Yet despite the sometimes confusing
variety of forms assumed by Neoplatonism, its continual mingling
with a rich diversity of extraneous teachings falsifying in advance
any very precise general delineation, there were a number of respects
in which it constantly remained faithful to its original source;
more especially in its placing of primary importance on the "two
things in which" it has been said, "Plato is more interested
than in the theory of ideas itself, for that theory is after all
only his way of satisfying these two requirements; first that
there is such a things as mind which can apprehend reality, and
second, that this reality which is the object of knowledge has
absolute and unqualified existence."(118b) Thus the epistemological
analysis offered by the Theaetetus, with its apparently
negative conclusions, is an illustration of the thesis that it
is impossible to extract knowledge from sensible appearance if
the world of true being is left out of account. This world is
known through the mind, it is the real reference of thought, for,
it is argued in the Parmenides (119b), a thought cannot
refer to nothing, to what "is not"; the Forms cannot
be mere thoughts, for a thought is always an act which
has something other than itself as an object, and the thinking
of Forms, which cannot be sensible perceptions, must therefore
be of "Real Forms." Every mental operation therefore
appears as the intuition of an object. The mind's direct insight
into reality is sometimes exemplified in the dialogues by the
way in which genuine new knowledge can arise from reflection,
can be born from the rearranging of words, the referential content
of each one of which taken singly was nevertheless apparently
fully known previously (for the Cratylus freely admits
that, whether single words can be held to "resemble"
things or no, they can only be significant for those who already
know the things they represent (120)). Since mind thus communicates
with a higher more extensive aspect of reality than the sense,
"opinion and reflection and thought, and art, and law, will
be prior to things hard and soft and heavy and light; and further
the works and actions that are great and primary will be those
of art; while those that are natural and nature itself, which
they [the scientists] wrongly call by this name, will be secondary
and will derive their origin from art and reason."(121) Such
a view of the character of mind, explains why, in the last resort
as well as for preliminary investigations, "Aucune demonstration
logique, aucune serie de deductions n'est superieure, pour Platon,
a la simple analyse psychologique de nos facultes intellectuelles"(122);
it accounts for the consciousness Platonism frequently displayed
of being - as Nietzsche said much philosophy had always been -
"a recognising, a remembering, a return, and a homecoming
to a far-off ancient common household...a kind of atavism of the
highest order"(123): for in the logical working out of this
view of mind it was usually found to be necessary to have recourse
to some theory of anamnesis, or of individual minds' participation
in, or illumination by, some unified intellect transcending them.
There was complete agreement between
the two schools that knowledge dealt with universals and not particulars,
and that logic - and perhaps also mathematics - was a necessary
preliminary discipline to other sciences. For instance, though
Bruno makes it subserve a special purpose, there is nothing in
the statement itself, which he employs fundamentally in his exposition
of the Lullian Art - "Subiectum considerationis est universum,
quod veri intelligibilis rationabilisque rationem subire valet,"(124)
that would distinguish it as either Aristotelian or Platonic;
nor is there much to which either party would not subscribe in
Hugh of St. Victor's insistence that logic and mathematics which
"treat of the intellectual comprehensions of things"
must be prior, in order of learning, to physical speculation since
they "put their consideration not in the actual state of
things where experience (experimentum) is deceitful, but in reason
alone, where unshaken truth dwells. Then with reason provided
for they could descend to the experience of things."(125)
But there is sharp contrast between their respective evaluations
of these sciences as direct contributions to positive knowledge,
and between the relationship allowed between the universal and
reality, as to whether it or the particulars falling under it
represented an approximation to the other. For Pico for instance
"La connaissance a pur but non pas la connaissance des choses
concretes mais celle de leur immuable modele. Le critere de la
verite de cette connaissance est sa concordance avec l'idee";
"si ut exemplari suo quam vocamus ideam secundum quam illas
condidit deus....respondent, verae dicuntur...." and the
formulation of a concept was "le comprehension de la substance
divine qui se devoile dans les choses."(126)
There was perforce, Cusa frequently
insisted unanimous agreement that the beginnings of all intellectual
knowledge was "faith," something which forming the ground
of discursive knowledge could not be proved by it but only taken
on trust; since in all spheres it was necessary to pose certain
premisses of this order from which the intellect drew the matter
of which it treated and its method of doing so; and on which ultimately
all intelligibility depended (127). Truth thus appears as a function
of a logical system, and the description of a proposition as true
