Rethinking the Fallacy of Hasty Generalization

This paper makes a case for a refined look at the so- called fallacy of hasty generalization by arguing that this expression is an umbrella term for two fallacies already distinguished by Aristotle. One is the fallacy of generalizing in an inappropriate way from a particular instance to a universal generalization containing a for all x quantification. The other is the secundum quid (in a certain respect) fallacy of moving to a conclusion that is supposed to be a universal generalization containing a for all x quantification while overlooking qualifications that have to be added to the more limited kind of generalization expressed in the premise. It is shown that these two fallacies relate to two different kinds of generalization.The classification of fallacious generalizations is based on a new theory of generalization that distinguishes three kinds of generalizations – the universal generalization of the for all x type, used in classical deductive logic, the inductive generalization, based on probability, and the presumptive generalization, which is defeasible, and allows for exceptions to a general rule. The resulting classification goes beyond a logic-oriented analysis by taking into account how a respondent may oppose a potentially fallacious generalizing move by falsifying it. Using a dialectical interpretation of premise-conclusion complexes, the paper outline a richer concept of generalizing argument moves embedded in a communicational reconstruction of the strategic uses of such moves in which two parties take part in an orderly dialectical exchange of viewpoints.     

On Alan Turing's anticipation of connectionism

It is not widely realised that Turing was probably the first person to consider building computing machines out of simple, neuron-like elements connected together into networks in a largely random manner. Turing called his networks unorganised machines. By the application of what he described as appropriate interference, mimicking education an unorganised machine can be trained to perform any task that a Turing machine can carry out, provided the number of neurons is sufficient. Turing proposed simulating both the behaviour of the network and the training process by means of a computer program. We outline Turing's connectionist project of 1948.In Memory of Robin Gandy     

“The story says that” operator in story semantics

In [2] a semantics for implication is offered that makes use of stories — sets of sentences assembled under various constraints. Sentences are evaluated at an actual world and in each member of a set of stories. A sentence B is true in a story s just when B s. A implies B iff for all stories and the actual world, whenever A is true, B is true. In this article the first-order language of [2] is extended by the addition of the operator the story ... says that ..., as in The story Flashman among the Redskins says that Flashman met Sitting Bull. The resulting language is shown to be sound and complete.     

Natural deduction rules for English

A system of natural deduction rules is proposed for an idealized form of English. The rules presuppose a sharp distinction between proper names and such expressions as the c, a (an) c, some c, any c, and every c, where c represents a common noun. These latter expressions are called quantifiers, and other expressions of the form that c or that c itself, are called quantified terms. Introduction and elimination rules are presented for any, every, some, a (an), and the, and also for any which, every which, and so on, as well as rules for some other concepts. One outcome of these rules is that Every man loves some woman is implied by, but does not imply, Some woman is loved by every man, since the latter is taken to mean the same as Some woman is loved by all men. Also, Jack knows which woman came is implied by Some woman is known by Jack to have come, but not by Jack knows that some woman came.     

On a problem of P(α, δ, π) concerning generalized Alexandroff s cube

Universality of generalized Alexandroff's cube plays essential role in theory of absolute retracts for the category of , -closure spaces. Alexandroff's cube. is an , -closure space generated by the family of all complete filters. in a lattice of all subsets of a set of power .Condition P(, , ) says that is a closure space of all , -filters in the lattice ( ), .Assuming that P (, , ) holds, in the paper [2], there are given sufficient conditions saying when an , -closure space is an absolute retract for the category of , -closure spaces (see Theorems 2.1 and 3.4 in [2]).It seems that, under assumption that P (, , ) holds, it will be possible to givean uniform characterization of absolute retracts for the category of , -closure-spaces.Except Lemma 3.1 from [1], there is no information when the condition P (, , ) holds or when it does not hold.The main result of this paper says, that there are examples of cardinal numbers, , , such that P (, , ) is not satisfied.Namely it is proved, using elementary properties of Lebesgue measure on the real line, that the condition P (, ₁, 2 ) is not satisfied.Moreover it is shown that fulfillment of the condition is essential assumption in, Theorems 2.1 and 3.4 from [1] i.e. it cannot be eliminated.     

