Online research in philosophy

A minimal second order modal logic of natural kinds is formulated. Concepts are distinguished from properties and relations in the conceptual-logistic background of the logic through a distinction between free and bound predicate variables. Not all concepts (as indicated by free predicate variables) need have a property or relation corresponding to them (as values of bound predicate variables). Issues pertaining to identity and existence as impredicative concepts are examined and an analysis of mass terms as nominalized predicates for kinds of stuff is proposed. The minimal logic is extendible through a summum genus, an infima species or a partition principle for natural kinds.

Current theories of grammar handle both extraction and anaphorization by introducing variables into syntactic representations. Combinatory categorial grammar eliminates variables corresponding to gaps. Using the combinator W, the paper extends this approach to anaphors, which appear to act as overt bound variables.

This paper makes explicit and takes issue with the bizarre view, which is unfortunately prevalent among social scientists, that causal relations are features of models only. There are some good reasons to represent causal factors with independent variables. But the association between causes and independent variables is only a desideratum in model construction. It is not a criterion for judging which things are causes and which are effects.

First we have individual variables, as usual in first-order logics. (We do not have individual constants, but this is a minor point.) The propositional logic LP has justification constants, but in FOLP these are generalized to allow individual variables as arguments. Thus we have as justification constants c, c(x), c(x, y), . . . . Similarly LP has justification variables, but in FOLP these can be parametrized with individual variables p, p(x), p(x, y), . . . . To keep terminology in line with past papers, we will still refer to things as justification constants and justification variables, even though they have structure to them. As in LP, justification terms are built up from justification constants and justification variables using ·, +, ! as usual. In addition there is a new constructor, genx, introduced by Artemov, and there is one further new constructor, exsx, introduced in this paper. If t is a justification term and x is an individual variable, genxt and exsxt are justification terms. An individual variable x is free in a justification term unless it is bound by genx or exsx. More specifically, the free variables of p(x, y, . . .) and of c(x, y, . . .) are {x, y, . . .}, the free variables of s · t and of s + t are the free variables of s together with the free variables of t, the free variables of !s are the free variables of s, and the free variables of genxt and of exsxt are the free variables of t except for x. Formulas are built up from atomic formulas, including ⊥, in the way standard in first-order logic, together with the additional formation rule: t:X is a formula provided t is a justification term, X is a formula, and all free variables of X occur in t. We assume ⊃, ⊥, and ∀ are basic, with other connectives and quantifier defined. The axiomatization used here is a combination of an LP axiomatization and a standard axiomatization of first-order logic, together with a version of the Barcan formula, and one additional axiom that corresponds to the converse Barcan formula..

It is “well known” that in linear models: (1) testable constraints on the marginal distribution of observed variables distinguish certain cases in which an unobserved cause jointly influences several observed variables; (2) the technique of “instrumental variables” sometimes permits an estimation of the influence of one variable on another even when the association between the variables may be confounded by unobserved common causes; (3) the association (or conditional probability distribution of one variable given another) of two variables connected by a path or pair of paths with a single common vertex (a trek) can be computed directly from the parameter values associated with each edge in the trek; (4) the association of two variables produced by multiple treks can be computed from the parameters associated with each trek; and (5) the independence of two variables conditional on a third implies the corresponding independence of the sums of the variables over all units conditional on the sums over all units of each of the original conditioning variables.

It is “well known” that in linear models: (1) testable constraints on the marginal distribution of observed variables distinguish certain cases in which an unobserved cause jointly influences several observed variables; (2) the technique of “instrumental variables” sometimes permits an estimation of the influence of one variable on another even when the association between the variables may be confounded by unobserved common causes; (3) the association (or conditional probability distribution of one variable given another) of two variables connected by a path or pair of paths with a single common vertex (a trek) can be computed directly from the parameter values associated with each edge in the trek; (4) the association of two variables produced by multiple treks can be computed from the parameters associated with each trek; and (5) the independence of two variables conditional on a third implies the corresponding independence of the sums of the variables over all units conditional on the sums over all units of each of the original conditioning variables.

For every finite n ≥ 4 there is a logically valid sentence φ n with the following properties: φ n contains only 3 variables (each of which occurs many times); φ n contains exactly one nonlogical binary relation symbol (no function symbols, no constants, and no equality symbol): φ n has a proof in first-order logic with equality that contains exactly n variables, but no proof containing only n - 1 variables. This result was first proved using the machinery of algebraic logic developed in several research monographs and papers. Here we replicate the result and its proof entirely within the realm of (elementary) first-order binary predicate logic with equality. We need the usual syntax, axioms, and rules of inference to show that φ n has a proof with only n variables. To show that φ n has no proof with only n - 1 variables we use alternative semantics in place of the usual, standard, set-theoretical semantics of first-order logic.

The paper rst lays out a non-congurational approach to scope ambiguities in which scope dependencies are treated as dependencies between evaluation indices of variables. The notions of dependent and domain variables are dened naturally in this framework. These concepts are then used to account for the distribution and interpretation of determiner reduplication in Hungarian, a phenomenon that has not received much attention so far.1 1. Introduction This paper contributes to the study of the semantics of indenites in natural language by introducing on the scene a new type of indenite, called dependent. We meet it in Hungarian, where one may reduplicate certain determiners, as illustrated in [1]-[3].

We show how sequent calculi for some generalized quantifiers can be obtained by generalizing the Herbrand approach to ordinary first order proof theory. Typical of the Herbrand approach, as compared to plain sequent calculus, is increased control over relations of dependence between variables. In the case of generalized quantifiers, explicit attention to relations of dependence becomes indispensible for setting up proof systems. It is shown that this can be done by turning variables into structured objects, governed by various types of structural rules. These structured variables are interpreted semantically by means of a dependence relation. This relation is an analogue of the accessibility relation in modal logic. We then isolate a class of axioms for generalized quantifiers which correspond to first-order conditions on the dependence relation.