Husserl and Frege on the analysis of the concept of number and primitive logical concepts.

Cognitive, or knowledge, agents, who are in some way aware of describing their own view of the world (based on their mental concepts), need to become concerned with the expressions of their own conceptions. My main supposition is that agents’ conceptions are mainly expressed in the form of linguistic expressions that are spoken, written, and represented based on e.g. letters, numbers, or symbols. This research especially focuses on symbolic conceptions (that are agents’ conceptions that are manifested in the form of (...) their symbols). I attempt to logically (and using ????LSYM) analyse symbolic conceptions in terminological systems. ????LSYM is an assertional fragment of my developed Conception Language (????L), which is utilised as a formal-logical system for representing and explicating agents’ conceptions of the world. Keywords: assertional logic; cognitive agent; knowledge agent; conception language; conception; symbol; symbolic conception. (shrink)

The passionate and staunch defence of logic of the controversial thinker Ibn Ḥazm, Abū Muḥammad ʿAlī b. Aḥmad b. Saʿīd of Córdoba (384-456/994-1064), had lasting consequences in the Islamic world. Indeed, his book Facilitating the Understanding of the Rules of Logic and Introduction Thereto, with Common Expressions and Juristic Examples (Kitāb al-Taqrīb li-ḥadd al-manṭiq wa-l-mudkhal ilayhi bi-l-alfāẓ al-ʿāmmiyya wa-l-amthila al-fiqhiyya), composed in 1025-1029, was well known and discussed during and after his time; and it paved the way for the studies (...) of his compatriots Ibn Bājjah (d. 1138), Ibn Ṭufayl (1185), and Ibn Rushd (1198), who each gave demonstrative reasoning a privileged place within the methods of attaining knowledge. Unfortunately, as too often in the history of science, Ibn Ḥazm’s innovative perspectives and contributions in logic have been overlooked or considered with an attitude of contempt. On the one hand, his work has been seen, at best, as promulgating the benefits of studying Aristotle’s logic, so that his contribution is assessed as more didactical than conceptual. And on the other hand, those who do examine his innovations often consider them to be mistaken. As indicated by Chejne (1984, p. 2) contempt towards the logical work of Ibn Ḥazm was also present in its reception by the Eastern philosophers who accused him of deviating from Aristotelian logic and of dabbling in things beyond his capability. However, a reassessment of his work on logic has since begun, by delving into the ways the thinker of Córdoba studied the links between deontic and modal qualification of propositions. In this context Lameer’s (2013) paper on the logical sources of Ibn Ḥazm is worth mentioning; the author (p. 417, footnote 1) observes that, although, strictly speaking, it was al-Fārābī who first drew the parallelism between deontic and modal concepts, it was Ibn Ḥazm who developed it and worked it out in a more precise manner. A primary aim of this paper is to help fill some of these gaps by stressing the role of the work of Ibn Ḥazm in developing a notion of deontic necessity deeply rooted in legal normativity, and in explicitly discussing the transference between deontic and modal concepts. According to our view; the basic units of Islamic deontic logic are what we might call, indulging in terminological anachronism, heteronomous imperatives. As it turns out, the heteronomy of imperatives within Islamic legal systems contrasts with those of the purely moral realm, which seem to be closer to an autonomous conception of moral law. There it concurs again with Leibniz’s proposal to define obligatory as “what is necessary for a good person to do”. In the present paper, we will focus on the heteronomous imperatives of legal systems rather than on the imperatives of the purely moral realm. In this context, the work of Ibn Ḥazm extends the parallelism between the necessity of events and that of human actions stressed by his predecessors. According to our understanding, Ibn Ḥazm’s parallelism can be rendered explicit formally by means of a conditional (or hypothetical) structure shared by both deontic and modal propositions. Moreover, this structure makes apparent that this parallelism displays an underlying system of “degrees”. Indeed, while in the domain of events, given some conditions, it makes sense to distinguish between an event that is more likely to happen than another. Ibn Ḥazm speaks of near and distant possibility (such as the higher degree of likelihood of rain, given the condensation of clouds in December, and its lower degree, when the condensation occurs in summer); and, in the domain of actions, the Islamic notion of weighting actions determines degrees of virtue (or of legal and moral value). So whereas the degree of virtue of performing a forbidden act as determined by the distribution of sanction and reward is 0, we obtain the same value by pondering the likelihood of an impossible event to take place. Furthermore, as discussed in section II.3.2, the system of values at work in the parallelism can be seen as opening the way to a more direct correspondence. Thus, while in the realm of nature, likelihood of occurrence of an event is dependent upon the conditions specific to the occurrence of that event; while, in the realm of jurisprudence, likelihood of performing an action is dependent upon the distribution of reward and sanction specific to that action (being that, given the choice to perform or not perform a given action, those that will be rewarded are more likely to be performed than those that are not). According to this perspective, the point of the parallelism is that both deontic and modal qualifications measure the degree of an action or event to become actual; that is – indulging once more in anachronism (but this time from the Leibnizian background) – the degree measures how feasible (facile) an action or event may be. This suggests that Ibn Ḥazm’s perspectives already herald the links to probability and possibility explored by Leibniz six centuries later – see for example Leibniz’s (1671, A VI, I, p. 424-26) use of probability in the context of conditional right. Nevertheless, it also shows a crucial difference to the approach developed in the Elementa Jura Naturalis: whereas Leibniz’s studies seek to define what is to be just or virtuous, the logical system of deontic imperatives within Islamic jurisprudence presupposes that what is to be virtuous has already been settled. Determining what is to be virtuous is not achieved by logical reasoning within the system of legal jurisprudence, but by delving into the higher objectives of the Sharīʿa. While developing our point, we will delve into the logical structure of the heteronomous imperatives. This distinguishes our contribution from the existing literature, such as the papers of Chejne (1984), Lameer (2014), and Guerrero (1997, 2010, 2014), which do not provide a logical analysis of the deontic concepts put into work by Ibn Ḥazm. The true antecedent to the present paper is the work of Farid Zidani (2007, 2015), who, so far as we know, was the first to undertake such a task. Some of our own developments and general epistemological thoughts go beyond Ibn Ḥazm’s framework and motivations; mainly those contained in sections II.3.2 and IV. However, according to our view, these reflections suggest that Ibn Ḥazm’s approach has the substance for a broader and deeper exploration of the logic of norms. The paper is structured as follows:I.Ibn Ḥazm’s Logic of Heteronomous Imperatives. After presenting some extracts of the relevant text, we proceed by providing a formal reconstruction of the five forms of deontic modalities. II. A Landmark in the History of the Logical Analysis of Norms. Duties and Modalities. In this section, we study the transferences from deontic to modal necessity and possibility. We briefly compare the deontic system of Islamic Jurisprudence with that of Leibniz.III. Leibniz and Hypothetical Imperatives in Law.IV. Beyond Ibn Ḥazm: Conclusions and the Work Ahead. We will conclude the paper by discussing briefly some conceptual points that distinguish the logic of heteronomous imperatives from contemporary deontic logic. Our final words will discuss deontic-modal parallelism in the context of Ibn Ḥazm’s rejection of reasoning by conjecture and what we call “the internalization of nature.”. (shrink)

