(1994). The correspondence between James Hutton (1726–1797) and James Watt (1736–1819) with two letters from Hutton to George Clerk-Maxwell (1715–1784): Part I. Annals of Science: Vol. 51, No. 6, pp. 637-653.

The words I wish to delete in 48-9 spoil a ‘tricolon crescendo’ whose three members are clearly marked and whose verbs are perhaps deliberately varied in person and tense. The parataxis by means of hic is awkward, and the words seem to be a versified gloss. The Scholiast says : id est: to nobilis tantum et imperitus. nam de plebe, id est de humili familia, eloquentes exeunt, qui nobilium imperitorum causas defendunt; but that could be a paraphrase based on the (...) text as it stands in our manuscripts. (shrink)

The words I wish to delete in 48-9 spoil a ‘tricolon crescendo’ whose three members are clearly marked and whose verbs are perhaps deliberately varied in person and tense . The parataxis by means of hic is awkward, and the words seem to be a versified gloss. The Scholiast says : id est: to nobilis tantum et imperitus. nam de plebe, id est de humili familia, eloquentes exeunt, qui nobilium imperitorum causas defendunt; but that could be a paraphrase based on (...) the text as it stands in our manuscripts. (shrink)

In this paper we prove that the free pseudocomplemented residuated lattices are decomposable if and only if they are Stone, i.e., if and only if they satisfy the identity ¬ x ∨ ¬¬ x = 1. Some applications are given.

In this paper we prove that the free pseudocomplemented residuated lattices are decomposable if and only if they are Stone, i.e., if and only if they satisfy the identity ¬x ∨ ¬¬x = 1. Some applications are given.

Writing of Terence'sAndria(‘The Girl from Andros’) in 1952, Duckworth said: ‘In theAndriathe second love affair is unusual; Charinus’ love for a respectable girl whose virtue is still intact has been considered an anticipation of a more modern attitude towards love and sex. More frequently in Plautus and Terence the heroine, if of respectable parentage, has been violated before the opening of the drama (Aulularia, Adelphoe), or she is a foreigner, a courtesan, or a slave girl' (Duckworth (1952), p. 158). Perhaps (...) in 1993 it does not seem quite so ‘modern’ that Charinus is not only in love with a respectable virgin but wishes to marry her. (shrink)

This study investigated individual differences in the belief bias effect, which is the tendency to accept conclusions because they are believable rather than because they are logically valid. It was observed that the extent of an individual's belief bias effect was unrelated to a number of measures of reasoning competence. Instead, as predicted by mental models theory, it was related to a person's ability to generate alternative representations of premises: the more alternatives a person generated, the less likely they were (...) to show a belief bias effect. In contrast to belief effects, which were predicted by the number of alternatives generated, scores on logical reasoning tasks were predicted by an individual's understanding of the concept of logical necessity. These two mediating variables, ability to generate alternatives and understanding of logical necessity, were themselves predicted by similar variables, such as cognitive motivation and abstract reasoning ability. Our findings strongly support the mental models interpretation of the belief bias effect, and suggest that individual differences in this effect are associated with a specific ability to generate alternatives, rather than with a general logical competence. (shrink)

In his article ‘Did the Athenians Regard Seduction as a Worse Crime than Rape?’, CQ 40, 370–7, Edward M. Harris rightly casts doubt on the value of Lysias 1.30–5, which has generally been accepted as evidence that the Athenians did indeed regard seduction as the worse of the two crimes. Euphiletos in this speech is defending himself on a charge of murder, and, as Harris says, ‘Euphiletus’ presentation of the Athenian statutes regarding rape and seduction is dictated by the rhetorical (...) constraints of his case. It is not a reflection of widely held social attitudes.'. (shrink)

We show that the class of all isomorphic images of Boolean Products of members of SR [1] is the class of all archimedean W-algebras. We obtain this result from the characterization of W-algebras which are isomorphic images of Boolean Products of CW-algebras.