can mean only, and exactly, that it has been implied by a previous
proposition in a manner admitted as valid, and also that
this proposition, or the first term of the series of propositions
standing in such a relationship to each other has been taken for
granted, accepted as an axiom of the system. Now it is clear
that two kinds of suppositions are made here: firstly concerning
valid formal logical procedures, secondly, if the system is to
have any experiential reference, and a chain of deductions is
ever to conclude in a synthetic statement, then at least one proposition
must be initially postulated, having synthetic content (that something
is thus or thus), and which is susceptible only of empirical verification,
and only thus saved from being merely conditional. These two
Aristotelianisms separated as Platonism did not. The various
principles of logic, it held, admitted not of absolute proof but
only of one "ad hominem" (128) they were accepted perhaps
as "natural facts," but not treated as "hypotheses"
- as statements in a metaphysic proceeding from higher principles
on which they could be satisfactorily believed to depend whether
or not the nature of these was directly accessible to human reason;
while "verification" was ultimately to be sought in
the data provided by the sense concerning objects totally independent
of mind. The limits of logical thought were to correct to some
extent errors in the data - discrepancies between various appearances
of the same object - and to reveal reality already entirely present
in these objects, though perhaps not fully manifest at any one
time since they were all undergoing processes of generation and
corruption - its function was merely to explain the sensible world
by a rational organisation of it in terms, as far as possible,
of selected privileged aspects of perception. In contrast, Platonism
did not restrict experience - in so far as this term refers to
the source of genuine synthetic knowledge - to the senses; the
necessary preliminary synthetic propositions could be found in
the mind itself and the direct experiential verification of them
was, if not yet fully, an ability of the soul; indeed abstract
thought, imagination and sense, were all fragments of one final
experience, represented under various guises, of the unity of
things, which, since it was an experience which included all knowledge
in itself, necessarily implied the otherwise "hypothetical,"
principles of logic. Indeed the hierarchies of existence, reason
and value were considered as only complementary aspects of the
same reality, inseparable and mutually implicative; there is an
insistence on what has been called "the fact that the ontological
predicates are meanings that depend for their meaning on the acknowledgment
of values,"(129) and that the intellect is orientated towards
values; while these values are, understandably, accepted in such
neo-Platonic systems as actual and transcendent since such Renaissance
systems do not of course consider, and therefore make no allowance
for, the only other possible alternative, that it is the orientation
of the intellect (in man) which itself defines, and by giving
a form to, in effect gradually creates, values.
The final and unique belief for
Plato, which would supply the equivalent of a direct inspectional
verification of fact by a genuine intuition of reality, and also
a guarantee of formal correctness of logical method, was the Idea
of the Good, which was at once the goal of life, the condition
of knowledge and the sustaining cause of the World. For Christian
Platonists such as Clement the Idea of the Good becomes fused
with the nature of God as known by scriptural revelation and by
the "illumination" of all individual minds, proceeding
mediatedly from God, but which is only thoroughly certified by
the acceptance of some revelation. But when Clement insists (120)
on the dependence of all knowledge, indeed of the very possibility
of knowledge, on such revelation, that there can be no third term
between a self communication of the divine and absolute scepticism,
he is not advancing such revelation as exhausting the form or
content of all accessible knowledge, but claiming it merely as
a premise which having absolute certainty, and universal application,
guarantees retrospectively the validity of all human knowledge
which can be exhibited in a unified coherency; and this by the
mere fact that its own existence certifies that there is knowledge
and that it may be possessed by the mind, hence any proposition
that can be shown to belong integrally to such an ordered system
in any connection may then be taken as wholly compatible with,
and certified by, revelation.
Where recourse was not made to such
revelation, the possible, though rare, attainment of contact with
the One, or Idea of the Good, by the individual mind was employed,
to demonstrate the existence of ultimate grounds of certainty
for thought, resulting in the emphasis on what has been called
"interiority" of the Neoplatonism of Plotinus and thereafter
of the majority of thinkers in this tradition, which provides
a sharp contrast to classical thought in general. Since the idea
of the Good was much richer in content than single experiences,
was not an intellectual abstraction from them, but all-comprehensive,
and involved the complete reconciliation and co-existence of apparent
contraries, it thus transcended all intellectual knowledge employing
division and discrimination, and rejected all descriptions that
any form of discursive thought might attempt to impose on it.