The book deals with conceptualization of time in different languages and in different kinds of discourse (folklore, poetry, fiction). Special attention is paid to some culture-specific models of time as well as to linguistic means related to temporal semantics: nouns, adjectives, adverbs, prepositions, prefixes, particles, and other temporal modifiers. The concept of time is also considered in its logical, axiological and historical aspects.

Abstract Introduction Logically valid deductive arguments are clear examples of abstract recursive computational proce‐ dures on propositions or on probabilities. However, it is not known if the cortical time‐consuming inferential pro‐ cesses in which logical arguments are eventually realized in the brain are in fact physically different from other kinds of inferential processes. Methods In order to determine whether an electrical EEG discernible pattern of logical deduction exists or not, a new experimental paradigm is proposed contrasting logically valid (...) and invalid inferences with exactly the same content (same premises and same relational variables) and distinct logical complexity (propositional truth‐functional operators). Electroencephalographic signals from 19 subjects (24.2 ± 3.3 years) were acquired in a two‐condition para‐ digm (100 trials for each condition). After the initial general analysis, a trial‐by‐trial approach in beta‐2 band allowed to uncover not only evoked but also phase asynchronous activity between trials. Results showed that (i) deductive inferences with the same content evoked the same response pattern in logically valid and invalid conditions, (ii) mean response time in logically valid inferences is 61.54% higher, (iii) logically valid inferences are subjected to an early (400 ms) and a late reprocessing (600 ms) verified by two distinct beta‐2 activa‐ tions (p‐value < 0,01, Wilcoxon signed rank test). Conclusion We found evidence of a subtle but measurable electrical trait of logical validity. Results put forward the hypothesis that some logically valid deductions are recursive or computational cortical events. Keywords Beta‐2 band, Evoked potentials, Induced potentials, Deductive inference, Logical validity, Cortical bases of logical reasoning. (shrink)

This paper presents a semantical analysis of the Weak Kleene Logics Kw3 and PWK from the tradition of Bochvar and Halldén. These are three-valued logics in which a formula takes the third value if at least one of its components does. The paper establishes two main results: a characterisation result for the relation of logical con- sequence in PWK – that is, we individuate necessary and sufficient conditions for a set.

