is conceived through itself: in other words, that of which a conception can be formed independently of any oth

Method

How the graph is read

The graph is parsed from the Elwes translation the site’s Ethics reader publishes. A citation is any reference in an item’s enunciation, proof, corollaries or notes, in all of Elwes’s forms: Prop. xvi., Part i. Prop. xxv., III. xiii. liv., II. Post. v., and the definitions of the emotions. Notes count, since Spinoza argues in them too, so the chains are generous rather than minimal.

Three citations point forward to a later item. They are real references, not premises, so the tracer sets them aside:

10 first principles are never cited anywhere in the geometric order: E1a2, E1a7, E2a5, E2post2, E2post6, E3post2, E3GDA, E4d4, E4d5, E4d7.