scholarly journals A contextualist treatment of negative existentials

2021 ◽  
Vol 18 (3) ◽  
pp. 415-424
Author(s):  
Alberto Voltolini
Keyword(s):  
Comparison Group ◽  
Existential Quantifier ◽  
Truth Values ◽  
First Order ◽  
Fictional Entities ◽  
Unrestricted Domain ◽  
Truth Value ◽  
Negative Existentials

Abstract In this paper, I want to vindicate the contextualist treatment that is typically applied by artefactualists on fictional entities (ficta) both to general and to singular negative existentials. According to this treatment, the truth value of a negative existential, whether general or singular, changes according to whether the existential quantifier or the first-order existence predicate is contextually used as respectively ranging over and applying to a restricted or an unrestricted domain of beings. In (2003), Walton has criticized this treatment with respect to singular negative existentials in particular. First of all, however, as (Predelli, Stefano. 2002. ‘Holmes’ and Holmes. A Millian analysis of names from fiction. Dialectica 56. 261–279) has shown, this treatment can be applied to singular predications in general, independently of the existential case. Moreover, not only does applying it to singular negative existentials explain why we may contextually use the quantifier restrictedly in general negative existentials, but also it accounts for why comparative negative existentials, both singular and general, may have different truth values as well depending on the comparison group they mobilize.

A weak completeness theorem for infinite valued first-order logic

1963 ◽  
Vol 28 (1) ◽  
pp. 43-50 ◽  
Author(s):  
L. P. Belluce ◽  
C. C. Chang
Keyword(s):  
Completeness Theorem ◽  
Unit Interval ◽  
Order Logic ◽  
First Order Logic ◽  
Order System ◽  
First Order ◽  
Recursively Enumerable ◽  
Weak Completeness ◽  
Truth Value

This paper contains some results concerning the completeness of a first-order system of infinite valued logicThere are under consideration two distinct notions of completeness corresponding to the two notions of validity (see Definition 3) and strong validity (see Definition 4). Both notions of validity, whether based on the unit interval [0, 1] or based on linearly ordered MV-algebras, use the element 1 as the designated truth value. Originally, it was thought by many investigators in the field that one should be able to prove that the set of valid sentences is recursively enumerable. It was first proved by Rutledge in [9] that the set of valid sentences in the monadic first-order infinite valued logic is recursively enumerable.

The Predicate of Existence

2019 ◽  
pp. 14-37
Author(s):  
Palle Yourgrau
Keyword(s):  
Bertrand Russell ◽  
Gottlob Frege ◽  
Order Property ◽  
Saul Kripke ◽  
Existential Quantifier ◽  
Modern Logic ◽  
First Order ◽  
David Kaplan ◽  
Theory Of Descriptions ◽  
Nathan Salmon

Kant famously declared that existence is not a (real) predicate. This famous dictum has been seen as echoed in the doctrine of the founders of modern logic, Gottlob Frege and Bertrand Russell, that existence isn’t a first-order property possessed by individuals, but rather a second-order property expressed by the existential quantifier. Russell in 1905 combined this doctrine with his new theory of descriptions and declared the paradox of nonexistence to be resolved without resorting to his earlier distinction between existence and being. In recent years, however, logicians and philosophers like Saul Kripke, David Kaplan, and Nathan Salmon have argued that there is no defensible reason to deny that existence is a property of individuals. Kant’s dictum has also been re-evaluated, the result being that the paradox of nonexistence has not, after all, disappeared. Yet it’s not clear how exactly Kripke et al. propose to resolve the paradox.

A NOTE ON THE ASYMPTOTIC PROBABILITIES OF EXISTENTIAL SECOND-ORDER MINIMAL GÖDEL SENTENCES WITH EQUALITY

1995 ◽  
Vol 06 (04) ◽  
pp. 339-351
Author(s):  
WIESŁAW SZWAST
Keyword(s):  
Dense Subset ◽  
Unit Interval ◽  
Second Order ◽  
Existential Quantifier ◽  
First Order ◽  
Order Part ◽  
Universal Quantifiers

The minimal Gödel class is the class of first-order prenex sentences whose quantifier prefix consists of two universal quantifiers followed by just one existential quantifier. We prove that asymptotic probabilities of existential second-order sentences, whose first-order part is in the minimal Gödel class, form a dense subset of the unit interval.

scholarly journals ON EXISTENTIAL DECLARATIONS OF INDEPENDENCE IN IF LOGIC

2013 ◽  
Vol 6 (2) ◽  
pp. 254-280 ◽  
Author(s):  
FAUSTO BARBERO
Keyword(s):  
Expressive Power ◽  
Inference Rules ◽  
Declaration Of Independence ◽  
Truth Values ◽  
First Order ◽  
If Logic ◽  
Knowledge Memory ◽  
Special Classes

