1,059 research outputs found
Two Squares of Opposition: for Analytic and Synthetic Propositions
In the paper I prove that there are two squares of opposition. The
unconventional one is built up for synthetic propositions. There a, i are
contrary, a, o (resp. e, i) are contradictory, e, o are subcontrary, a, e
(resp. i, o) are said to stand in the subalternation
Towards Theory of Massive-Parallel Proofs. Cellular Automata Approach
In the paper I sketch a theory of massively parallel proofs using cellular
automata presentation of deduction. In this presentation inference rules play
the role of cellular-automatic local transition functions. In this approach we
completely avoid axioms as necessary notion of deduction theory and therefore
we can use cyclic proofs without additional problems. As a result, a theory of
massive-parallel proofs within unconventional computing is proposed for the
first time.Comment: 13 page
Neutrality and Many-Valued Logics
In this book, we consider various many-valued logics: standard, linear,
hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We
survey also results which show the tree different proof-theoretic frameworks
for many-valued logics, e.g. frameworks of the following deductive calculi:
Hilbert's style, sequent, and hypersequent. We present a general way that
allows to construct systematically analytic calculi for a large family of
non-Archimedean many-valued logics: hyperrational-valued, hyperreal-valued, and
p-adic valued logics characterized by a special format of semantics with an
appropriate rejection of Archimedes' axiom. These logics are built as different
extensions of standard many-valued logics (namely, Lukasiewicz's, Goedel's,
Product, and Post's logics). The informal sense of Archimedes' axiom is that
anything can be measured by a ruler. Also logical multiple-validity without
Archimedes' axiom consists in that the set of truth values is infinite and it
is not well-founded and well-ordered. On the base of non-Archimedean valued
logics, we construct non-Archimedean valued interval neutrosophic logic INL by
which we can describe neutrality phenomena.Comment: 119 page
Quantum Non-Objectivity from Performativity of Quantum Phenomena
We analyze the logical foundations of quantum mechanics (QM) by stressing
non-objectivity of quantum observables which is a consequence of the absence of
logical atoms in QM. We argue that the matter of quantum non-objectivity is
that, on the one hand, the formalism of QM constructed as a mathematical theory
is self-consistent, but, on the other hand, quantum phenomena as results of
experimenter's performances are not self-consistent. This self-inconsistency is
an effect of that the language of QM differs much from the language of human
performances. The first is the language of a mathematical theory which uses
some Aristotelian and Russellian assumptions (e.g., the assumption that there
are logical atoms). The second language consists of performative propositions
which are self-inconsistent only from the viewpoint of conventional
mathematical theory, but they satisfy another logic which is non-Aristotelian.
Hence, the representation of quantum reality in linguistic terms may be
different: from a mathematical theory to a logic of performative propositions.
To solve quantum self-inconsistency, we apply the formalism of non-classical
self-referent logics
Modal Calculus of Illocutionary Logic
The aim of illocutionary logic is to explain how context can affect the
meaning of certain special kinds of performative utterances. Recall that
performative utterances are understood as follows: a speaker performs the
illocutionary act (e.g. act of assertion, of conjecture, of promise) with the
illocutionary force (resp. assertion, conjecture, promise) named by an
appropriate performative verb in the way of representing himself as performing
that act. In the paper I proposed many-valued interpretation of illocutionary
forces understood as modal operators. As a result, I built up a non-Archimedean
valued logic for formalizing illocutionary acts. A formal many-valued approach
to illocutionary logic was offered for the first time.Comment: 15 page
Did Nāgārjuna Know Modal Logic?
Did Nāgārjuna Know Modal Logic
A lattice for the language of Aristotle’s syllogistic and a lattice for the language of Vasiľév’s syllogistic
In this paper an algebraic system of the new type is proposed (namely, a vectorial lattice). This algebraic system is a lattice for the language of Aristotle’s syllogistic and as well as a lattice for the language of Vasiľév’s syllogistic. A lattice for the language of Aristotle’s syllogistic is called a vectorial lattice on \cap-semilattice and a lattice for the language of Vasiľév’s syllogistic is called a vectorial lattice on closure \cap-semilattice. These constructions are introduced for the first time
Concert recording 2016-11-05
[Tracks 1-4]. Bassoon sonata no. 5 / Antoine Dard -- [Track 5]. Sonatine for bassoon and piano / Alexandre Tansman -- [Track 6]. Monolog for bassoon / Isang Yun -- [Tracks 7-9]. Concerto in F major / Carl Maria von Weber
On the history of logic in the Russian Empire (1850–1917)
In 1850 a very important decision for the whole history of humanities and social sciences in Russia was made by Nicholas I, the Emperor of Russia: to eliminate the teaching of philosophy in public universities in order to protect the regime from the Enlightenment ideas. Only logic and experimental psychology were permitted, but only if taught by theology professors. On the one hand, this decision caused the development of the Russian theistic philosophy enhanced by modern methodology represented by logic and psychology of that time. On the other hand, investigations in symbolic logic performed mainly at the Kazan University and the Odessa University were a bit marginal. Because of the theistic nature of general logic, from 1850 to 1917 in Russia there was a gap between philosophical and mathematical logics
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