I apply Kooi and Tamminga's (2012) idea of correspondence analysis for many-valued logics to strong three-valued logic (K3). First, I characterize each possible single entry in the truth-table of a unary or a binary truth-functional operator that could be added to K3 by a basic inference scheme. Second, I define a class of natural deduction systems on the basis of these characterizing basic inference schemes and a natural deduction system for K3. Third, I show that each of the resulting (...) natural deduction systems is sound and complete with respect to its particular semantics. Among other things, I thus obtain a new proof system for Lukasiewicz's three-valued logic. (shrink)

An examination of McTaggart’s [1908] argument for the unreality of time.

Review of Russell’s Philosophy of Logical Atomism 1897–1905, by Jolen Galaugher (Palgrave Macmillan 2013).

Judaic Logic is an original inquiry into the forms of thought determining Jewish law and belief, from the impartial perspective of a logician. Judaic Logic attempts to honestly estimate the extent to which the logic employed within Judaism fits into the general norms, and whether it has any contributions to make to them. The author ranges far and wide in Jewish lore, finding clear evidence of both inductive and deductive reasoning in the Torah and other books of the Bible, and (...) analyzing the methodology of the Talmud and other Rabbinic literature by means of formal tools which make possible its objective evaluation with reference to scientific logic. The result is a highly innovative work – incisive and open, free of clichés or manipulation. Judaic Logic succeeds in translating vague and confusing interpretative principles and examples into formulas with the clarity and precision of Aristotelean syllogism. Among the positive outcomes, for logic in general, are a thorough listing, analysis and validation of the various forms of a-fortiori argument, as well as a clarification of dialectic logic. However, on the negative side, this demystification of Talmudic/Rabbinic modes of thought (hermeneutic and heuristic) reveals most of them to be, contrary to the boasts of orthodox commentators, far from deductive and certain. They are often, legitimately enough, inductive. But they are also often unnatural and arbitrary constructs, supported by unverifiable claims and fallacious techniques. Many other thought-processes, used but not noticed or discussed by the Rabbis, are identified in this treatise, and subjected to logical review. Various more or less explicit Rabbinic doctrines, which have logical significance, are also examined in it. In particular, this work includes a formal study of the ethical logic (deontology) found in Jewish law, to elicit both its universal aspects and its peculiarities. With regard to Biblical studies, one notable finding is an explicit formulation (which, however, the Rabbis failed to take note of and stress) of the principles of adduction in the Torah, written long before the acknowledgement of these principles in Western philosophy and their assimilation in a developed theory of knowledge. Another surprise is that, in contrast to Midrashic claims, the Tanakh (Jewish Bible) contains a lot more than ten instances of qal vachomer (a-fortiori) reasoning. In sum, Judaic Logic elucidates and evaluates the epistemological assumptions which have generated the Halakhah (Jewish religious jurisprudence) and allied doctrines. Traditional justifications, or rationalizations, concerning Judaic law and belief, are carefully dissected and weighed at the level of logical process and structure, without concern for content. This foundational approach, devoid of any critical or supportive bias, clears the way for a timely reassessment of orthodox Judaism (and incidentally, other religious systems, by means of analogies or contrasts). Judaic Logic ought, therefore, to be read by all Halakhists, as well as Bible and Talmud scholars and students; and also by everyone interested in the theory, practise and history of logic. (shrink)

In this paper we propose an non-machine learning artificial intelligence (AI) based approach for telecom data analysis, with a special focus on clique detection. Clique detection can be used to identify households, which is a major challenge in telecom data analysis and predictive analytics. Our approach does not use any form of machine learning, but another type of algorithm: satisfiability for propositional logic. This is a neglected approach in modern AI, and we aim to demonstrate that for certain (...) tasks, it may be a good alternative to machine learning-based approaches. We have used a simple DPLL satisfiability solver over an artificially generated telecom dataset (due to GDPR regulations), but our approach can be implemented on any telecom data by following the SAT encoding we have developed, and the DPLL solver can be substituted by a more advanced alternative such as CDCL. This paper extends the method presented in [1] for banking logs to data containing caller information, and proposes a more efficient encoding. -/- . (shrink)

