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and infinite essence of God。
》》》》》ProofThe human mind has ideas （II。 xxii。）； from which （II。
xxiii。） it perceives itself and its own body （II。 xix。） and
external bodies （II。 xvi。 Cor。 i。 and II。 xvii。） as actually
existing； therefore （II。 xlv。 and xlvi。） it has an adequate
knowledge of the eternal and infinite essence of God。 Q。E。D。
*****NoteHence we see； that the infinite essence and the
eternity of God are known to all。 Now as all things are in God；
and are conceived through God； we can from this knowledge infer
many things； which we may adequately know； and we may form that
third kind of knowledge of which we spoke in the note to II。
xl。； and of the excellence and use of which we shall have
occasion to speak in Part V。 Men have not so clear a knowledge
of God as they have of general notions； because they are unable
to imagine God as they do bodies； and also because they have
associated the name God with images of things that they are in
the habit of seeing； as indeed they can hardly avoid doing；
being； as they are； men； and continually affected by external
bodies。 Many errors； in truth； can be traced to this head；
namely； that we do not apply names to things rightly。 For
instance； when a man says that the lines drawn from the centre
of a circle to its circumference are not equal； he then； at all
events； assuredly attaches a meaning to the word circle different
from that assigned by mathematicians。 So again； when men make
mistakes in calculation； they have one set of figures in their
mind； and another on the paper。 If we could see into their
minds； they do not make a mistake； they seem to do so； because
we think； that they have the same numbers in their mind as they
have on the paper。 If this were not so； we should not believe
them to be in error； any more than I thought that a man was in
error； whom I lately heard exclaiming that his entrance hall had
flown into a neighbour's hen； for his meaning seemed to me
sufficiently clear。 Very many controversies have arisen from the
fact； that men do not rightly explain their meaning； or do not
rightly interpret the meaning of others。 For； as a matter of
fact； as they flatly contradict themselves； they assume now one
side； now another； of the argument； so as to oppose the
opinions； which they consider mistaken and absurd in their
opponents。
XLVIII。 In the mind there is no absolute or free will； but the
mind is determined to wish this or that by a cause； which has
also been determined by another cause； and this last by another
cause； and so on to infinity。
》》》》》ProofThe mind is a fixed and definite mode of thought （II。
xi。）； therefore it cannot be the free cause of its actions （I。
xvii。 Cor。 ii。）； in other words； it cannot have an absolute
faculty of positive or negative volition； but （by I。 xxviii。） it
must be determined by a cause； which has also been determined by
another cause； and this last by another； &c。 Q。E。D。
*****NoteIn the same way it is proved； that there is in the
mind no absolute faculty of understanding； desiring； loving； &c。
Whence it follows； that these and similar faculties are either
entirely fictitious； or are merely abstract and general terms；
such as we are accustomed to put together from particular
things。 Thus the intellect and the will stand in the same
relation to this or that idea； or this or that volition； as
〃lapidity〃 to this or that stone； or as 〃man〃 to Peter and
Paul。 The cause which leads men to consider themselves free has
been set forth in the Appendix to Part I。 But； before I proceed
further； I would here remark that； by the will to affirm and
decide； I mean the faculty； not the desire。 I mean； I repeat；
the faculty； whereby the mind affirms or denies what is true or
false； not the desire； wherewith the mind wishes for or turns
away from any given thing。 After we have proved； that these
faculties of ours are general notions； which cannot be
distinguished from the particular instances on which they are
based； we must inquire whether volitions themselves are anything
besides the ideas of things。 We must inquire； I say； whether
there is in the mind any affirmation or negation beyond that；
which the idea； in so far as it is an idea； involves。 On which
subject see the following proposition； and II。 Def。 iii。； lest
the idea of pictures should suggest itself。 For by ideas I do
not mean images such as are formed at the back of the eye； or in
the midst of the brain； but the conceptions of thought。
XLIX。 There is in the mind no volition or affirmation and
negation； save that which an idea； inasmuch as it is an idea；
involves。
》》》》》ProofThere is in the mind no absolute faculty of positive
or negative volition； but only particular volitions； namely；
this or that affirmation； and this or that negation。 Now let us
conceive a particular volition； namely； the mode of thinking
whereby the mind affirms； that the three interior angles of a
triangle are equal to two right angles。 This affirmation
involves the conception or idea of a triangle； that is； without
the idea of a triangle it cannot be conceived。 It is the same
thing to say； that the concept A must involve the concept B； as
it is to say； that A cannot be conceived without B。 Further；
this affirmation cannot be made （II。 Ax。 iii。） without the idea
of a triangle。 Therefore； this affirmation can neither be nor
be conceived； without the idea of a triangle。 Again； this idea
of a triangle must involve this same affirmation； namely； that
its three interior angles are equal to two right angles。
Wherefore； and vice versa； this idea of a triangle can neither be
nor be conceived without this affirmation； therefore； this
affirmation belongs to the essence of the idea of a triangle；
and is nothing besides。 What we have said of this volition
（inasmuch as we have selected it at random） may be said of any
other volition； namely； that it is nothing but an idea。 Q。E。D。
ProofWill and understanding are nothing beyond the
individual volitions and ideas （II。 xlviii。 and note）。 But a
particular volition and a particular idea are one and the same
（by the foregoing Prop。）； therefore； will and understanding are
one and the same。 Q。E。D。
*****NoteWe have thus removed the cause which is commonly
assigned for error。 For we have shown above； that falsity
consists solely in