On a certain class ofm-address machines

Conclusion It follows from the proved theorems that ifM =Q, (whereQ={0,q ₁,q ₂,...,q }) is a machine of the classM _F then there exist machinesM _i such thatM _i(1,c)=M (q _i,c) andQ _i={0, 1, 2, ..., +1} (i=1, 2, ..., ).And thus, if the way in which to an initial function of content of memorycC a machine assigns a final onecC is regarded as the only essential property of the machine then we can deal with the machines of the formM ={0, 1, 2, ..., }, and processes (t) (wheret=1,c,cC) only.Such approach can simplify the problem of defining particular machines of the classM _F , composing and simplifying them.Allatum est die 19 Januarii 1970     

Contextualism and the Skeptic: Comments on Engel

Mylan Engels paper (2004) is divided into two parts: a negative part, criticizing the costs of contextualism and a constructive part proposing a noncontextualist resolution of the skeptical problem. I will only address the constructive part here. The constructive part is composed of three elements: (i) a reconstruction or reformulation of the original skeptical argument, which draws on the notion of epistemic possibility (e-possibility), (ii) a distinction between two senses of knowledge (and two corresponding kinds of e-possibility): fallibilistic and infallibilistic, and (iii) an argument which tries to hoist the skeptic by their own petard, namely the closure principle (CP). As I will argue, there are two ways to understand Engels anti-skeptical argument. Only in one interpretation does the argument depend on the proposed reconstruction of the skeptical argument in terms of e-possibility. But this version of the argument is unsound. More importantly, the skeptic has a strong prima facie objection at her disposal, which applies to both interpretations of the argument. If this objection is valid, Engels argument does not hold. But once it is invalidated, his argument is superfluous.     

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 defining necessity in terms of entailment

In their book Entailment, Anderson and Belnap investigate the consequences of defining Lp (it is necessary that p) in system E as (pp)p. Since not all theorems are equivalent in E, this raises the question of whether there are reasonable alternative definitions of necessity in E. In this paper, it is shown that a definition of necessity in E satisfies the conditions { _E Lpp, _EL(pq)(LpLq), _E pLp} if and only if its has the form C ₁.C₂ .... C_np, where each C _iis equivalent in E to either pp or ((pp)p)p.     

Happiness and virtue in Socrates' moral theory

Conclusion In Section IV above we start with texts whose prima facie import speaks so strongly for the Identity Thesis that any interpretation which stops short of it looks like a shabby, timorous, thesis-saving move. What else could Socrates mean when he declares with such conviction that no evil can come to a good man (T19), that his prosecutors could not harm him (T16(a)), that if a man has not been made more unjust he has not been harmed (T20), that all of happiness is in culture and justice (T16(a)), that living well is the same as living justly (T15)? But then doubts begin to creep in. Recalling that inflation of the quantifier is normal and innocuous in common speech (that job means everything to him, he'll do anything to get it, will stick at nothing) we ask if there is really no chance at all that no evil in T19, not harmed in T20 might be meant in the same way? The shift from no harm at T16(a) to no great harm at T16(b), once noticed, strengthens the doubt. It gets further impetus in T21(b) when to explain how all of happiness is in culture and justice he depicts a relation (that recurs more elaborately in T22) which, though still enormously strong, is not quite as strong as would be required by identity. The doubt seeps into T15 when we note that current usage did allow just that relation as a respectable use of the same.At that point we begin to wonder if resort to the Identity Thesis might not be just a first approximation to a subtler, more finely nuanced, doctrine which would give Socrates as sound a foundation for what we know he wants to maintain at all costs - the Sovereignty of Virtue - without obliterating the eudaemonic value of everything else in his world. We cast about for a credible model of such a relation of virtue to happiness and hit on that multicomponent pattern sketched on p. 9 above. We ascertain that this will afford a comprehensively coherent eudaemonist theory of rational action, while its rival would not, and will fit perfectly a flock of texts in Section V which the latter will not fit at all. Are we not entitled to conclude that this is our best guide to the true relation of virtue to happiness in Socrates' thought - the one for which he would have declared if he had formulated explicitly those two alternative theses and made a reasoned choice between them?The Socrates of this paper is the protagonist of Plato's earlier dialogues. I list these (by self-explanatory abbreviations), borrowed from T. Irwin, Plato's Moral Theory [1974] (hereafter PMT): Ap., Ch., Cr., Eud., Eu., G., HMa., HMi, Ion, La., Ly., Pr., R., I. I assume, but shall not argue here, that in this segment of his corpus, Plato aims to recreate the doctrines and arguments of his teacher in dramatic scenes, all of which (except for the Ap.) may be, and most of which undoubtedly are, fictional; I shall be referring these works, under this proviso, as Plato's Socratic dialogues. (I did not include the Menexenus in the above list, since the parody of a funeral oration in this dialogue is implicitly dissociated from Socrates.)     

