33,091 research outputs found
Questions and Answers about Oppositions
A general characterization of logical opposition is given in the present paper, where oppositions are defined by specific answers in an algebraic question-answer game. It is shown that opposition is essentially a semantic relation of truth values between syntactic opposites, before generalizing the theory of opposition from the initial Apuleian square to a variety of alter- native geometrical representations.
In the light of this generalization, the famous problem of existential import is traced back to an ambiguous interpretation of assertoric sentences in Aristotle's traditional logic. Following Abelard’s distinction between two alternative readings of the O-vertex: Non omnis and Quidam non, a logical difference is made between negation and denial by means of a more fine- grained modal analysis.
A consistent treatment of assertoric oppositions is thus made possible by an underlying abstract theory of logical opposition, where the central concept is negation. A parallel is finally drawn between opposition and consequence, laying the ground for future works on an abstract operator of opposition that would characterize logical negation just as does Tarski’s operator of consequence for logical truth
Is Incompatibilism Compatible with Fregeanism?
This paper considers whether incompatibilism, the view that negation is to be explained in terms of a primitive notion of incompatibility, and Fregeanism, the view that arithmetical truths are analytic according to Frege’s definition of that term in §3 of Foundations of Arithmetic, can both be upheld simultaneously. Both views are attractive on their own right, in particular for a certain empiricist mind-set. They promise to account for two philosophical puzzling phenomena: the problem of negative truth and the problem of epistemic access to numbers. For an incompatibilist, proofs of numerical non-identities must appeal to primitive incompatibilities. I argue that no analytic primitive incompatibilities are forthcoming. Hence incompatibilists cannot be Fregeans
Epistemic Pluralism
The present paper wants to promote epistemic pluralism as an alternative view of non-classical logics. For this purpose, a bilateralist logic of acceptance and rejection is developed in order to make an important di erence between several concepts of epistemology, including information and justi cation. Moreover, the notion of disagreement corresponds to a set of epistemic oppositions between agents. The result is a non-standard theory of opposition for many-valued logics, rendering total and partial disagreement in terms of epistemic negation and semi-negations
Sartre's Postcartesian Ontology: On Negation and Existence
This article maintains that Jean-Paul Sartre’s early masterwork, Being and
Nothingness, is primarily concerned with developing an original approach to
the being of consciousness. Sartre’s ontology resituates the Cartesian cogito
in a complete system that provides a new understanding of negation and a
dynamic interpretation of human existence. The article examines the role of
consciousness, temporality and the relationship between self and others in the
light of Sartre’s arguments against “classical” rationalism. The conclusion suggests
that Sartre’s departure from modern foundationalism has “postmodern”
implications that emerge in the areas of ontology, existential analytics and the
ethics of human freedom
On the isomorphism problem of concept algebras
Weakly dicomplemented lattices are bounded lattices equipped with two unary
operations to encode a negation on {\it concepts}. They have been introduced to
capture the equational theory of concept algebras \cite{Wi00}. They generalize
Boolean algebras. Concept algebras are concept lattices, thus complete
lattices, with a weak negation and a weak opposition. A special case of the
representation problem for weakly dicomplemented lattices, posed in
\cite{Kw04}, is whether complete {\wdl}s are isomorphic to concept algebras. In
this contribution we give a negative answer to this question (Theorem
\ref{T:main}). We also provide a new proof of a well known result due to M.H.
Stone \cite{St36}, saying that {\em each Boolean algebra is a field of sets}
(Corollary \ref{C:Stone}). Before these, we prove that the boundedness
condition on the initial definition of {\wdl}s (Definition \ref{D:wdl}) is
superfluous (Theorem \ref{T:wcl}, see also \cite{Kw09}).Comment: 15 page
Søren Kierkegaard’s Repetition. Existence in Motion
This article tries to make sense of the concept of repetition in Søren Kierkegaard’s works. According to Kierkegaard repetition is a temporal movement of existence. What is repetition and what is its meaning for human existence? In answering this question the Danish philosopher depicts repetition by comparing three different approaches to life. Throughout the article I try to develop a coherent argument on ‘the new philosophical category’by analysing the three types of repetition and their corresponding human prototypes. I consider repetition a key concept in summarizing Kierkegaard’s theory of existence, where existence pictures the becoming of the human-self that follows several stages. Constantin Constantius’s repetition is an unsuccessful attempt, an aesthetic expression of human-life. The young lover’s repetition is spiritual, albeit not yet authentic, religious, but more poetic, even if he regains his self. Only Job’s repetition is an authentic movement of existence, an expression of a spiritual trial and of genuine faith
A one-valued logic for non-one-sidedness
Does it make sense to employ modern logical tools for ancient philosophy? This well-known debate2 has been re-launched by the indologist Piotr Balcerowicz, questioning those who want to look at the Eastern school of Jainism with Western glasses. While plainly acknowledging the legitimacy of Balcerowicz's mistrust, the present paper wants to propose a formal reconstruction of one of the well-known parts of the Jaina philosophy, namely: the saptabhangi, i.e. the theory of sevenfold predication. Before arguing for this formalist approach to philosophy, let us return to the reasons to be reluctant at it
Ultimate-Grounding Under the Condition of Finite Knowledge. A Hegelian Perspective
Hegel's Science of Logic makes the just not low claim to be an absolute, ultimate-grounded knowledge. This project, which could not be more ambitious, has no good press in our post-metaphysical age. However: That absolute knowledge absolutely cannot exist, cannot be claimed without self-contradiction. On the other hand, there can be no doubt about the fundamental finiteness of knowledge. But can absolute knowledge be finite knowledge? This leads to the problem of a self-explication of logic (in the sense of Hegel) and further, as will be shown, to a new definition of the dialectical procedure. The stringency of which results from the fact that always exactly that implicit content is explicated that was generated by the preceding explication step itself and is thus concretely comprehensible. At the same time, a new implicit content is generated by this act of explication, which requires a new explication step, and so forth. In the dialectical procedure reinterpreted in this way, dialectical arguments are not beheld, guessed at or even surreptitiously obtained, but are methodically accountable. Thereby dialectics is understood as a self-explication of logic by logical means and thus as a proof of the possibility of ultimate-grounding in the form of absolute and nevertheless finite – and thus also fallible – knowledge
The Paraconsistent Approach to Quantum Superpositions Reloaded: Formalizing Contradictory Powers in the Potential Realm
In [7] the authors of this paper argued in favor of the possibility to
consider a Paraconsistent Approach to Quantum Superpositions (PAQS). We claimed
that, even though most interpretations of quantum mechanics (QM) attempt to
escape contradictions, there are many hints -coming from present technical and
experimental developments in QM- that indicate it could be worth while to
engage in a research of this kind. Recently, Arenhart and Krause have raised
several arguments against the PAQS [1, 2, 3]. In [11, 12] it was argued that
their reasoning presupposes a metaphysical stance according to which the
physical representation of reality must be exclusively considered in terms of
the equation: Actuality = Reality. However, from a different metaphysical
standpoint their problems disappear. It was also argued that, if we accept the
idea that quantum superpositions exist in a (contradictory) potential realm, it
makes perfect sense to develop QM in terms of a paraconsistent approach and
claim that quantum superpositions are contradictory, contextual existents.
Following these ideas, and taking as a standpoint an interpretation in terms of
the physical notions of power and potentia put forward in [10, 12, 15], we
present a paraconsistent formalization of quantum superpositions that attempts
to capture the main features of QM.Comment: 26 pages, no figures. arXiv admin note: substantial text overlap with
arXiv:1502.05081, arXiv:1404.5186, arXiv:1506.0737
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