The contemplation of it could take place in a mystic trancelike
state which Plotinus, employing the paths suggested in the Symposium,
frequently achieved, according to Porphyry, who also claims to
have once, at the age of sixty-eight, similarly approached near,
and been united with, the supreme divinity; while Procus, says
Marinus, by his mental purifications attained at last to
and "by his own eyes he saw those truly blessed visions
of Reality, no longer obtaining this knowledge by reasoning or
demonstration, but as if by vision, and by simple and immediate
perception of the intuitive faculty - viewing the ideal form in
the Divine Mind."(131)
Nevertheless the process was thoroughly
intellectual (as opposed to something won through moral discipline
or the exploitation of emotional feelings). "I believe we
are not permitted to think that God dwells in any other part of
us than the intellect," wrote Synesius, whose work on divination,
and some confusion with the homonymous alchemist contributed to
his high reputation in the Renaissance (132). The passage to
the One for Plotinus could only be effected when noumena were
fully realised as arising from the world of the sense. The attainment
of the One was, following Plato's analogy of the line, represented
as the final term of a progressive intellectual ascent. The hierarchy
in which science and modes of knowing could be arranged, could
thus, even in the absence of direct experience of the One, or
Idea of the Good, by the observed direction of its development
define as it were, the position of this, and the sciences in their
successive higher generalities, could indicate something of the
nature of that on which they were all ultimately dependent. Such
a connected hierarchy of knowledge leading upwards to a source
which alone verifies its content is described by Proclus, in the
commentary on the Euclid: "l'ascension des connaissances
va des choses plus particulaieres aux plus generale jusqu'au moment
ou l'on s'eleve a la science meme de l'etre en tant qu'etre....cette
science est la plus collective de toutes et...toutes se ressentent
des principes qui viennent d'elle; car celles ci suggerent toujours
les premieres hypotheses au dessus de celles qui leur sont subordonnees,
tandis que celle-la fournit d'elle-meme, et comme etant la plus
parfaite des sciences, des principes a toutes, universels pour
les unes et plus particuliers pour les autres."(133) The
confirmation of all certitude however remained necessarily dependent
upon some direct experience to be found at the upper termination
of such a scale, this final experience, which involves all knowledge,
and is its actual source and logical foundation, Augustine identified
with the "beatific vision."(134) It became a familiar
analogy to compare the Reason's elation to God with that of the
eye of the sun - it was a power that remained helpless until things
were illuminated for it by God (135). In the seventeenth century
Henry More still employs similar ideas when he speaks of "a
certain principle more noble and inward than reason itself, and
without which reason will falter or at least reach but to mean
and frivolous things," and which is of so "retruse a
nature" that he hesitates to name it, but finally calls it
"Divine Sagacity"; it is "a more inward compendious
and comprehensive presentation of truth, even antecedaneous"
to reason, though the activities of reason serve to confirm and
illustrate it (136). Similarly John Smith founds truth and knowledge
on "an intellectual touch of Him," and distinguishes,
following Proclus, ascending degrees of knowledge beginning and
ending in "intuition," from a "naked perception"
through a miscellaneous collation of impressions, Discourse, Reason,
Mathematics and Dialectic, to a "naked intuition of eternal
truth," the realisation of the last being not wholly possible
in life, for "imaginative Powers, which are constantly attending
the highest acts of our soul, will be breathing a gross dew upon
the pure glass of our understandings."(137)
The doctrine of a scale of degrees
of knowledge, the higher whatever the immediate efficient causal
occasion for their appearance in the individual mind, being functionally
independent of the lower and successively approximating more closely
to Reality and True Being, is a marked feature of neoplatonism.
