Spinoza postulated three different kinds of knowledge in his Ethica:
Ex omnibus supra dictis clare apparet nos multa percipere et notiones universales formare I° ex singularibus nobis per sensus mutilate,
confuse et sine ordine ad intellectum repræsentatis (vide corollarium propositionis 29 hujus) et ideo tales perceptiones cognitionem ab
experientia vaga vocare consuevi. II° ex signis exempli gratia ex eo quod auditis aut lectis quibusdam verbis rerum recordemur et earum quasdam
ideas formemus similes iis per quas res imaginamur (vide scholium propositionis 18 hujus). Utrumque hunc res contemplandi modum
, opinionem vel imaginationem in posterum vocabo. III° denique ex eo quod notiones communes rerumque proprietatum ideas adæquatas
habemus (vide corollarium propositionis 38 et propositionem 39 cum ejus corollario et propositionem 40 hujus) atque hunc rationem et
vocabo. Præter hæc duo cognitionis genera datur, ut in sequentibus ostendam, aliud tertium quod scientiam intuitivam vocabimus.
Atque hoc cognoscendi genus procedit ab adæquata idea essentiæ formalis quorundam Dei attributorum ad adæquatam cognitionem essentiæ rerum.
[Ethica, pars II, prop. XL, scholium II]
(From all that has been said above it is clear, that we, in many cases, perceive and form our general notions :— (1.) From particular things
represented to our intellect fragmentarily, confusedly, and without order through our senses (II. xxix. Coroll.) ; I have settled to call such
perceptions by the name of knowledge from the mere suggestions of experience. (2.) From symbols, e.g., from the fact of having read or heard
certain words we remember things and form certain ideas concerning them, similar to those through which we imagine things (II. xviii. note).
I shall call both these ways of regarding things knowledge of the first kind, opinion, or imagination. (3.) From the fact that we have notions
common to all men, and adequate ideas of the properties of things (II. xxxviii. Coroll., xxxix. and Coroll. and xl.) ; this I call reason and
knowledge of the second kind. Besides these two kinds of knowledge, there is, as I will hereafter show, a third kind of knowledge, which we will
call intuitive knowledge. This kind of knowledge proceeds from an adequate idea of the absolute essence of certain attributes of God to the
adequate knowledge of the essence of things.)
The third kind of knowledge, scientia intuitiva or intuitive knowledge, has been interpreted by commentators in different ways.
It is a knowledge superior to reason by which reality is grasped adequately in one comprehensive act of vision. It is not a mystical knowledge
but the knowledge of the essence of particular things. It follows from the second kind of knowledge, reason. Reason, however, abstracts
from particular things and derives common notions and concepts.
Quo magis res singulars intelligimus, eo magis Deum intelligimus.
[Ethica, part V, prop. XXIV]
(The more we understand individual things, the more we understand God)
This return to individual things through intuitive knowledge lets us understand, according to Spinoza, the essence of a thing, which is the
eternal aspect of a thing, under which a thing is conceived adequately (sub species aeternitatis).
This intellectual contemplation of the eternal and infinite in us and in individual things provides us with the most comprehensive understanding
of reality possible based on our finite mind and limited experience. It is the eternal in us that helps us understand the eternal
in everything and thus grasp the underlying unity of reality.
What does Spinoza mean by 'adequate knowledge' or 'adequate ideas'?
Per ideam adaequatam intelligo ideam, quae, quatenus in se sine relatione ad objectum consideratur, omnes verae ideae proprietates,
sive denominations intrinsecas habet.
[Ethica, part II, def. IV]
(By adequate idea I understand an idea, which, if it is considered in itself without relation to the object, has all the properties
or intrinsic denominations of a true idea.)
An adequate idea is a true idea, not because of the correspondence with its object, but because of the intrinsic features of its essence,
which refers to the eternal aspect of the idea, or the relation of it to reality (God or Nature).
Spinoza defines 'essence' as follows:
Ad essentiam alicujus rei id pertinere dico, quo dato res necessario ponitur, & quo sublato res necessario tollitur; vel id, sine quo res,
vice versa wuod sine re nec esse, nec concipi potest.
[Ethica, part II, def. II]
(I say that to the essence of any thing belongs that which, being given, the thing is necessarily posited and which, being taken away,
the thing is necessarily taken away; or that without which the thing can neither be nor be conceived, and which can neither be nor be conceived without the thing)
A thing cannot be or be conceived without its essence, and similarly, the essence of a thing (its identity) cannot be or be conceived without the thing.
This reciprocal relationship also maintains that each thing has its own unique essence. Furthermore, by 'actual essence' [essentia actualis],
Spinoza means a singular thing's striving [conatus] to persevere in its being. It is of actual essences that intuitive knowledge can reach adequate knowledge.
Furthermore, Spinoza says:
Hinc videmus, Dei infinitam essentiam, ejusque aeternitatem omnibus esse notam. Cum autem omnia in Deo sint, & per Deum concipiantur, sequitur,
nos ex cognition hae plurima posse deducere, quae adaequate cognoscamus, atque adeo terium illud cognitions genus formare...
[Ethica, part II, prop. 47, scholium]
(From this we see that God's infinite essence and his eternity is known to all. And since all things are in God and conceived through God,
it follows that we can deduce from this knowledge a great many things which we know adequately, and so can form the third kind of knowledge...)
We can substitute 'reality' for Spinoza's term 'God' in the previous passage for a more general understanding.
There is some similarity between Spinoza's adequate ideas and Leibniz's concept of distinct perceptions
(see my blog here).
Both include the notion of a comprehensive understanding of a thing and not just the fragmented and abstracted view we have of things
through our experience and the second kind of knowledge, i.e. reason.
I found another cognate concept in Schopenhauer's theory of the pure subject of cognition (reines Subjekt des Erkennens).
Um also sich zur Erkenntnis der Ideen zu erheben, muss im erkennenden Subjekt eine Veränderung vorgehen, vermöge welcher es nicht mehr Individuum ist,
sondern entsprechend der ganzen Art des Objekts (der Idee), welche ebenfalls nicht einzelnes Ding, nicht Individuum ist, zum reinen Subjekt des
Erkennens wird, welches die Dinge nicht mehr in ihrer Beziehung zum individuellen Willen, sondern in ihrem selbsteigenen Wesen auffasst.
[Julius Frauenstädt: Schopenhauer-Lexikon, Vol 1, p. 346]
(In order to raise to the cognition of [Platonic] Ideas, a change must occur in the subject of cognition, through which it is no longer an individual,
but according to the whole kind of the object (the Idea), which also is not a single thing nor an individual. It becomes the pure subject of cognition,
which grasps things no longer in their relation to an individual will, but in their own inner essence.)
The 'idea' is Schopenhauer's term for essence, or the grade of objectification of the will in a particular thing. So, all these concepts
– intuitive knowledge, distinct perceptions, pure subject of cognition – attempt to describe a superior way of knowing the essence of things,
not as concepts or abstractions, but as what these particular things essentially are in themselves.