The aim of this paper is to give a description of the free algebras in some varieties of Glivenko MTL-algebras having the Boolean retraction property. This description is given (generalizing the results of [9]) in terms of weak Boolean products over Cantor spaces. We prove that in some cases the stalks can be obtained in a constructive way from free kernel DL-algebras, which are the maximal radical of directly indecomposable Glivenko MTL-algebras satisfying the equation in the title. We include examples (...) to show how we can apply the results to describe free algebras in some well known varieties of involutive MTL-algebras and of pseudocomplemented MTL-algebras. (shrink)

The classical Glivenko theorem asserts that a propositional formula admits a classical proof if and only if its double negation admits an intuitionistic proof. By a natural expansion of the BCK-logic with negation we understand an algebraizable logic whose language is an expansion of the language of BCK-logic with negation by a family of connectives implicitly defined by equations and compatible with BCK-congruences. Many of the logics in the current literature are natural expansions of BCK-logic with negation. The validity of (...) the analogous of Glivenko theorem in these logics is equivalent to the validity of a simple one-variable formula in the language of BCK-logic with negation. (shrink)

The aim of this paper is to give a description of the free algebras in some varieties of Glivenko MTL-algebras having the Boolean retraction property. This description is given (generalizing the results of [9]) in terms of weak Boolean products over Cantor spaces. We prove that in some cases the stalks can be obtained in a constructive way from free kernel DL-algebras, which are the maximal radical of directly indecomposable Glivenko MTL-algebras satisfying the equation in the title. We include examples (...) to show how we can apply the results to describe free algebras in some well known varieties of involutive MTL-algebras and of pseudocomplemented MTL-algebras. (shrink)

Using the theory of BL-algebras, it is shown that a propositional formula ϕ is derivable in Łukasiewicz infinite valued Logic if and only if its double negation ˜˜ϕ is derivable in Hájek Basic Fuzzy logic. If SBL is the extension of Basic Logic by the axiom (φ & (φ→˜φ)) → ψ, then ϕ is derivable in in classical logic if and only if ˜˜ ϕ is derivable in SBL. Axiomatic extensions of Basic Logic are in correspondence with subvarieties of the (...) variety of BL-algebras. It is shown that the MV-algebra of regular elements of a free algebra in a subvariety of BL-algebras is free in the corresponding subvariety of MV-algebras, with the same number of free generators. Similar results are obtained for the generalized BL-algebras of dense elements of free BL-algebras. (shrink)

Twenty-two years after Charles Darwin began to think of character divergence from a common ancestor in his Notebook B, the now famous and iconic branching diagram appeared in the fourth chapter of On the Origin of Species.

Let ${\mathbb{BRL}}$ denote the variety of commutative integral bounded residuated lattices (bounded residuated lattices for short). A Boolean retraction term for a subvariety ${\mathbb{V}}$ of ${\mathbb{BRL}}$ is a unary term t in the language of bounded residuated lattices such that for every ${{\bf A} \in \mathbb{V}, t^{A}}$ , the interpretation of the term on A, defines a retraction from A onto its Boolean skeleton B(A). It is shown that Boolean retraction terms are equationally definable, in the sense that there is (...) a variety ${\mathbb{V}_{t} \subsetneq \mathbb{BRL}}$ such that a variety ${\mathbb{V} \subsetneq \mathbb{BRL}}$ admits the unary term t as a Boolean retraction term if and only if ${\mathbb{V} \subseteq \mathbb{V}_{t}}$ . Moreover, the equation s(x) = t(x) holds in ${\mathbb{V}_{s} \cap \mathbb{V}_{t}}$ . The radical of ${{\bf A} \in \mathbb{BRL}}$ , with the structure of an unbounded residuated lattice with the operations inherited from A expanded with a unary operation corresponding to double negation and a a binary operation defined in terms of the monoid product and the negation, is called the radical algebra of A. To each involutive variety ${\mathbb{V} \subseteq \mathbb{V}_{t}}$ is associated a variety ${\mathbb{V}^{r}}$ formed by the isomorphic copies of the radical algebras of the directly indecomposable algebras in ${\mathbb{V}}$ . Each free algebra in such ${\mathbb{V}}$ is representable as a weak Boolean product of directly indecomposable algebras over the Stone space of the free Boolean algebra with the same number of free generators, and the radical algebra of each directly indecomposable factor is a free algebra in the associated variety ${\mathbb{V}^{r}}$ , also with the same number of free generators.A hierarchy of subvarieties of ${\mathbb{BRL}}$ admitting Boolean retraction terms is exhibited. (shrink)

In any variety of bounded integral residuated lattice-ordered commutative monoids the class of its semisimple members is closed under isomorphic images, subalgebras and products, but it is not closed under homomorphic images, and so it is not a variety. In this paper we study varieties of bounded residuated lattices whose semisimple members form a variety, and we give an equational presentation for them. We also study locally representable varieties whose semisimple members form a variety. Finally, we analyze the relationship with (...) the property “to have radical term”, especially for k-radical varieties, and for the hierarchy of varieties k>0 defined in Cignoli and Torrens. (shrink)

