Reduction and Elimination in Philosophy and the Sciences

properties are located. This process transforms a sense
proposition until it says nothing but it shows its logical
form.
The method could be represented as in Figure 1.
Please notice that the generalization process it’s
much more subtle than how it seems. Especially the 3 th
generalization step it’s critical, because assuming a
general sensorial space, it’s not enough to derive a logical
form from the propositions obtained from the 2 nd
generalization: also the sensorial properties expressions
(in Wittgenstein’s use of the term ‘expression’, see again
propositions 3.311-3.313) must be considered akin a priori.
This is actually not guaranteed by the sensorial space
structure.
The process applied to write the logical form of the sensorial propositions
At the end of the generalization process, at the level of the
logical form, the sensorial space structure is still in evidence.
The critical point of the whole process is once
again the assumption of the structure of the sensorial
spaces (derived from 6.3751) as a logic place where it is
possible, defining the “position” of an object, to negate the
remaining space for the same object.
4. The Contradiction
Because of the dependency between a sense proposition
‘Ra’ and all the propositions about ‘a’ related through that
space properties, the strange “exclusion” in Table 1 is not
more needed. If ‘a is red’ is ‘Ra’ and ‘a is green’ is ‘Ga’, the
logical product became:
It is always possible to write 2 :
because S S R G ∈ and RS ∈ GS
( RSa ∧ GSa)
∧ ~ ( RSa
∧ GSa)
( a ∧ G a)
∧ ~ ( G a ∧ R a)
RS S S S
.
2 In a slightly generalized sense, RS and GS indicates here the classes of
the properties different from R and G in space S.
The Logic of Sensorial Propositions — Luca Modenese
With this method we finally obtain a genuine contradiction
and also the first line in Table 1 is clearly managed and the
difficulty by it generated resolved: the first line must be
considered valid in the same way as the other and its apparent
absurdity is resolved thanks to the second “hidden”
term discovered by the analysis of the sensorial propositions.
A consequence of sensorial propositions logical
form is that a logic product between propositions of the
same sensorial space can be only a contradiction or a
tautology (considering the same space-temporal
coordinate of course). The logic product of propositions
belonging to different spaces instead is never neither a
contradiction nor a tautology.
The investigation here presented can be considered
an example of the clarifying possibilities of logical analysis.
5. Conclusion
The method described in proposition 3.315 of the Tractatus
was used to clarify the nature of sensorial propositions,
after the assumption for all the sensorial spaces of
the logic structure of colours presented in proposition
6.3751. Considering sensorial spaces that are fully involved
when a single point of them is used to define an
object, it is shown how truth tables derived from sensorial
propositions can be expressed in a complete and clear
way, useful to investigate their logical properties.
The assumptions and critical points of the process
developed have been stressed in a way so that anyone
could decide by himself if accept or refuse such a way of
proceeding.
Literature
Anscombe, Gertrude E. M. 1959 An introduction to Wittgenstein’s
Tractatus, London: Hutchinson&Co.
Kenny, Anthony J. P. 1973 Wittgenstein, London: Allen Lane The
Penguin Press.
Ramsey, Frank P. 1923 Critical notice of L. Wittgenstein’s Tractatus
Logico-Philosophicus, Mind, XXXII, 128, 465-478.
Wittgenstein, L. 1984 Tractatus logico-philosophicus, in: Werkausgabe
in 8 Baenden, Band 1, Frankfurt am Main: Suhrkamp.
Wittgenstein, L. 1929 Some Remarks on Logical Form, Proceedings
of the Aristotelian Society Suppl. vol. 9 162-171.
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