The relevance of Habermas' communicative turn

This paper points out the way in which educational and communicative action (Habermas) are to be related. It is shown that earlier attempts to put Habermas ideas to use have led to a dead end because they do not realize clearly that the new basic notion introduced by Habermas, namely communicative action, is the expression of a communicative turn. It is argued that Habermas' concept expresses a radical new attempt to grasp the intersubjective character of social action. Next implications of this communicative turn for the concept of education as a social praxis are indicated. Education can be conceived of as a praxis responding to the vulnerability of a communicative self.     

Variations in use of the term “or”

Two studies showed that adults' responses to questions involving the term or varied markedly depending upon the type of question presented. When presented with various objects (A's and B's) and asked to circle all things which are A or B subjects tended to circle A's as well as B's, whereas when asked to circle all the A's or B's subjects showed a relatively stronger tendency to circle one or the other. Moreover the nature of the sets of objects (As and Bs) influenced behavior as well. There was also evidence that the effects due to question wording or set type transferred.     

Leadership of antireligious propaganda in the Soviet Union

Re-emergent scientific atheism bears the marks of its historical origins in the efforts of Bon-Bruevi and Jaroslavskij. The disciples of the Lenin generation use their fathers somewhat as second-level classics.     

On Łukasiewicz-Moisil algebras of fuzzy sets

The set (X, J) of fuzzy subsetsf:XJ of a setX can be equipped with a structure of -valued ukasiewicz-Moisil algebra, where is the order type of the totally ordered setJ. Conversely, every ukasiewicz-Moisil algebra — and in particular every Post algebra — is isomorphic to a subalgebra of an algebra of the form (X, J), whereJ has an order type . The first result of this paper is a characterization of those -valued ukasiewicz-Moisil algebras which are isomorphic to an algebra of the form (X, J) (Theorem 1). Then we prove that (X, J) is a Post algebra if and only if the setJ is dually well-ordered (Theorem 2) and we give a characterization of those -valued Post algebras with are isomorphic to an algebra of the form (X, J) (Theorem 3 and Proposition 2).     

On finite approximability of ψ-intermediate logics

The aim of this note is to show (Theorem 1.6) that in each of the cases: = {, }, or {, , }, or {, , } there are uncountably many -intermediate logics which are not finitely approximable. This result together with the results known in literature allow us to conclude (Theorem 2.2) that for each : either all -intermediate logics are finitely approximate or there are uncountably many of them which lack the property.     

Syntactical investigations intoBI logic andBB′I logic

In this note, we will study four implicational logicsB, BI, BB and BBI. In [5], Martin and Meyer proved that a formula is provable inBB if and only if is provable inBBI and is not of the form of » . Though it gave a positive solution to theP - W problem, their method was semantical and not easy to grasp. We shall give a syntactical proof of the syntactical relation betweenBB andBBI logics. It also includes a syntactical proof of Powers and Dwyer's theorem that is proved semantically in [5]. Moreover, we shall establish the same relation betweenB andBI logics asBB andBBI logics. This relation seems to say thatB logic is meaningful, and so we think thatB logic is the weakest among meaningful logics. Therefore, by Theorem 1.1, our Gentzentype system forBI logic may be regarded as the most basic among all meaningful logics. It should be mentioned here that the first syntactical proof ofP - W problem is given by Misao Nagayama [6].Presented byHiroakira Ono     

Model theoretic results for infinitely deep languages

We define a subhierarchy of the infinitely deep languagesN described by Jaakko Hintikka and Veikko Rantala. We shall show that some model theoretic results well-known in the model theory of the ordinary infinitary languages can be generalized for these new languages. Among these are the downward Löwenheim-Skolem and o's theorems as well as some compactness properties.     

A metacompleteness theorem for contraction-free relevant logics

I note that the logics of the relevant group most closely tied to the research programme in paraconsistency are those without the contraction postulate(A.AB).AB and its close relatives. As a move towards gaining control of the contraction-free systems I show that they are prime (that wheneverA B is a theorem so is eitherA orB). The proof is an extension of the metavaluational techniques standardly used for analogous results about intuitionist logic or the relevant positive logics.The main results of this paper were presented at the Paraconsistent Logic conference in Canberra in 1980. The author wishes to thank the participants in that conference for comments and suggestions made at the time.     