AbstractWe analyze the behaviour of declarations of independence between existential quantifiers in quantifier prefixes of Independence-Friendly (IF) sentences; we give a syntactical criterion to decide whether a sentence beginning with such prefix exists, such that its truth values may be affected by removal of the declaration of independence. We extend the result also to equilibrium semantics values for undetermined IF sentences.The main theorem defines a schema of sound and recursive inference rules; we show more explicitly what happens for some simple special classes of sentences.In the last section, we extend the main result beyond the scope of prenex sentences, in order to give a proof of the fact that the fragment of IF sentences with knowledge memory has only first-order expressive power.

Some properties of epistemic set theory with collection

1986 ◽  
Vol 51 (3) ◽  
pp. 748-754 ◽  
Author(s):  
Andre Scedrov
Keyword(s):  
Set Theory ◽  
Intuitionistic Logic ◽  
Existential Quantifier ◽  
Modal Interpretation ◽  
Conservative Extension ◽  
Disjunction Property ◽  
First Order ◽  
Slight Extension ◽  
Order Arithmetic ◽  
Epistemic Systems

Myhill [12] extended the ideas of Shapiro [15], and proposed a system of epistemic set theory IST (based on modal S4 logic) in which the meaning of the necessity operator is taken to be the intuitive provability, as formalized in the system itself. In this setting one works in classical logic, and yet it is possible to make distinctions usually associated with intuitionism, e.g. a constructive existential quantifier can be expressed as (∃x) □ …. This was first confirmed when Goodman [7] proved that Shapiro's epistemic first order arithmetic is conservative over intuitionistic first order arithmetic via an extension of Gödel's modal interpretation [6] of intuitionistic logic.Myhill showed that whenever a sentence □A ∨ □B is provable in IST, then A is provable in IST or B is provable in IST (the disjunction property), and that whenever a sentence ∃x.□A(x) is provable in IST, then so is A(t) for some closed term t (the existence property). He adapted the Friedman slash [4] to epistemic systems.Goodman [8] used Epistemic Replacement to formulate a ZF-like strengthening of IST, and proved that it was a conservative extension of ZF and that it had the disjunction and existence properties. It was then shown in [13] that a slight extension of Goodman's system with the Epistemic Foundation (ZFER, cf. §1) suffices to interpret intuitionistic ZF set theory with Replacement (ZFIR, [10]). This is obtained by extending Gödel's modal interpretation [6] of intuitionistic logic. ZFER still had the properties of Goodman's system mentioned above.

ENRICHED INTERVAL BILATTICES AND PARTIAL MANY-VALUED LOGICS: AN APPROACH TO DEAL WITH GRADED TRUTH AND IMPRECISION

1994 ◽  
Vol 02 (01) ◽  
pp. 37-54 ◽  
Author(s):  
FRANCESC ESTEVA ◽  
PERE GARCIA-CALVÉS ◽  
LLUÍS GODO
Keyword(s):  
Approximate Reasoning ◽  
Truth Values ◽  
Partial Models ◽  
Truth Value ◽  
The Many ◽  
Available Information ◽  
States Of Knowledge

Within the many-valued approach for approximate reasoning, the aim of this paper is two-fold. First, to extend truth-values lattices to cope with the imprecision due to possible incompleteness of the available information. This is done by considering two bilattices of truth-value intervals corresponding to the so-called weak and strong truth orderings. Based on the use of interval bilattices, the second aim is to introduce what we call partial many-valued logics. The (partial) models of such logics may assign intervals of truth-values to formulas, and so they stand for representations of incomplete states of knowledge. Finally, the relation between partial and complete semantical entailment is studied, and it is provedtheir equivalence for a family of formulas, including the so-called free well formed formulas.

The cylindric algebras of three-valued logic

1998 ◽  
Vol 63 (4) ◽  
pp. 1201-1217
Author(s):  
Norman Feldman
Keyword(s):  
Effective Procedure ◽  
Cylindric Algebras ◽  
Truth Values ◽  
Recursive Functions ◽  
Partial Recursive Functions ◽  
Truth Value ◽  
The One ◽  
Definition Of