This book was completed by the early 1960s and published in 1984 but it has not lost its topicality, for it contains an important re-assessment of the relations of two main streams of contemporary philosophy - the Analytical and the Dialectic. Adherents and critics of these traditions tend to assurnethat they are diametrically opposed, that their roots, concerns and approaches contradict each other, and that no reconciliation is possible. In contradistinction Russell derives both traditions from the common root of the (...) dissatisfaction with the arguments against speculative philosophy. These according to the author leave a lacuna - certain elementsof our Weltanschaaung have been removed, but they cannot be removed without replacement lest we have an incomplete world view, so incomplete in fact that it cannot be viable. According to Russell part of this vacuum is taken up by the analytical tradition but this tradition is not capable of taking up the remainder of it. That portion of the vacant space is however taken up by the dialectical tradi tion, which in turn cannot itself handle the whole of the problem. Thus the two reactions to the demise of speculative philosophy appear to be complementary in at least this sense. But the author goes further, for according to hirn the analytical arguments themselves clearly point to the emergence of dialectical problems, and the dialectical problems themselves need some such background to arise. (shrink)

Logic and psychology overlap in judgment, inference and proof. The problems raised by this commonality are notoriously difficult, both from a historical and from a philosophical point of view. Sundholm has for a long time addressed these issues. His beautiful piece of work [A Century of Inference: 1837-1936] begins by summarizing the main difficulty in the usual provocative manner of the author: one can start, he says, by the act of knowledge to go to the object, as the Idealist does; (...) one can also start by the object to go to the act, in the Realist mood; never the two shall meet. He is himself inclined to accept the first perspective as the right one and he has eventually developed an original version of antirealism which starts, not from considerations about the publicity of meaning, in the manner of Dummett, but from an epistemic standpoint, trying to search in a non-Fregean tradition of analysis of judgement and cognate notions a way of founding constructivist semantics. The present paper ploughes the same field. We concentrate on the significance, for Sundholm’s program, of the perspective that has been opened by Twardowski in his important essay on acts and products (1912. (shrink)

The huge change brought about by the corona virus pandemic contains some structural characteristics that define it as a catastrophe. The text explores and offers an outline of a possible analysis of some of the logical and normative features of this phenomenon.

This paper discusses the theoretical assumptions behind the conception of the logic of faith and deed (LF&D) and outlines its formal-axiomatic frame and its method of construction, which enable us to understand it as a kind of deductive science. The paper is divided into several sections, starting with the logical analysis of the ambiguous terms of 'faith’ and 'action', and focusing in particular on the concepts of religious faith and deed as a type of conscious activity relating to (...) a matter or matters of social importance. After outlining the main ideas and basic assumptions of the theoretical conception of the LF&D as an axiomatic theory, the author introduces some axiom systems for: 1) the logics of faith LF (doxastic logics), 2) the logic of deed LD, and 3) certain logics of norms DL (deontic logics) connected with "duties" and concerning actions/deeds. Lastly, the paper outlines the scientific LF&D based on the three types of logic 1)-3). (shrink)

In the fifth version of our response-paper [26] to Imamura’s criticism, we recall that NonStandard Neutrosophic Logic was never used by neutrosophic community in no application, that the quarter of century old neutrosophic operators (1995-1998) criticized by Imamura were never utilized since they were improved shortly after but he omits to tell their development, and that in real world applications we need to convert/approximate the NonStandard Analysis hyperreals, monads and binads to tiny intervals with the desired accuracy – otherwise (...) they would be inapplicable. We point out several errors and false statements by Imamura [21] with respect to the inf/sup of nonstandard subsets, also Imamura’s “rigorous definition of neutrosophic logic” is wrong and the same for his definition of nonstandard unit interval, and we prove that there is not a total order on the set of hyperreals (because of the newly introduced Neutrosophic Hyperreals that are indeterminate), whence the Transfer Principle from R to R* is questionable. After his criticism, several response publications on theoretical nonstandard neutrosophics followed in the period 2018-2022. As such, I extended the NonStandard Analysis by adding the left monad closed to the right, right monad closed to the left, pierced binad (we introduced in 1998), and unpierced binad - all these in order to close the newly extended nonstandard space (R*) under nonstandard addition, nonstandard subtraction, nonstandard multiplication, nonstandard division, and nonstandard power operations [23, 24]. Improved definitions of NonStandard Unit Interval and NonStandard Neutrosophic Logic, together with NonStandard Neutrosophic Operators are presented. (shrink)

This paper considers non-standard analysis and a recently introduced computational methodology based on the notion of ①. The latter approach was developed with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework and in all the situations requiring these notions. Non-standard analysis is a classical purely symbolic technique that works with ultrafilters, external and internal sets, standard and non-standard numbers, etc. In its turn, the ①-based methodology does not use any (...) of these notions and proposes a more physical treatment of mathematical objects separating the objects from tools used to study them. It both offers a possibility to create new numerical methods using infinities and infinitesimals in floating-point computations and allows one to study certain mathematical objects dealing with infinity more accurately than it is done traditionally. In these notes, we explain that even though both methodologies deal with infinities and infinitesimals, they are independent and represent two different philosophies of Mathematics that are not in a conflict. It is proved that texts :539–555, 2017; Gutman and Kutateladze in Sib Math J 49:835–841, 2008; Kutateladze in J Appl Ind Math 5:73–75, 2011) asserting that the ①-based methodology is a part of non-standard analysis unfortunately contain several logical fallacies. Their attempt to show that the ①-based methodology can be formalized within non-standard analysis is similar to trying to show that constructivism can be reduced to the traditional Mathematics. (shrink)