Toward an empirical subclassification of “learning disabilitiesℍ: A psychophysiological comparison of “hyperactiveℍ and “nonhyperactiveℍ subgroups

The diagnostic category of learning disabilities is a heterogeneous one, but few empirical attempts have been made to distinguish subgroups. Recent research, however, suggests that it may be meaningful to discriminate between hyperactive and nonhyperactive learning-disabled children. In the present study, 21 learning-disabled children identified as hyperactive through teacher nominations and ratings were compared to 15 learning-disabled children identified as nonhyperactive in the same manner. The two groups differed on rated behavior, birth order, amount of prescribed stimulant medication, amount of psychosocial stress, and Verbal, Performance, and Full Scale WISC-R IQ scores. They did not differ, however, on several demographic variables, the number of perinatal complications, reading achievement, and a number of tonic and phasic measures of autonomie activity. These findings support the distinction between hyperactive and nonhyperactive subgroups of learning-disabled children, but suggest that the two subgroups may have a similar biological substrate.We wish to express our sincere appreciation to Douglas Carmichael, Martha Stewart, Kay Richmond, and the teachers of Clarke County for their kind and sophisticated assistance, and to David Coleman and David Hammer for their technical assistance.     

Partially-Ordered (Branching) Generalized Quantifiers: A General Definition

Following Henkins discovery of partially-ordered (branching) quantification (POQ) with standard quantifiers in 1959, philosophers of language have attempted to extend his definition to POQ with generalized quantifiers. In this paper I propose a general definition of POQ with 1-place generalized quantifiers of the simplest kind: namely, predicative, or cardinality quantifiers, e.g., most, few, finitely many, exactly , where is any cardinal, etc. The definition is obtained in a series of generalizations, extending the original, Henkin definition first to a general definition of monotone-increasing (M) POQ and then to a general definition of generalized POQ, regardless of monotonicity. The extension is based on (i) Barwises 1979 analysis of the basic case of M POQ and (ii) my 1990 analysis of the basic case of generalized POQ. POQ is a non-compositional 1st-order structure, hence the problem of extending the definition of the basic case to a general definition is not trivial. The paper concludes with a sample of applications to natural and mathematical languages.     

The ω-rule

We prove that all proofs in -logic (a first order logic with -rule added) in which -rule is used finitely many times can be turned into proofs in which the -rule is used at most one time. Next, we prove that the word finitely above cannot be changed by the word infinitely.     

On the Way to a Postmodern Curriculum Theory -- Moving from the Question of Unity to the Question of Difference

This article will examine the consequences of highlighting subject and difference in one of the curriculum theories that has been inspired by postmodernism. The term postmodernism is here first and foremost meant to signify the attempt to combine politics and morality with epistemology in accordance with Levinas, Lyotard and Bauman. The article will highlight some themes that need to be developed further for a postmodernism-inspired curriculum theory. A starting-point is a critique of the type of curriculum theory which has its base in the new sociology of education. From this critique, focused on universal claims, the Habermasian-inspired universalism is quickly and critically dropped and left behind, and another form of reasoning is embarked upon. The latter is inspired by a minotarian politics concept and tries to dissolve universalism as a prerequisite for critical conversations. With this background and with the help of Levinas, the article sets out to talk about difference without reduction to the Same and finally suggest a direction for a postmodern curriculum theory with a normative focus on knowledge.     

Dowód aksjomatyzowalności pewnychn-wartościowych rachunków zdań

Praca ta zostaa wykonana pod kierunkiem prof. drJerzego Supeckiego. Jej szczególny przypadek dotyczcyn-wartociowego rachunku zda o jednej wartoci wyrónionej by referowany w Warszawie na zjedzie Grupy Logiki Instytutu Filozofii i Socjologii PAN. Streszczenie tego referatu [5] zostao wydrukowane w Sprawozdaniach Wydziau Nauk Spoecznych PAN.Allatum est die 19 Aprilis 1963     

Supererogation in Deontic Logic: Metatheory for DWE and Some Close Neighbours

In "Doing Well Enough: Toward a Logic for Common Sense Morality", Paul McNamara sets out a semantics for a deontic logic which contains the operator It is supererogatory that. As well as having a binary accessibility relation on worlds, that semantics contains a relative ordering relation, . For worlds u, v and w, we say that u w v when v is at least as good as u according to the standards of w. In this paper we axiomatize logics complete over three versions of the semantics. We call the strongest of these logics DWE for Doing Well Enough.     

On a statistic arising in testing correlation

This paper is devoted to the study of a certain statistic,u, defined on samples from a bivariate population with variances ₁₁, ₂₂ and correlation . Let the parameter corresponding tou be . Under binormality assumptions the following is demonstrated. (i) If ₁₁ = ₂₂, then the distribution ofu can be obtained rapidly from theF distribution. Statistical inferences about = may be based onF. (ii) In the general case, allowing for _{11 22}, a certain quantity involvingu,r (sample correlation between the variables) and follows at distribution. Statistical inferences about may be based ont. (iii) In the general case a quantityt may be constructed which involves only the statisticu and only the parameter . If treated like at distributed magnitude,t admits conservative statistical inferences. (iv) TheF distributed quantity mentioned in (i) is equivalent to a certaint distributed quantity as follows from an appropriate transformation of the variable. (v) Three test statistics are given which can be utilized in making statistical inferences about = in the case ₁₁ = ₂₂. A comparison of expected lengths of confidence intervals for obtained from the three test statistics is made. (vi) The use of the formulas derived is illustrated by means of an application to coefficient alpha.This research was supported by the National Institute of Child Health and Human Development, under Research Grant 1 PO1 HD01762.     