It appears occasionally with an admixture of Aristotelian doctrine
in Boethius (138), but in the work of Avicenna, who was according
to Roger Bacon the vehicle for the last of the four great revelations
made to mankind by God, and to whose "Theology" Dee
notes his adherence, it achieved formalised, explicit and influential
expression for the middle ages and Renaissance. Rejecting the
original Platonic Ideas - though only in the guise under which
Aristotle had critically exposed them as useless or self-contradictory
- he distinguishes four degrees of "abstraction": that
supplied through the senses in the presence of the material object,
secondly imagination which continues to envisage the object in
its absence through its sensible attributes, thirdly the "vis
estimativa," which allows of particular judgments which discover
certain immaterial ideas in the object, through which alone the
mind becomes aware of them - the lamb's recognition of "enmity"
in the wolf is an example - while although these surpass the apparent
content of the data supplied by any one of the senses, they are
still rather considered as possessed of presentational immediacy,
as essentially connected with the character of the object in the
nature of things than as imported into sensation by the mind as
a product of educated association; and lastly, accessible only
to rational beings such as Man, the Universal. The materials
for the first three operations are all furnished by the "intelligence"
and represent the extent of its unaided capacity for taking account
of the external world it perceives through the senses; but in
knowing the universal, the intellect becomes "actual"
in a way not determined, by particular objects, while since what
exists potentially only becomes "active" by the assistance
of something already "active" of the same nature as
itself, a separated Intelligence is postulated by Avicenna, which
governs the sublunar world, gives forms to all things, and transmits
"intelligible forms" to the human intellect, which then
becomes "active" in applying them to the three lower
types of knowledge already in its possession. As regards these
"universals" or "intelligible forms," Avicenna
asserts even God's knowledge is of the same order as man's, and
thought comprehending everything past and future at once, yet
still requires a "discursus," though of a non-temporal
kind (139). In the Latin West the activity of the separated intelligence
was usually interpreted, as for example in Gundissalinus' de
Anima which closely followed and "Christianised"
Avicenna's arguments, as the Augustinian illumination of the mind
by God; Avicenna himself being accepted as having formalized a
philosophy implicit in the theological writings of Augustine:
"Il parut d'abord offrir une sorte de developpement de Saint
Augustin, et les rapports que l'on pouvait etablir de l'un a l'autre
furent la raison de l'influence profonde excercee par Avicenne
dans l'Ecole Franciscaine."(140)
The view of the nature and powers
of the mind here presented is a general and distinguishing feature
of neoplatonism. Thus Anselm's ontological "proof"
of God's existence, which Albertus Magnus significantly stigmatised
as "a Pythagorean sophism," it has been observed,
"was an expression of his conviction that thought penetrates
significantly to the ultimate nature of things."(141) The
understanding, said Cusa, is always directed towards being, it
is nourished on truths which recall it to the Divine Wisdom, from
which its activities derive, and of which, since it tends towards
it, it has already some slight "foretaste" or precognition
(142). Cassirer drawing attention to Galileo's frequent use of
the Meno, particularly the incident of the slave's solving
without instruction a problem in geometry by "natural"
reason, stimulated by questioning, remarks, "Galileo seems
to accept all the consequences drawn by Plato from this fact.
He declares that truth being necessary and eternal cannot be
attained and cannot be proved by experience alone. Experience
gives us accidental facts, but it cannot teach us any necessary
truth. The necessary things, that is to say those for which it
is impossible to be otherwise, the human mind either knows by
itself (da per se) or it is impossible for it sever to learn them"(143)
(an example which illustrates the connection of this stream of
thought with the new science - Descartes similarly was to locate
the Archimedean point of the philosopher within the mind)(144).
Again Cudworth, in the same tradition, holds that universals
cannot be derived from things, but "things" are perceived
via universals: these exist already, and completely, within the
mind, and seem to stimulate it into activity. "The essence
of nothing is reached into not by the senses looking outwards
but by the mind's looking inwards into itself." The "primary
and immediate objects of intellection and knowledge are not things
existing without the mind but the ideas of the mind itself actively
exerted"; that is the mind itself must supply the intelligible
"reason of things" and judges of truth and being, by
the degree to which its innate standards of coherence are satisfied,
for "the entity of all theoretical truth is nothing else
but clear intelligibility; and what is clearly conceived is an
entity and a truth,"(145) for even omnipotence could not
create a mind capable of forming a clearly intelligible idea of
a falsehood.