A analysis of some concepts of logic is proposed, around the work of Edelcio de Souza. Two of his related issues will be emphasized, namely: opposition, and quasi-truth. After a review of opposition between logical systems [2], its extension to many-valuedness is considered following a special semantics including partial operators [13]. Following this semantic framework, the concepts of antilogic and counterlogic are translated into opposition-forming operators [15] and specified as special cases of contradictoriness and contrariety. Then quasi-truth [5] (...) is introduced and equally translated as a product of two partial operators. Finally, the reflections proposed around opposition and quasi-truth lead to a third new logical concept: quasi-opposition, borrowing the central feature of partiality and opening the way to a potential field of new investigations into philosophical logic. (shrink)

This paper presents an account of what it is for a property or relation (or ‘attribute’ for short) to be logically simple. Based on this account, it is shown, among other things, that the logically simple attributes are in at least one important way sparse. This in turn lends support to the view that the concept of a logically simple attribute can be regarded as a promising substitute for Lewis’s concept of a perfectly natural attribute. At least in part, the (...) advantage of using the former concept lies in the fact that it is amenable to analysis, where that analysis—i.e., the account put forward in this paper—requires the adoption neither of an Armstrongian theory of universals nor of a primitive notion of naturalness, fundamentality, or grounding. (shrink)

Item analysis is a general term that refers to the specific methods used in education to evaluate test items, typically for the purpose of test construction and revision. Construction and analysis of science examinations in high school curricula needs the integration of integrated process and skill type which help students develop their rational and logical thinking. This exploratory study aimed to investigate the comparative results of item analyses using Rasch Model Analysis and SPSS. It examined the (...) reliability, mean difficulty, mean ability, discrimination index, mean trend scores, infit and misfit, and item-person and fit maps using the results of the Basic & Integrated Science Process and Skill Test (BISPST) administered to secondary science high school teachers in the Division of Nueva Vizcaya. The Rasch Model Analysis and SPSS revealed the same unsatisfactory value of internal consistency or the reliability coefficient Cronbach’s alpha (0.66 and 0.67), mean score (19.52) and standard deviation (4.53) of the BISPST. The mean item difficulty was set at 0 by definition (SD = 2.02) and the mean examinee ability was 1.56 (SD = 0.98), which means that the examinees were able to correctly answer 61% of items on average. 33 items with difficulty lower than the least able examinee. The mean ability using Rasch Model Analysis per item showed that high performers in the test got the correct answers compared to the low performing group. This is the same and consistent with the results of the mean trend scores of the upper, middle and lower groups as generated by the SPSS. Choices in the BISPST were found to be effective distracters. Although most items needs revision as revealed by the values generated by both softwares, no items were found to be misfit in the distribution. (shrink)

In this paper, partly historical and partly theoretical, after having shortly outlined the development of the meta-ethics in the 1900?s starting from the Tractatus of Wittgenstein, I argue it is possible to sustain that emotivism and intuitionism are unsatisfactory ethical conceptions, while on the contrary, reason (intended in a logical-deductive sense) plays an effective role both in ethical discussions and in choices. There are some characteristics of the ethical language (prescriptivity, universalizability and predominance) that cannot be eluded (pain the (...) non significativity of the same language) by those who want to morally reason, i.e. by those who intend to regulate their own behaviour on the basis of knowledged and coherent principles. These characteristics can be found whether or not all possible ontological-metaphysics foundations of morals are taken into account. Furthermore the deontic logic systems allow the formalization of ethical theories and - at least in principle - a rigorous critical discussion of the same, but obviously nothing can be affirmed on the value of truth of the axioms of a system. In the deontic logic systems Hume?s law is assumed as an implicit result of inferential (conventional) rules and the acceptance of Hume?s law as a logical-linguistic thesis does not involve the cancellation of values (nihilism) or ethical relativism or indifferentism. (shrink)

The usage of Quantum Similarity through the equation Z = {∀Θ∈Z→∃s ∈ S ʌ ∃t ∈ T: Θ= (s,t)}., represents a way to analyze the way communication works in our DNA. Being able to create the object set reference for z being (s,t) in our DNA strands, we are able to set logical tags and representations of our DNA in a completely computational form. This will allow us to have a better understanding of the sequences that happen in our (...) DNA. With this approach, we can also utilize mathematical formulas such as the Euler–Mascheroni constant, regressional analysis, and computational proofs to answer important questions on Quantum biology, Quantum similarity, and Theoretical Physics. (shrink)