Branching space-time

Branching space-time is a simple blend of relativity and indeterminism. Postulates and definitions rigorously describe the causal order relation between possible point events. The key postulate is a version of everything has a causal origin; key defined terms include history and choice point. Some elementary but helpful facts are proved. Application is made to the status of causal contemporaries of indeterministic events, to how splitting of histories happens, to indeterminism without choice, and to Einstein-Podolsky-Rosen distant correlations.     

Barker and Achinstein on Goodman

Barker and Achinstein think that it is not possible for a predicate like grue to serve as well as a predicate like green in the role of a qualitative or non-positional predicate. Their arguments consist in a number of attempts to show that one who possesses green in his language can do things with that predicate which one who must work with grue instead cannot do. However, they succeed in showing only that a qualitative predicate is better adapted to our needs than its positional counterpart, rather than that grue is not capable of being a qualitative predicate.     

PROXY FUNCTIONS,TRUTH AND REFERENCE

Quines ontological relativity is related to Tarskis theory of truth in two ways: Quine repudiates term-by-term-correspondence, as does Tarskis rule of truth; and Quines proxy argument in support of relativity finds exact formulation in Tarskis truth definition.Unfortunately, relativity is threatened by the fact that the proxy argument doesnt comply with the rule of truth (Tarskis celebrated condition (T)). Despite Quines express allegiance to (T), use of proxy schemes does not generate all of the true sentences condition (T) requires.A possible adjustment is to drop (T), retain the satisfaction definition and proxy argument, and appeal to the theory of observation and indeterminacy of reference as grounds of relativity. But as we shall see Quines theories of assent to observation sentences and of reference-learning dont square easily with his naturalism. The first attributes intentional attitudes to observers; and the second assumes a holistic context principle and a concept of individuation which do not withstand scrutiny as empirical notions. Both appear to violate Quines behavorist canon.A saving alternative is a theory of term-reference that appears in Roots of Reference and affords a return to behaviorism, and reinstatement of the proxy argument and relativity in a way compatible with Tarskis (T).     

Three theories of nominalized predicates

By the term nominalization I mean any process which transforms a predicate or predicate phrase into a noun or noun phrase, e.g. feminine is transformed into feminity. I call these derivative nouns abstract singular terms. Our aim is to provide a model-theoretic interpretation for a formal language which admits the occurrence of such abstract singular terms.     

Intuitionistic uniformity principles for propositions and some applications

This note deals with the prepositional uniformity principlep-UP: p x N A (p, x) x N p A (p, x) ( species of all propositions) in intuitionistic mathematics.p-UP is implied by WC and KS. But there are interestingp-UP-cases which require weak KS resp. WC only. UP for number species follows fromp-UP by extended bar-induction (ranging over propositions) and suitable weak continuity. As corollaries we have the disjunction property and the existential definability w.r.t. concrete objects. Other consequences are: there is no non-trivial countable partition of;id is the only injective function from to; there are no many-place injective prepositional functions; card () is incomparable with the cardinality of all metric spaces containing at least three elements.     

Increasing correct identifications by children

Four new lineup procedures were examined with the goal of increasingchildren's identification accuracy. Participants (329 children aged 10 and11 years, 426 children aged 12 to 14 years, and 265 adults) were presentedwith either a target-present or target-absent lineup. Proceduralmodifications included providing a salient "I don't know" response option,extending standard instructions, and modeling correct responses eitherusing an identification demonstration video or a handout. These conditionswere compared to a standard (control) lineup procedure. Extendingstandard instructions increased correct identifications by the youngerchildren. Presenting a salient "I don't know" response increased overallchoosing for both target-present and target-absent lineups. Experimentalprocedures did not influence correct rejection rates. These data demonstratea variety of techniques that may be useful for improving the identificationaccuracy of child witnesses. Future directions are discussed.     

A calculus for the common rules of ∧ and ∨

We provide a finite axiomatization of the consequence , i.e. of the set of common sequential rules for and . Moreover, we show that has no proper non-trivial strengthenings other than and . A similar result is true for , but not, e.g., for ⁺.To the memory of Jerzy Supecki     

Независимость одной системы аксиом и правила вывода пропозиционального исчисления

- Allatum est die 5 Martii 1970