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Unformatted text preview: lve abstract ideas. It would seem to follow that the forming of
abstract ideas is too difficult to be necessary for communication, which is so easy and
familiar for all sorts of people. But, we are told ·by Locke, replying to this point·, if adults
find abstract ideas easy to form, that is only because they have become good at it through
long practice. Well, I would like to know when it is that people are busy overcoming that
difficulty and equipping themselves with what they need for communication! It can’t be
when they are grown up, for by then ·they can communicate, so that· it seems the difficulty
is behind them; so it has to be something they do in their childhood. But surely the labour
of forming abstract notions  with so many to be formed, and each of them so difficult  is
too hard a task for that tender age. Who could believe that a couple of children cannot
chatter about sugarplums and toys until they have first tacked together numberless
inconsistencies and so formed abstract general ideas in their minds, attaching them to
every common name they make use of? 7
15 intro. Abstract ideas are no more needed, in my opinion, for the growth of knowledge
than they are for communication. I entirely agree with the widespread belief that all
knowledge and demonstration concerns universal notions; but I cannot see that those are
formed by abstraction. The only kind of universality that I can grasp does not belong to
anything’s intrinsic nature; a thing’s universality consists how it relates to the particulars
that it signifies or represents. That is how things, names, or notions that are intrinsically
particular are made to be universal ·through their relation to the many particulars that they
represent·. When I prove a proposition about triangles, for instance, I am of course
employing the universal idea of a triangle; but that doesn’t involve me in thinking of a
triangle that is neither equilateral nor scalenon nor equicrural! All it means is that the
particular triangle I have in mind, no matter what kind of triangle it may be, is ‘universal’
in the sense that it equally stands for and represents all triangles whatsoever. All this seems
to be straightforward and free of difficulties.
16 intro. You may want to make this objection:
How can we know any proposition to be true of all particular triangles unless we
first see it demonstrated of the abstract idea of a triangle that fits all the particular
ones? Just because a property can be demonstrated to belong to some one
particular triangle, it doesn’t follow that it equally belongs to any other triangle
that differs in some way from the first one. For example, having demonstrated of
an isosceles rightangled triangle that its three angles are equal to two right ones,
I cannot conclude from this that the same holds for all other triangles that don’t
have a right angle and two equal sides. If we are to be certain that this proposition
is universally true, it seems, we must either Ÿprove it for every particular triangle
(which is impossible) or Ÿprove it once and for all of the abstract idea of a triangle,
in which all the particulars are involved and by which they are all equally
represented.
To this I answer that although the idea I have in view while I make the demonstration may
be (for instance) that of an isosceles rightangled triangle whose sides are of a determinate
length, I can still be certain that it applies also to all other triangles, no matter what their
sort or size. I can be sure of this because neither the right angle nor the equality of sides
nor length of the sides has any role in the demonstration. It is true that the diagram I have
in view ·in the proof· includes all these details, but they are not mentioned in the proof of
the proposition. It is not said that the three angles are equal to two right ones because one
of them is a right angle, or because the sides that form it are of the same length. This
shows that the demonstration could have held good even if the right angle had been
oblique and the sides unequal. That is why I conclude that the proposition holds for all
triangles, having Ÿdemonstrated it ·in a certain way· to hold for a particular rightangled
isosceles triangle  not because I Ÿdemonstrated it to hold for the abstract idea of a
triangle! I do not deny that a man can abstract in that he can consider a figure merely as
triangular, without attending to the particular qualities of the angles or relations of the
sides. But that doesn’t show that he can form an abstract general inconsistent idea of a
triangle. Similarly, because all that is perceived is not considered, we may think about
Peter considered as a man, or considered as an animal, without framing the abstract idea
of man or of animal. 8
17 intro. It would be an endless and a useless task to trace the scholastic philosophers
[that is, mediaeval followers of Aristotle], those great masters of abstraction, through all
the tangling labyrinths of error and dispute that their doctrine of abstract natures and
notions seem...
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 Spring '13
 mendetta
 Philosophy

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