When scientists seek further confirmation of their results, they often attempt to duplicate the results using diverse means. To the extent that they are successful in doing so, their results are said to be robust. This paper investigates the logic of such "robustness analysis" [RA]. The most important and challenging question an account of RA can answer is what sense of evidential diversity is involved in RAs. I argue that prevailing formal explications of such diversity are unsatisfactory. I propose (...) a unified, explanatory account of diversity in RAs. The resulting account is, I argue, truer to actual cases of RA in science; moreover, this account affords us a helpful, new foothold on the logic undergirding RAs. (shrink)

It is here proposed an analysis of symbolic and sub-symbolic models for studying cognitive processes, centered on emergence and logical openness notions. The Theory of logical openness connects the Physics of system/environment relationships to the system informational structure. In this theory, cognitive models can be ordered according to a hierarchy of complexity depending on their logical openness degree, and their descriptive limits are correlated to Gödel-Turing Theorems on formal systems. The symbolic models with low logical (...) openness describe cognition by means of semantics which fix the system/environment relationship, while the sub-symbolic ones with high logical openness tends to seize its evolutive dynamics. An observer is defined as a system with high logical openness. In conclusion, the characteristic processes of intrinsic emergence typical of “bio-logic” - emerging of new codes-require an alternative model to Turing- computation, the natural or bio-morphic computation, whose essential features we are going here to outline. (shrink)

Logical analysis of the applicability of nominals (which are introduced by hybrid logic) in the formal descriptions of the world (within modern knowledge representation and semantics-based systems) is very important because nominals, as second sorts of propositional symbols, can support logical identification of the described world at specific [temporal and/or spacial] states. This paper will focus on answering the philosophical-logical question of ‘how a fundamental world description in description logic (DL) and a nominal can be related (...) to each other?’. Based on my assumption that nominals can support more adequate identification of the world in DL, this paper will deal with the concept of ‘world identification’. Accordingly, based on a logical-terminological analysis of nominals, the paper will analyse hybridised fundamental world descriptions. The research will finally reach the idea that we can have a hybrid description logic based on the analysed concepts. (shrink)

The main goal of the article is a further development of the usage of income and comparable approaches to company valuation aimed at defining market capitalization sensitivity to value changing in the conditions of dynamization of internal and external business parameters. The relevance of the researched topic is determined by the importance of establishing the factors influencing the change in company market capitalization based on the synthesis of approaches to company valuation. To obtain the results of the study, the following (...) methods were used: structural and logical analysis – to improve the process approach to company valuation in the context of determining the impact of its change on market capitalization; discounted cash flow method (DCF-model) – to determine the value of the enterprise based on the income approach; comparable companies method – to determine the value of the company on the basis of a market approach; factor analysis method – to assess the impact of changes in value on company market capitalization; generalization and logical analysis – in conclusions building. The results of critical analysis of publications of domestic and foreign scientists on the application of company valuation methods identified the need of improvement the process approach to company valuation in the context of determining the impact of its change on the company market capitalization. To adequately assess company value, the use of a synthesis of income and market approaches is proposed. The implementation of the DCF-model and comparable companies valuation method while valuation of Private Joint-Stock Company “SKF Ukraine” allowed to establish that the greatest impact on the target metric (company market capitalization) has an average industry multiplier EV/EBITDA, terminal growth rate and weighted average cost of capital – 5.9 %, 3.2% and 2.7% respectively. The practical value of the results of the study is determined by the importance of forming a full analytical basis for establishing the attractiveness of the performance of joint-stock companies in the market and consolidating management decisionsin order to increase market capitalization. (shrink)

(...) However, whether we chose a weak or strong approximation, the set would not make any sense at all, if (once more) this choice would not be justified in either temporal or spatial sense or given the context of possible applicability of the set in different circumstances. This would obviously represent a dualism in itself as we would (for instance) posit and apply a full identity-equality-equivalence of x and y when applying Newtonian physics to certain observations we make (it would (...) be the case of neural correlates), and we would posit and apply a non - identity-equality-equivalence of x and y when applying Quantum mechanics to other observations. Following this dualism in and of theories, the same sate would need to be slightly modified: U2:(x~y)∪(x≈y); U3:(x~y)∩(x≈y); U4a:(x~y)⊆(x≈y) vs. U4b:(x~y)⊇(x≈y). (shrink)