Act Without Denial: Slavoj Žižek on Totalitarianism,Revolution and Political Act

iek's thinking departs from the Lacanian claim that we live in a symbolic order, not a real world, and that the Real is what we desire, but can never know or grasp. There is a fundamental virtuality of reality that points to the lie in every truth-claim, and there are two ways of dealing with this:repression and denial. An ideology, a system or a regime becomes totalitarian when it denies the virtual character of both its world and its subject (democracy represses truth's basic lie, which makes it possible for the repressed to return). iek's analysis of totalitarianism, particularly Stalinism, shows how a totalitarian system denies its subject, which, being desire for the Real, cannot act in the name of truth but must acknowledge the contingency of its action (a political act can fail to reach its goal), whereas an established system can no longer fail and has to deny its flaws. Any political act disrupts the (evolution of) the symbolic order and thus is revolutionary, creating an event ex nihilo. An act is a jump into the inconsistency of the symbolic order, i.e. into das Ding, a jump both into and out of the nihil in which our world is grounded. Politics therefore can never be Realpolitik. The realization that politics is a symbolic phenomenon, supported not by the real, but by signifiers, is the Lacanian foundation of iek's political theory.     

A topological logic of action

We consider a quantifier-free language in which there are terms as well as formulas. The proposition-forming propositional operators are the usual ones, and the term-making term operators are the usual lattice theoretical ones. In addition there is a formula-making term operator, does. We study a new logic in which does is claimed to approximate some features of the informal concept the agent performs the action .     

Some modifications of Scott's theorem on injective spaces

D. Scott in his paper [5] on the mathematical models for the Church-Curry -calculus proved the following theorem.A topological space X. is an absolute extensor for the category of all topological spaces iff a contraction of X. is a topological space of Scott's open sets in a continuous lattice.In this paper we prove a generalization of this theorem for the category of , -closure spaces. The main theorem says that, for some cardinal numbers , , absolute extensors for the category of , -closure spaces are exactly , -closure spaces of , -filters in , >-semidistributive lattices (Theorem 3.5).If = and = we obtain Scott's Theorem (Corollary 2.1). If = 0 and = we obtain a characterization of closure spaces of filters in a complete Heyting lattice (Corollary 3.4). If = 0 and = we obtain a characterization of closure space of all principial filters in a completely distributive complete lattice (Corollary 3.3).     

The logical structure of linguistic commitment II: Systems of relevant commitment entailment

In The Logical Structure of Linguistic Commitment I (The Journal of Philosophical Logic 23 (1994), 369–400), we sketch a linguistic theory (inspired by Brandom's Making it Explicit) which includes an expressivist account of the implication connective, : the role of is to make explicit the inferential proprieties among possible commitments which proprieties determine, in part, the significances of sentences. This motivates reading (A B) as commitment to A is, in part, commitment to B. Our project is to study the logic of . LSLC I approximates (A B) as anyone committed to A is committed to B, ignoring issues of whether A is relevant to B. The present paper includes considerations of relevance, motivating systems of relevant commitment entailment related to the systems of commitment entailment of LSLC I. We also consider the relevance logics that result from a commitment reading of Fine's semantics for relevance logics, a reading that Fine suggests.     

On two arguments for the indeterminacy of personal identity

Both arguments are based on the breakdown of normal criteria of identity in certain science-fictional circumstances. In one case, normal criteria would support the identity of person A with each of two other persons, B and C; and it is argued that, in the imagined circumstances, A=B and A=C have no truth value. In the other, a series or spectrum of cases is tailored to a sorites argument. At one end of the spectrum, persons A and B are such that A=B is clearly true; at the other end, A and B are such that the identity is clearly false. In between, normal criteria of identity leave the truth or falsehood of A=B undecided, and it is argued that in these circumstances A=B has no truth value.These arguments are to be understood counterfactually. My claim is that, so understood, neither establishes its conclusion. The first involves a pair of counterfactual situations that are equally possible or tied. If A=B and A=C have no truth value, a counterfactual conditional with one of them as consequent and an antecedent that is true in circumstances in which either is true should have no truth value. Intuitively, however, any such counterfactual is false. The second argument can be seen to invite an analogous response. If this is right, however, there is an important disanalogy between this and the classical paradox of the heap. If the disanalogy is only apparent, the argument shows at most that the existence of persons can be indeterminate.     

Логистическая система, исходными связками которой являются эквивалентность и дизъюнкция

- Allatum est die 5 Martii 1970