EBL 2014 – Session Philosophy of Logic I
April 8th
What does it mean to negate a
proposition?
Marcos Silva
[email protected]
Four preliminary remarks:
1) What is the nature of negation? What is its logical behavior? Do we need
negative facts in order to understand true negated propositions or false
propositions?
•Addition
•Suppression
•Absurd (inconsistencies)
•Inversion of truth conditions (neutral switcher)
•Primitive Incompatibility or Oppositions
•Exclusion
2) Many philosophical consequences! For instance, the need for a transition
from a neutral switcher between discrete states (syntax and logical atomism)
to some fine articulation of oppositions (semantics and holism)
3) For that, we will concentrate on two exemplary responses in Early Analytic
Philosophy: (Wittgenstein 1918) and (Demos 1917 and Wittgenstein 1929)
4) Cat on the table!
Some goals:
• To have two kinds of exclusion means to have at least two
negations. One for contradiction (classical and tractarian negation),
and another one for contrarieties (non-classical negation)
• The criterion is the presence or absence of the Principle of
Excluded Middle (PEM). We may have Bivalence, but not PEM.
Explosion of alternatives. Analogy to Demos 1917.
• This covers the collapse of the tractarian project (the first great
challenge for his truth-functionality, tautology and contradiction)
• This suggests a mandatory rise of non-classical logic inside of
Wittgenstein´s early philosophy. Semantics and holism (systems)
are much more sophisticated than his tractarian neutral operators
and logical atomism.
Outline:
I. A image of Logic (neutrality, truth-functionality,
tautology and contradiction)
II. Colors as a logical problem or how colors
challenge an image of logic TLP (1918). Not just
colors, but measurement and degrees (1929)
III. Demos (1917): another paradigm of negation
as exclusion (contradiction X contrariety)
IV. Conclusion (Richness of contrariety, Holism
and Systems)
I.
But, what is logic in the tractarian period?
(Neutral) Formal logic, truth-functionality, extensionality, tautology and
contradiction
5.551
Our fundamental principle is that every question which can
be decided at all by logic can be decided without further
trouble. (And if we get into a situation where we need to
answer such a problem by looking at the world, this shows
that we are on a fundamentally wrong track.)
Letter to Russell from Norway, 1913
“I want to repeat what I wrote about logic in my last letter,
putting it in a different way: All propositions of logic are
generalizations of tautologies and all generalizations of
tautologies are propositions of logic. There are no logical
propositions but these. (I consider this to be definitive.) [Dies
halte ich für definitiv].” (Tagebücher 14-16, p. 127).
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II. Colors as a logical problem or how colors challenge TLP
Truth table (1918):
Logicism: 1) It has a unique logical form; 2) it is hidden (not visible); 3) it is
very complex; 4) it must be discovered!
Truth table (1929):
Some lines have to be ruled out, “mutilated”. Some combinations must be ad
hoc blocked. We must add up rules to restrict logical space.
Question: Which are the status of these rules? They seem to be necessary and
a priori. But are they formal? Are they analytical? Synthetic a priori? How to
operate with this exclusion? Is this a contradiction? No! Contrariety!
Ok, but why are colors there? Three new topics at this time (1929):
1) Neutral and static facts and state of affairs should be phenomena! He keeps
full analyze but talks about phenomenological rules.
2) Not just colors, but measurement (degrees)
3) Very general and far-reaching problem, since virtually every empirical
quality allows degrees!
III.Why would be relevant to bring Demos (1917) to this discussion?
a)From the beginning, Demos 1) acknowledges contradiction X contrariety and 2) holds
explicitly another paradigm of negation, by embracing exclusions by contrariety to
understand denial.
b)Historically simultaneous, (but independent?)
c)Philosophically under influence of Russell (1905)
d)Non Negative facts!
e)Negation should be propositional.
f)But, to negate p is to oppose p with q, which is contrary to p.
For that, we need propositions which cannot be (logically) independent of another, because
they must be organized, inserted in systems! Plurality of systems!
Horn (2001), criticizing Demos´ denial interpretation, also acknowledges this explosion of
alternatives and the consequent challenge for PEM also as a logical result of understanding
negation in terms of contrariety rather than contradiction: “But which contrary does the
negation denote? If John is not at home, there are infinitely many true positive propositions
which entail that he is not at home, each of which constitutes a contrary of ‘John is at
home’.” (HORN, p.67, our italics.)
IV. Some Conclusions so far:
1.
Negation should be held as an equivocal term, since we must have at least two: The
teacher´s negation and the student´s negation.
2.
The paradigm of contrarieties is logically much more sophisticated than the paradigm
of contradictions. To operate with contrarieties, we need to understand a whole
system. Only with contradictions we cannot deal with phenomena, for instance.
Phenomena are logically organized, but not through tautologies, formal logic, and
truth-functionality (extensional connectives). We need other operators!
3.
Satzsysteme: If we do have elementary propositions, they should be all inserted in
several different systems, which are organized through exclusions by contrariety. The
denial “explodes” in alternatives. We may have bivalence, but not PEM (disjunctive
syllogism). Non-classical logic in the heart of TLP. To operate propositions we should
know the whole system in which the proposition is inserted to see which
combinations are allowed or not.
4.
Holism (instead of logical atomism): No proposition is logically isolated. You may
analyze them to an end. But this end will not have (logically) independent
propositions anymore. They are actually dense in relations (numerous implications
and exclusions). To reduce the former to the later is just a (philosophical) illusion. We
live in a (phenomenological) world of oppositions.
Obrigado pela atencao.
Thank you for your attention.
Some Literature:
DEMOS, Raphael. (1917). A Discussion of a Certain Type of negative Proposition. Mind 26: 188196.
SILVA, Marcos. Muss Logik für sich selber sorgen? On the Color Exclusion Problem, the truth table
as a notation, the Bildkonzeption and the Neutrality of Logic in the Collapse and Abandonment of
the Tractatus. PHD Thesis - Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro,
2012.
______. On Degrees of Exclusion within and among Systems. Revista Argumentos. (10). Fortaleza,
2013
______. Wittgenstein, Cores e Sistemas: aspectos logico-notacionais do colapso do Tractatus.
Revista Analytica. Rio de Janeiro, 2011.
______. Sobre a fragmentação do espaço lógico tractariano. Revista Brasileira de Filosofia. São
Paulo, 2014. Forthcoming.
VON WRIGHT, Georg Henrik. On Colour: a logic-philosophical Fantasy. In Six Essays in
Philosophical Logic. Acta Philosophica Fennica. Vol. 60, Helsinki, 1996. (pp. 9-16).
WITTGENSTEIN, Ludwig. Philosophische Bemerkungen. Werkausgabe Band 2. Frankfurt am
Main: Suhrkamp, 1984.
______. Some Remarks on Logical Form. Proceedings of the Aristotelian Society, Supplementary
Volumes, Vol. 9, Knowledge, Experience and Realism (1929), pp. 162-171 Published by:
Blackwell Publishing on behalf of The Aristotelian Society.
______. Tractatus Logico-philosophicus. Tagebücher 1914-16. Philosophische Untersuchungen.
Werkausgabe Band 1. Frankfurt am Main: Suhrkamp, 1984.
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