Philosophical Logic

How Fundamental is the Fundamental Assumption?

by Nils Kürbis

published in Teorema XXXI/2 (2012), pp.5-19.

The fundamental assumption of Dummett’s and Prawitz’ proof-theoretic justification of deduction is that ‘if we have a... more The fundamental assumption of Dummett’s and Prawitz’ proof-theoretic justification of deduction is that ‘if we have a valid argument for a complex statement, we can construct a valid argument for it which finishes with an application of one of the introduction rules governing its principal operator’. I argue that the assumption is flawed in this general version, but should be restricted, not to apply to arguments in general, but only to proofs. I also argue that Dummett’s and Prawitz’ project of providing a logical basis for metaphysics only relies on the restricted assumption.

Misyurov D.A. Dialectical formulas based on the binary notation as the development formulas // Credo New. 2012. №2

by Dmitry Misyurov

The article suggests dialectical formulas based on the binary notation as the development formulas: formula with... more The article suggests dialectical formulas based on the binary notation as the development formulas: formula with dominant and the non-dominant elements; universal formula; formula with symbolic weight of elements; tautological formula. For example, it suggests an opportunity to use the dialectical formulas for modeling and artificial intelligence creation, etc.

T-EQUIVALENCES FOR POSITIVE SENTENCES

by Cezary Cieslinski

published The Review of Symbolic Logic 2011, volume 4, issue 02, pp. 319-325. Copyright © Association for Symbolic Logic 2011

Answering a question formulated by Halbach (2009), I show that a disquotational truth theory, which takes as axioms... more Answering a question formulated by Halbach (2009), I show that a disquotational truth theory, which takes as axioms all positive substitutions of the sentential T-schema, together with all instances of induction in the language with the truth predicate, is conservative over its syntactical base.

On the Possibility of a Proof-Theoretical Solution to the Categoricity Problem for Logical Inferentialism

by James Kirkpatrick

BA Dissertation

Three-valued logic, indeterminacy and quantum mechanics

by Tomasz Bigaj

published in 'Journal of Philosophical Logic', 2001 (30), pp. 97-119

The paper consists of two parts. The first part begins with the problem of
whether the original three-valued... more The paper consists of two parts. The first part begins with the problem of
whether the original three-valued calculus, invented by J. Łukasiewicz, really conforms to
his philosophical and semantic intuitions. I claim that one of the basic semantic assumptions
underlying Łukasiewicz’s three-valued logic should be that if under any possible
circumstances a sentence of the form “X will be the case at time t” is true (resp. false) at
time t , then this sentence must be already true (resp. false) at present. However, it is easy
to see that this principle is violated in Łukasiewicz’s original calculus (as the cases of the
law of excluded middle and the law of contradiction show). Nevertheless it is possible to
construct (either with the help of the notion of “supervaluation”, or purely algebraically)
a different three-valued, semi-classical sentential calculus, which would properly incorporate
Łukasiewicz’s initial intuitions. Algebraically, this calculus has the ordinary Boolean
structure, and therefore it retains all classically valid formulas. Yet because possible valuations
are no longer represented by ultrafilters, but by filters (not necessarily maximal), the
new calculus displays certain non-classical metalogical features (like, for example, nonextensionality
and the lack of the metalogical rule enabling one to derive “p is true or q is
true” from “ ‘p _ q’ is true”).
The second part analyses whether the proposed calculus could be useful in formalizing
inferences in situations, when for some reason (epistemological or ontological) our
knowledge of certain facts is subject to limitation. Special attention should be paid to the
possibility of employing this calculus to the case of quantum mechanics. I am going to
compare it with standard non-Boolean quantum logic (in the Jauch–Piron approach), and
to show that certain shortcomings of the latter can be avoided in the former. For example, I
will argue that in order to properly account for quantum features of microphysics, we do not
need to drop the law of distributivity. Also the idea of “reading off” the logical structure of
propositions from the structure of Hilbert space leads to some conceptual troubles, which
I am going to point out. The thesis of the paper is that all we need to speak about quantum
reality can be acquired by dropping the principle of bivalence and extensionality, while
accepting all classically valid formulas.

SEMANTICS AND PROPERTY THEORY

by Raymond Turner

Semantics and Property Theory
Gennaro Chierchia and Raymond Turner
Linguistics and Philosophy
Vol. 11, No. 3 (Aug., 1988), pp. 261-302
(article consists of 42 pages)
Published by: Springer
Stable URL: http://www.jstor.org/stable/25001311

Semantic Conception of Truth. What It Is and What It Is Not

by Ladislav Koren

This is a slightly corrected and revised version of the thesis for PhD degree: "Truth and Meaning: the Dialectics of Theory and Practice".