Quantum information is discussed as the universal substance of the world. It is interpreted as that generalization of classical information, which includes both finite and transfinite ordinal numbers. On the other hand, any wave function and thus any state of any quantum system is just one value of quantum information. Information and its generalization as quantum information are considered as quantities of elementary choices. Their units are correspondingly a bit and a qubit. The course of time is what generates choices (...) by itself, thus quantum information and any item in the world in final analysis. The course of time generates necessarily choices so: The future is absolutely unorderable in principle while the past is always well-ordered and thus unchangeable. The present as the mediation between them needs the well-ordered theorem equivalent to the axiom of choice. The latter guarantees the choice even among the elements of an infinite set, which is the case of quantum information. The concrete and abstract objects share information as their common base, which is quantum as to the formers and classical as to the latters. The general quantities of matter in physics, mass and energy can be considered as particular cases of quantum information. The link between choice and abstraction in set theory allows of “Hume’s principle” to be interpreted in terms of quantum mechanics as equivalence of “many” and “much” underlying quantum information. Quantum information as the universal substance of the world calls for the unity of physics and mathematics rather than that of the concrete and abstract objects and thus for a form of quantum neo-Pythagoreanism in final analysis. (shrink)

Logic played an important role in Wittgenstein’s work over the entire period of his philosophizing, from both the point of view of the philosopher of logic and that of the logician. Besides logical analysis, there is another kind of logical activity that characterizes Wittgenstein’s philosophical work after a certain point during his experience as a soldier and, later, as an officer in the First World War – if not earlier. This other kind of logical activity has (...) to do with what appears to be the literary form of Wittgenstein’s philosophical prose, and it is likely to be seen as the most modernist feature of his preoccupation with logic. (shrink)

Information-based epistemology maintains that ‘being informed’ is an independent cognitive state that cannot be reduced to knowledge or to belief, and the modal logic KTB has been proposed as a model. But what distinguishes the KTB analysis of ‘being informed’, the Brouwersche schema (B), is precisely its downfall, for no logic of information should include (B) and, more generally, no epistemic logic should include (B), either.

This article discusses the logical form of action sentences with particular attention to the role of adverbial modification, reviewing and extending the event analysis of action sentences.

In some recent works, Crupi and Iacona have outlined an analysis of ‘if’ based on Chrysippus’ idea that a conditional holds whenever the negation of its consequent is incompatible with its antecedent. This paper presents a sound and complete system of conditional logic that accommodates their analysis. The soundness and completeness proofs that will be provided rely on a general method elaborated by Raidl, which applies to a wide range of systems of conditional logic.

Conceptual engineers have made hay over the differences of their metaphilosophy from those of conceptual analysts. In this article, I argue that the differences are not as great as conceptual engineers have, perhaps rhetorically, made them seem. That is, conceptual analysts asking ‘What is X?’ questions can do much the same work that conceptual engineers can do with ‘What is X for?’ questions, at least if conceptual analysts self-understand their activity as a revisionary enterprise. I show this with a study (...) of Russell's metaphilosophy, which was just such a revisionary conception of conceptual analysis. (shrink)

In this paper I argue that pluralism at the level of logical systems requires a certain monism at the meta-logical level, and so, in a sense, there cannot be pluralism all the way down. The adequate alternative logical systems bottom out in a shared basic meta-logic, and as such, logical pluralism is limited. I argue that the content of this basic meta-logic must include the analogue of logical rules Modus Ponens and Universal Instantiation. I show (...) this through a detailed analysis of the ‘adoption problem’, which manifests something special about MP and UI. It appears that MP and UI underwrite the very nature of a logical rule of inference, due to all rules of inference being conditional and universal in their structure. As such, all logical rules presuppose MP and UI, making MP and UI self-governing, basic, unadoptable, and required in the meta-logic for the adequacy of any logical system. (shrink)

This paper aims to analyze the relationship between applied social sciences and practical wisdom. Utilizing conceptual analysis methodology, it begins by defining application, action, and practice, then delves into the conceptual analysis of applied social sciences and practical wisdom. The concept of phronesis in Aristotle's philosophy and practical wisdom in Muslim philosophers are studied and analyzed. By examining different definitions of practical wisdom among Muslim scholars and comparing their views with those of Aristotle, the paper evaluates their perspectives. (...) Subsequently, it focuses on exploring the relationship between applied social sciences and practical wisdom, analyzing their points of divergence and convergence. Considering the inherent nature of applied social sciences as technological and practical, contrasted with the virtue-based nature of practical wisdom, the paper raises the question of whether phronesis can logically benefit from pure applied social sciences as theoretical wisdom to guide individuals towards virtuous action. It also questions whether this scenario could be considered a form of applied social sciences. (shrink)