Before noting some of the effects
of such doctrines on views as to general structure of the world,
the use and status of mathematics and their relations with the
scientific outlook of the Renaissance, something must be said
of the considerable transformations the Theory of Ideas underwent,
retaining something of the vocabulary but little of the probably
meaning of the original Platonic statement. In some respects
a belief in separated forms was more congruous with Christian
teachings than the Aristotelian position that they were only definitions
embodied in matter, while it did not pass unnoticed from the earliest
times that Aristotle himself had not been able universally to
apply this postulate, since although he denied the existence of
form apart from matter, the Prime Mover, on which the whole dynamics
of his cosmology depended, was itself nothing but Pure Form.
Boethius who, as an accepted source and authority, transmitted
to the Middle Ages a presentation of classical philosophy, in
which elements from Plato, Aristotle, the Stoics, later Platonists
and perhaps Augustine, were inextricably commingled, exhibits
confusion and offers apparently contradictory statements on this
point. He denied for instance on the one hand that the world
is framed by God after any models (146) and in another place addresses
God, "thou dost all creatures' forms from highest patterns
take."(147) In one treatise he can state "essences
indeed can have a general existence in universals but they have
particular existence in particulars alone, for it is from particulars
that all our comprehensions of universals is taken,"(148)
yet in De Trinitate, after setting out an Aristotelian
analysis of essence depending on an only abstractedly separable
form, and the three grades of speculative sciences Physics, Mathematics
and Theology distinguished in accordance with this, he adds that
matter is "subjected to" universals, and that "we
misname the entities that reside in Bodies, when we call them
forms; they are mere images; they only resemble those forms which
are not incorporate in matter."(149) Indeed even after the
time of Aquinas, except among Averroists, until the late Renaissance
it would seem to have been usual, for professed followers of Aristotle,
while accepting Aristotelian doctrines as undoubtedly true as
far as human knowledge was concerned, nevertheless to admit, that
as regards God, essences were possessed of existence independent
of, and prior to, particulars. Mandonnet thus writes of Albertus:
"Pour lui tout en admettant avec Aristote, qu'il n'y a que
des singuliers dans la nature et que l'universel est dans l'intelligence
humaine, il ajoute a cette double donnee l'affirmation de l'existence
d'un universel anterieur a sa realisation dans les singuliers,
et independent du fait de son actualite."(150)
Plato's postulation of the Ideas
provided a certain foundation of knowledge, relating it directly
with reality, such as could not be derived from the sensible world,
and also provided a mediate realm, logically ordered and accessible
to mind, between the sensible world and the Idea of the Good.
This last was acutely necessary, since the Idea of the Good is
nowhere directly discussed in the dialogues and indeed perhaps
could not have been by Plato without employing terms, which although
readily acceptable to later "platonists" who were able
to regard the Parmenides as expressing a mystic theology,
would have suggested to the classical Greek mind, had the representation
of this formless absolute been then attempted, only the horrors
then invariably associated with the undetermined, and unlimited,
which were properties pertaining rather to what lay below the
level of what was intelligible, denoting deficiency, evil, and
primitive unqualified matter (151). Many difficulties regarding
the theory Plato directly or by implication did successfully resolve;
thus as to apparently contradictory assertions about the immanence
or transcendence of Ideas, his general treatment may be taken
as showing that, he "eut accepte les deux theses, et selon
son expression: pris les deux a la fois: en distinguant les
point de vue" (152) and the application of the "Third
Man," with its consequence of setting up an infinite regress,
would thus not be a valid objection. However, large groups of
"Ideas" - those of the mathematicals, or connecting
modes or structures of thought are the chief exceptions - lie
open to Aristotle's objection of being a useless and unnecessary
duplication of the external world. For they themselves seem to
be almost concrete entities, differing from the sensibly perceived
only in being permanent and stable - and also lie, it would frequently
seem to be implied, outside mind - though the mind may have innate
memories of them - for they are objects of knowledge for it, to
be reached by its activities, they are not mental phenomena belonging
to some higher intelligence, in which individual minds participate,
but rather "things," endowed with all the qualities
that would be at first intuitively ascribed absolutely to sensible
objects (qualities the Greeks seem never to have wholly disassociated
from their fundamental assumptions about what the nature of Reality
must be), but which a later critical analysis - such as the Heraclitean
- shows to be indefensible, as a view of merely sensible objects.