In this paper we prove that the equational class generated by bounded BCK-algebras is the variety generated by the class of finite simple bounded BCK-algebras. To obtain these results we prove that every simple algebra in the equational class generated by bounded BCK-algebras is also a relatively simple bounded BCK-algebra. Moreover, we show that every simple bounded BCK-algebra can be embedded into a simple integral commutative bounded residuated lattice. We extend our main results to some richer subreducts of the class (...) of integral commutative bounded residuated lattices and to the involutive case. (shrink)

Hanc quoque ‘iucunditatem’, si vis, transfer in animum , rnodo intellegas inter ilium qui dicat Tanta laetitia auctus sum ut nihil constet et eum qui Nunc demum mihi animus ardet, quorum alter laetitia gestiat, alter dolore crucietur, esse ilium medium [Quamquam haec inter nos nuper notitia admodum est] qui nee laetetur nee angatur, itemque inter eum qui potiatur corporis expetitis voluptatibus et eum qui crucietur summis doloribus esse eum qui utroque careat.

Hanc quoque ‘iucunditatem’, si vis, transfer in animum, rnodo intellegas inter ilium qui dicat Tanta laetitia auctus sum ut nihil constet et eum qui Nunc demum mihi animus ardet, quorum alter laetitia gestiat, alter dolore crucietur, esse ilium medium [Quamquam haec inter nos nuper notitia admodum est] qui nee laetetur nee angatur, itemque inter eum qui potiatur corporis expetitis voluptatibus et eum qui crucietur summis doloribus esse eum qui utroque careat.

In a classical paper [15] V. Glivenko showed that a proposition is classically demonstrable if and only if its double negation is intuitionistically demonstrable. This result has an algebraic formulation: the double negation is a homomorphism from each Heyting algebra onto the Boolean algebra of its regular elements. Versions of both the logical and algebraic formulations of Glivenko’s theorem, adapted to other systems of logics and to algebras not necessarily related to logic can be found in the literature (see [2, (...) 9, 8, 14] and [13, 7, 14]). The aim of this paper is to offer a general frame for studying both logical and algebraic generalizations of Glivenko’s theorem. We give abstract formulations for quasivarieties of algebras and for equivalential and algebraizable deductive systems and both formulations are compared when the quasivariety and the deductive system are related. We also analyse Glivenko’s theorem for compatible expansions of both cases. (shrink)

In this paper we characterize the MV-algebras containing as subalgebras Post algebras of finitely many orders. For this we study cyclic elements in MV-algebras which are the generators of the fundamental chain of the Post algebras.

Michel Onfray est l'un des philosophes français les plus connus - mais que sait-on de lui au juste? Apprécié ou controversé, il déclenche des réactions viscérales, trop souvent approximatives. Si certains l'aiment et le défendent sans réserve, d'autres le détestent sans le lire. De fait, on a souvent réduit son travail à deux ou trois livres médiatisés alors qu'il a écrit plus de soixante ouvrages, fort divers, où il est question de philosophie, de littérature, de poésie, de musique, de peinture, (...) de photographie. Cet essai biographique se propose donc d'explorer l'originalité de sa démarche. Il retrace, à partir des textes de Michel Onfray, les rencontres décisives qui ont propulsé ou infléchi sa pensée. Et dégage les caractéristiques d'une écriture singulière, tissée de morale, de vécu et de métaphysique incandescente. (shrink)

In this paper we see that the answer of this question is affirmative. We prove this for Dco-algebras and as special case we obtain the result for Positive Implication algebras. First we give, without proof, the properties of Dco-algebras and S-algebras and their connection with Positive Implication algebras and Implication algebras. These results can be found in [T] and [IT].

The main objective of this paper was to analyze gender representation in Mexican elementary education materials from 1960 to the present, particularly on the topic of human evolution, as this is a fundamental subject for the understanding of our ancestry as a species, and for its relationship with questions about human nature. Using gender as a category and an approach that included both qualitative and quantitative methods, a comparison of three generations of textbooks for elementary school and “monographs” was carried (...) out. The results show a deeply entrenched and systemic problems of gender representation in Mexican pedagogical tools past and present. (shrink)

The concept of humoral control--the direction of bodily processes by complex organic fluids--has gained ascendancy in recent decades, and enlisted the interest of more than humoral specialists.

We give a presentation of Post algebras of ordern+1 (n1) asn+1 bounded Wajsberg algebras with an additional constant, and we show that a Wajsberg algebra admits a P-algebra reduct if and only if it isn+1 bounded.