Alfred Tarski’s semantic conception of truth is arguably the most influential – certainly, most discussed - modern... more Alfred Tarski’s semantic conception of truth is arguably the most influential – certainly, most discussed - modern conception of truth. It has provoked many different interpretations and reactions, some thinkers celebrating it for successfully explicating the notion of truth, whereas others have argued that it is no good as a philosophical account of truth. The aim of this work is to offer a systematic and critical investigation of its nature and significance, based on the thorough explanation of its conceptual, technical as well as historical underpinnings.

The methodological strategy adopted in the thesis reflects the author’s belief that in order to evaluate the import of Tarski’s conception we need to understand what logical, mathematical and philosophical aspects it has, what role they play in his project of theoretical semantics, which of them hang in together, and which should be kept separate. Chapter 2 therefore starts with a detailed exposition of the conceptual and historical background of Tarski’s semantic conception of truth and his method of truth definition for formalized languages, situating it within his project of theoretical semantics, and Chapter 3 explains the formal machinery of Tarski’s truth definitions for increasingly more complex languages. Chapters 4 - 7 form the core of the thesis, all being concerned with the problem of significance of Tarski’s conception. Chapter 4 explains its logico-mathematical import, connecting it to the related works of Gödel and Carnap. Having explained the seminal ideas of the model-theoretic approach to semantics, Chapter 5 tackles the question to what extent Tarski’s ‘The Concept of Truth in Formalized Languages’ (and related articles from the 1930s) anticipates this approach, and what elements might be missing from it. Chapter 6 then deals with the vexed question of its philosophical import and value as a theory of truth, reviewing a number of objections and arguments that purport to show that the method fails as an explanation (explication) of the ordinary notion of truth, and, in particular, that it is a confusion to think that Tarski’s truth definitions have semantic import. Finally, Chapter 7 is devoted to the question whether Tarski’s theory of truth is a robust or rather a deflationary theory of truth.

On the basis of a careful analysis, the thesis aims to substantiate the following view. [A] Tarski’s theory with its associated method of truth definition was primarily designed to serve logico-mathematical purposes. [B] It can be regarded a deflationary theory of a sort, since it completely abstracts from meta- semantical issues concerning the metaphysical or epistemological basis or status of semantic properties. Indeed, [C] this can be interpreted as its laudable feature, since by separating formal (or logico-mathematical) from meta-semantical (or foundational) aspects it usefully divides the theoretical labour to be done in the area of meaning and semantic properties in general. [D] In spite of the fact that Tarski’s conception of truth has this deflationary flavour, the formal structure of its method of truth-definition is quite neutral in that it can be interpreted and employed in several different ways, some of them deflationary, others more robust.

Il n’y a pas de rapport sexuel: The Irresolvability of the Gadamer-Habermas Debate

by William J. Urban

class paper written Good Friday, April 6, 2012

‘Aristotle on Begging the Question Between Dialectic, Logic and Epistemology’, Logical Analysis and History of Philosophy, XV (2012), forthcoming.

by Luca Castagnoli

The Principle of Bivalence in De interpretatione 4

by Francesco Ademollo

Oxford Studies in Ancient Philosophy 38 (2010), 97–113.

A szerszám és a módszer. Következtetés az arisztoteliánus és az ind logikai tradícióban.

by Ferenc Ruzsa

"The tool and the method. Inference in the Aristotelian and the Indian logical tradition"

The analysis given of the structure and function of the Indian 'syllogism' suggests that it is essentially inductive... more The analysis given of the structure and function of the Indian 'syllogism' suggests that it is essentially inductive and intensional and its focus is on the third member, the example. It seems quite independent from the Aristotelian tradition. It is more like a method of research (and proof) than an inference. Also it is quite misleading to translate Nyaya as logic; 'methodology' would do, but better we should leave it untranslated.

Négy mahájána mester

by Ferenc Ruzsa

Four Mahayana masters. Review of the Book Buddhista logika.

A Nágárdzsuna, Vaszubandhu, Sankaraszvámin (?) és Kamalasíla egy-egy szövegét bemutató tanulmánykötet részletes... more A Nágárdzsuna, Vaszubandhu, Sankaraszvámin (?) és Kamalasíla egy-egy szövegét bemutató tanulmánykötet részletes elemzése.