In the reinterpretation of the theory, which became general from
the early centuries of the Christian era onwards, "apprehension
of the ideas is not so much a result reached by the activity of
intelligence, as the presence in the intellect of, or the illumination
of the intellect by, the Ideas."(153)
Thus Alcinous in the first century,
conciliating Plato and Aristotle, situates the Ideas in the divine
Intelligence, they become as it were from thence forward the thoughts
of God, but thoughts which are active, "productive of things,"
an instrument of creation (154). In such a tradition Augustine
stresses that things exist because God knows them; He does
not know them because they are, for His thought, as opposed to
man's which is merely reflective and representative, is creative
and constitutive (155). Similarly the great principle of Avicenna's
system is, it has been said, "Penser, chez les substances
separees, signifie creer." (156)
A similar change occurs in what
the Ideas are considered to be for the individual mind and the
type of knowledge which this possesses per se. Porphyry when
he joined the school of Plotinus was, after much disputation,
led to reject his earlier view - perhaps nearer Plato's own -
that the ideas could exist as separate entities outside the mind.
But the concepts that are innate in the soul, to Plotinus are
no longer "objects" which in their qualitatively perceptible
aspects sensible things imitate as closely as possible; they are
the noetic activity of the soul, the principles according to which
it "energises." It was in some such form as this that
the theory of Ideas generally survived and developed, still claiming
to be "Platonic," so that in the seventeenth century
John Smith, drawing largely on Plotinus, defends "innate
ideas" as being in reality a reflection of the structure
of the mind, and as representing not discrete particular objects
of knowledge, but the functioning of an active nature latent within
us, and Henry More regards them as "our own modes of considering
sensible objects": cause and effect, like and unlike, whole
and part, for instance, being the "natural furniture of human
understanding."(157)
Such a view, although apparently
much looser and more vague as to the precise nature of the objects
and forms of a priori knowledge than the original Platonic statements,
proved in practice highly fertile in suggestiveness. A typical
Renaissance popular rather than philosophical expression of it
is offered by Eliot's Governour. Discussing "Sapience,"
he says "that god almyghtie infuded Sapience into the Memorye
of man...whiche, as a Treasory, hath power to retayne, and also
to erogate and distribute, when opportunitie hapneth....More over
Plato (in his boke called Timaeus), affirmeth that there is sette
in the soule of man commyng into the worlde certayne spices or
as it were sedes of thynges and Rules of Artes or sciences. Wherefore
Socrates (in the boke of Science) resembleth hymselfe to a mydwyfe...And
like as in houndes is a power or disposition to hunte, in horses
and grehoundes an aptitude to renne swifetly, so in the soules
of men is ingenerate a lerne of science, whiche with the mixture
of a terrestryall substaunce is obfuscate or made darke, but where
there is a perfeyte mayster prepared in tyme, then the brightnes
of the science appereth polite and clere," for it is to be
developed by practice and exercise (158). An example of the type
of knowledge which could be regarded as deriving from this source
is provided by Galileo's Dialogues of Two principle systems
of the World. When Galileo, in the person of Salviai, is
accused by Simplicius of erring with Plato, holding that "nostrum
scire sit quoddam reminisci," far from rebutting the charge,
he proceeds to lead on Simplicius and Sagredo to deduce
for themselves, on apparently a priori grounds, certain fundamental
propositions of mechanics and the true laws of physics (159).
In such a development as this it would seem that the Ideas, in
the form in which they are accepted as innate in the mind, become
in fact, however unconsciously on the part of those employing
such theories, increasingly connected with and solely taken as
indicating the particular way in which Mind apprehends Order.