In this paper we consider the three-valued logic used by Kleene [6] in the theory of partial recursive functions. This logic has three truth values: true (T), false (F), and undefined (U). One interpretation of U is as follows: Suppose we have two partially recursive predicates P(x) and Q(x) and we want to know the truth value of P(x) ∧ Q(x) for a particular x0. If x0 is in the domain of definition of both P and Q, then P(x0) ∧ Q(x0) is true if both P(x0) and Q(x0) are true, and false otherwise. But what if x0 is not in the domain of definition of P, but is in the domain of definition of Q? There are several choices, but the one chosen by Kleene is that if Q(X0) is false, then P(x0) ∧ Q(x0) is also false and if Q(X0) is true, then P(x0) ∧ Q(X0) is undefined.What arises is the question about knowledge of whether or not x0 is in the domain of definition of P. Is there an effective procedure to determine this? If not, then we can interpret U as being unknown. If there is an effective procedure, then our decision for the truth value for P(x) ∧ Q(x) is based on the knowledge that is not in the domain of definition of P. In this case, U can be interpreted as undefined. In either case, we base our truth value of P(x) ∧ Q(x) on the truth value of Q(X0).

scholarly journals First order quantifiers in monadic second order logic

2004 ◽  
Vol 69 (1) ◽  
pp. 118-136 ◽  
Author(s):  
H. Jerome Keisler ◽  
Wafik Boulos Lotfallah
Keyword(s):  
Expressive Power ◽  
Second Order ◽  
Order Logic ◽  
Existential Quantifier ◽  
Reachability Problem ◽  
Open Problems ◽  
First Order ◽  
Second Order Logic ◽  
Monadic Second Order Logic ◽  
Quantifier Alternation

AbstractThis paper studies the expressive power that an extra first order quantifier adds to a fragment of monadic second order logic, extending the toolkit of Janin and Marcinkowski [JM01].We introduce an operation existsn (S) on properties S that says “there are n components having S”. We use this operation to show that under natural strictness conditions, adding a first order quantifier word u to the beginning of a prefix class V increases the expressive power monotonically in u. As a corollary, if the first order quantifiers are not already absorbed in V, then both the quantifier alternation hierarchy and the existential quantifier hierarchy in the positive first order closure of V are strict.We generalize and simplify methods from Marcinkowski [Mar99] to uncover limitations of the expressive power of an additional first order quantifier, and show that for a wide class of properties S, S cannot belong to the positive first order closure of a monadic prefix class W unless it already belongs to W.We introduce another operation alt(S) on properties which has the same relationship with the Circuit Value Problem as reach(S) (defined in [JM01]) has with the Directed Reachability Problem. We use alt(S) to show that Πn ⊈ FO(Σn), Σn ⊈ FO(∆n). and ∆n+1 ⊈ FOB(Σn), solving some open problems raised in [Mat98].

Contextualism, minimalism, and situationalism

2007 ◽  
Vol 15 (1) ◽  
pp. 115-137 ◽  
Author(s):  
Eros Corazza
Keyword(s):  
Semantic Content ◽  
Truth Values ◽  
Context Dependent ◽  
Truth Value ◽  
True False

After discussing some difficulties that contextualism and minimalism face, this paper presents a new account of the linguistic exploitation of context, situationalism. Unlike the former accounts, situationalism captures the idea that the main intuitions underlying the debate concern not the identity of propositions expressed but rather how truth-values are situation-dependent. The truth-value of an utterance depends on the situation in which the proposition expressed is evaluated. Hence, like in minimalism, the proposition expressed can be truth-evaluable without being enriched or expanded. Along with contextualism, it is argued that an utterance’s truth-value is context dependent. But, unlike contextualism and minimalism, situationalism embraces a form of relativism in so far as it maintains that semantic content must be evaluated vis-à-vis a given situation and, therefore, that a proposition cannot be said to be true/false eternally.

scholarly journals Ontological Syncretistic Noneism

2018 ◽  
Vol 15 (2) ◽  
pp. 124
Author(s):  
Alberto Voltolini
Keyword(s):  
Second Order ◽  
Existential Quantifier ◽  
First Order

In this paper I want to claim, first, that despite close similarities, noneism (as developed in both Routley 1980 and Priest 20162) and Crane’s (2013) psychological reductionism are different ontological doctrines. For unlike the latter, the former is ontologically committed to objects that are nonentities. Once one splits ontological from existential commitment, this claim, I guess, is rather uncontroversial. Second, however, I want to claim something more controversial; namely, that this ontological interpretation of noneism naturally makes noneism be nonstandardly read as a form of allism, to be however appropriately distinguished from Quinean allism in terms of the different scope of the overall ontological domain on which the only particular/existential quantifier that there is ranges. This may orient a noneist towards a syncretistic view of existence, according to which, appearances notwithstanding, existence as a whole is captured both by means of second-order and by means of first-order related notions.

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