Hibás, de hol? Anzelm ontológiai istenérve

by Ferenc Ruzsa

There is an error, but where? The ontological argument of St. Anselm

In this paper a reconstruction of the ontological argument for the existence of God is attempted using a special... more In this paper a reconstruction of the ontological argument for the existence of God is attempted using a special epistemic formalization. There are separate sets of actual and putative objects and predicates and there are also relations (called R, ‘reflex’) connecting the two sets. The argument turns out to be correct: its premises do imply the conclusion; but also Gaunilo’s famous reductio ad absurdum will work – the existence of the most excellent imaginable island can also be proven.
In this analysis ‘exists1’ (or ‘really exists’, esse in re) means that for a given putative object there is an actual object of which it is the ‘reflex’. Now this ‘exists1’ seems to be a putative predicate (in so far as it can be properly said only of putative objects) – but it is not. It is transcendental: it connects the two worlds. If it is true it does imply the existence of a corresponding real object.
On the other hand when we think of a putative object that it exists2, this is a putative predicate, and it is the ‘reflex’ of the predicate ‘actual object’ (which is by definition true of all real things). And although most of the time we may be right when we think of a putative object that it exists, but it is not necessarily so. We might be convinced that Homer did exist but perhaps this is only a fiction.
Now the ontological argument works only if in the definition of God (id quo maius cogitari nequit) we include ‘exists1’ as one of his perfections: but we cannot do that as ‘exists1’ cannot be thought. We can conceive only ‘exists2’ but that unfortunately does not warrant real existence.

Stable Harmony

by Nils Kürbis

A talk I gave at Logica 2007. Not sure where the title came from ...

Negation: A Problem for the Proof-Theoretic Justification of Deduction

by Nils Kürbis

I won the Jacobsen Essay Price of the University of London for this essay!

What is Wrong with Classical Negation?

by Nils Kürbis

The focus of this paper are the meaning-theoretical arguments against classical logic that Dummett bases on... more The focus of this paper are the meaning-theoretical arguments against classical logic that Dummett bases on consideration about the meanings of negation. Using Dummettian principles, I shall outline three such arguments, of increasing strength, and show that they are unsuccessful by giving responses to each argument on behalf of the classical logician. What is crucial is that in responding to these arguments a classicist need not challenge any of the basic assumptions of Dummett’s outlook on the theory of meaning. In particular, I shall grant Dummett his general bias towards verificationism or justificationism, encapsulated in the slogan ‘meaning is use’. The second general assumption I see no need to question is Dummett’s particular breed of molecularism. Some of Dummett’s assumptions will have to be given up, if classical logic is to be vindicated in his meaning-theoretical framework. A major result of this paper will be that the meaning of negation cannot be defined by rules of inferences in the Dummettian framework.

Harmony, Normality and Stability

by Nils Kürbis

As the title says: my account of proof-theoretic harmony, normality and stability!

Gentzen mentions that it should be possible to specify a function that maps introduction rules onto elimination rules... more Gentzen mentions that it should be possible to specify a function that maps introduction rules onto elimination rules in systems of natural deduction. This paper specifies such a function. I specify two kinds of rules, one in which it is more natural to assume an introduction rule to be given and elimination rules are determined from it, and another kind in which it is an elimination rule which is given and the introduction rules are determined from it. The process also works the other way round, so that it doesn't really matter which rules are supposed to be given first. The process is very general and applies to a large class of logics. The paper begins with a discussion of the philosophical importance of this in connection with the notion of harmony. I discuss Dummett's ideas on harmony and stability, which is supposed to be stronger than harmony. Dummett suggests that normalisability is a formal criterion of harmony. However, he seems to aim at something else, and this criterion does not give an independent formally precise notion of stability. I propose formally precise definitions of harmony and stability, which are distinct from normalisability. My aim is not exegetical, and according to my definitions, classical as well as intuitionist logics count as governed by stable (and hence harmonious) rules of inference.

Kategoriler (Gilbert Ryle)

by Ilyas Altuner

Kutadgubilig Felsefe-Bilim Araştırmaları, 20, 2011

Bu makalesinde Ryle, yalnızca kategorilerin tarihsel seyrini Aristoteles, Kant ve analitik felsefe bağlamında ele... more Bu makalesinde Ryle, yalnızca kategorilerin tarihsel seyrini Aristoteles, Kant ve analitik felsefe bağlamında ele almamakta, aynı zamanda bu süreçte kategorilerin ele alınış biçimini ciddî eleştirilere tabi tutmaktadır. Ryle kategorileri tiplerden ayrı tutmamakta ve kategori-önermelerinin ve tiplerin nasıl oluştuklarını da ele almaktadır. Önermelerin başlığını bilmek, onlar hakkında her şeyi bilmek demektir.

Future Actuality

by Andrea Iacona

draft

According to a view that may be called "actualism" any future contingent has a truth-value that depends on... more According to a view that may be called "actualism" any future contingent has a truth-value that depends on what happens in one among the many futures that are possible, the actual future. This paper investigates the question of how actualism can be accommodated in a formal system, and suggests that three shared assumptions may hinder the way to an answer: the first is that a tree structure is needed, the second is that tenses are to be analyzed in terms of operators, the third is that actuality must be formally represented. Once these assumptions are put aside, it becomes clear that no formal work is required to couch the view. The logic is already there, so to say, in front of our eyes. It is the simplest quantied modal logic.

Logical Form and Truth-Conditions

by Andrea Iacona

draft