The resultant subtilization, or
rather radical change in the nature of the Ideas, is clearly to
be seen in the case of mathematical entities. After listing five
degrees of knowledge, distinguished by various instruments they
employ for representing reality, Plato writes "Every circle
that we draw or make in common life is full of characteristics
that contradict the fifth thing, the true circle, for it everywhere
coincides with a straight line, while the true circle as we said
has in it not the slightest element belonging to a contradictory
nature."(160) The idea of the circle is here, as it were,
a purification of an intuitive datum, existing by itself, and
unrelatedly, as a primitive atomic object of thought. On the
other hand, Cusa and Bruno introducing for this purpose infinity
into mathematics, find it of more importance to investigate, and
to reason and draw ontological conclusions from circles that coincide
throughout with straight lines, to reach Ideas which, produced
by rigorous logical thought and therefore intelligible, embrace
and unify under one principle, as many "contradictory natures"
as possible. Thus Cusa, rejecting imagination which, confined
to sensible things, obscures by false particularisation (161),
lists a number of descriptions of the maximum, employing apparently
widely differing entities, lines, triangles, and circles, and
then states that the originators of all these were, at the same
time, of one opinion and possessed of an "exact conception"
of the maximum (162), and asserts that the mind can arrive at
such concepts, which may be usefully and validly employed, even
though it is incapable of fully envisaging them (163). The limitation
of what may be said to be "conceived," or be described
as "a clear and distinct Idea," to the imaginative faculty
led of course to Berkeley's denial of existence to general abstract
ideas (e.g., Triangle), and similarly to Mill's remarks on the
geometrical line, that "the mind cannot form any such notion,
it cannot conceive length, without breadth; it can only in contemplating
objects attend to their length exclusively of their other
sensible qualities, and so determine what properties may be predicated
of them in virtue of their length alone. If this be true, the
postulate involved in the geometrical definition of a line is
the real existence, not of length without breadth, but merely
of length that is, of long objects."(164) These views illuminate
by contrast the attitude of much Renaissance neo-Platonism, particularly
that influenced by mathematics, diametrically opposed to them
in this respect. For already by the Renaissance to Platonists
the Idea is frequently thoroughly functional, to "conceive"
adequately is becoming translatable by "to be able to operate
with," to be clear and distinct is coming to signify a potentiality
for being subjected to an intelligible analysis within a system
of reasoning, existence is allowed to that of which a logical
account can be given. Indeed the standard that is here adopted
of what is "objectively" true, together with the recognition
of its origin in reason, may without much distortion be compared
to Frege's position: "So verstehe ich Objectivitat eine
Unabhangigkeit von unserm Empfinden, Anschauen und Vorstellen,
von dem Entwerfen innerer Bilder aus den Erinnerungen fruherer
Empfindunge, aber nicht eine Unabhangigkect von der Vernunft;
denn die Fragen beantworten, was die Dinge unabhangig von der
Vernunft sind, hiesse urtheilen, ohne zu urtheilen....Der grund
der Objectivitat kann ja nicht in dem Sinneseindrucke liegen,
der als Affection unserer Seele ganz subjectiv ist, sondern soweit
ich sehe, nur in der Vernunft" etc.(165) While as respects
neo-Platonic systems adopting a similar position, however doubtful
its truth as applied to the thought of Plato, the view may to
a large degree be maintained that "The Platonic Idea is the
expression of the simple thought that every rightly formed concept
has its solid basis in objective reality," since "every
representation as such as a universal relation, not the individual
phenomenon, as its content."(166)
The mind is supposed to attain these concepts by a process of discovery, an increasing self-consciousness, which usually remains fairly close to the original Platonic anamnesis - indeed the acceptance of such a doctrine can be shown to destroy the basis of Aristotle's attack in the Prior Analytics on the Platonic investigation by division, as a false syllogism, perpetually begging the questions, as well as much of his other criticisms and is perhaps the only firm basis for answering it. In this process the sensible world is of assistance in suggesting, and pointing to, the general truths from which it derives being. Thus in Plato's words "we see through not with the sense."(167) Thus "the geometrician and arithmetician," writes Plotinus, "knowing in the sensible object the imitation of that which subsists in intellection, they are as it were agitated and brought to the recollection of reality."(168) Some such stimulation may be necessary, but it provokes rather than controls the essentially active process of recollection: "Memory is not a certain repository of impressions, but a power of the soul exciting itself in such a way as to possess that which it had not."(169) Similarly Bacon's master, Grosseteste, taught in conjunction with a doctrine of "illumination" from Avicenna and Augustine, that the action of the sense, and their true function, was such as to excite the soul to a memory of its former acquaintance with incorruptible intellgibles. While, echoing the same thesis, in the seventeenth century, Henry More declares that doubts as to the existence of innate ideas can arise only through confusion of the "extrinsecal occasion" of thinking with its "adequate or principle cause," externals being rather "the reminders than the first begetters or implanters" of knowledge (170).