In ancient philosophy, there is no discipline called “logic” in the contemporary sense of “the study of formally valid arguments.” Rather, once a subfield of philosophy comes to be called “logic,” namely in Hellenistic philosophy, the field includes (among other things) epistemology, normative epistemology, philosophy of language, the theory of truth, and what we call logic today. This entry aims to examine ancient theorizing that makes contact with the contemporary conception. Thus, we will here emphasize the theories of the “syllogism” (...) in the Aristotelian and Stoic traditions. However, because the context in which these theories were developed and discussed were deeply epistemological in nature, we will also include references to the areas of epistemological theorizing that bear directly on theories of the syllogism, particularly concerning “demonstration.” Similarly, we will include literature that discusses the principles governing logic and the components that make up arguments, which are topics that might now fall under the headings of philosophy of logic or non-classical logic. This includes discussions of problems and paradoxes that connect to contemporary logic and which historically spurred developments of logical method. For example, there is great interest among ancient philosophers in the question of whether all statements have truth-values. Relevant themes here include future contingents, paradoxes of vagueness, and semantic paradoxes like the liar. We also include discussion of the paradoxes of the infinite for similar reasons, since solutions have introduced sophisticated tools of logical analysis and there are a range of related, modern philosophical concerns about the application of some logical principles in infinite domains. Our criterion excludes, however, many of the themes that Hellenistic philosophers consider part of logic, in particular, it excludes epistemology and metaphysical questions about truth. Ancient philosophers do not write treatises “On Logic,” where the topic would be what today counts as logic. Instead, arguments and theories that count as “logic” by our criterion are found in a wide range of texts. For the most part, our entry follows chronology, tracing ancient logic from its beginnings to Late Antiquity. However, some themes are discussed in several eras of ancient logic; ancient logicians engage closely with each other’s views. Accordingly, relevant publications address several authors and periods in conjunction. These contributions are listed in three thematic sections at the end of our entry. (shrink)

The paper presents a new analysis of Hempel’s conditions of adequacy, differing from the one in Carnap. Hempel, so it is argued, felt the need for two concepts of confirmation: one aiming at true theories, and another aiming at informative theories. However, so the analysis continues, he also realized that these two concepts were conflicting, and so he gave up the concept of confirmation aiming at informative theories. It is then shown that one can have the cake and (...) eat it: There is a logic of confirmation that accounts for both of these two conflicting aspects. (shrink)

The Bounds of Logic presents a new philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying modern Tarskian logic and inspired by mathematical and linguistic development. Extracting central philosophical ideas from Tarski’s early work in semantics, Sher questions whether these are fully realized by the standard first-order system. The answer lays the foundation for a new, broader conception of logic. By generally characterizing logical terms, Sher establishes a fundamental result in (...) semantics. Her development of the notion of logicality for quantifiers and her work on branching are of great importance for linguistics. Sher outlines the boundaries of the new logic and points out some of the philosophical ramifications of the new view of logic for such issues as the logicist thesis, ontological commitment, the role of mathematics in logic, and the metaphysical underpinning of logic. She proposes a constructive definition of logical terms, reexamines and extends the notion of branching quantification, and discusses various linguistic issues and applications. (shrink)

Logical monism is the view that there is ‘One True Logic’. This is the default position, against which pluralists react. If there were not ‘One True Logic’, it is hard to see how there could be one true theory of anything. A theory is closed under a logic! But what is logical monism? In this article, I consider semantic, logical, modal, scientific, and metaphysical proposals. I argue that, on no ‘factualist’ analysis (according to which ‘there is (...) One True Logic’ expresses a factual claim, rather than an attitude like approval), does the doctrine have both metaphysical and methodological import. Metaphysically, logics abound. Methodologically, what to infer from what is not settled by the facts, even the normative ones. I conclude that the only interesting sense in which there could be One True Logic is noncognitive. The same may be true of monism about normative areas, like moral, epistemic, and prudential ones, generally. (shrink)

There exists a relationship between logic and world-views. Why are there different worldviews, even of the same subject-matter? Why would two different persons analyse a particular subject-matter and come-up with different results of the analysis In attempting to answer the aforementioned posers, some scholars have maintained that it is only normal and expected that two different persons analysing the same subject-matter should come-up with different analysis-results of the subject-matter. This class of scholars hold this view because, as they (...) maintain, each "tribe", as it were, is naturally endowed by nature with its unique and peculiar logic with which it grapples with its own idiosyncratic issues confronting it. Therefore, the logic with which "A" grapples with a particular subject-matter is essentially unique to "A" and different from the logic with which "B" confronts the same subject-matter. It is because of the use of these unique and subjective "logics", the reasoning goes, that the end-results of the analyses of the same subjectmatter would usually, if not necessarily, be different. The thesis of this paper, however, is that logic qua logic, cannot be tribalised, much less manufactured to suit different peoples from different tribes. Logic is the given tools with which wo/man grapples with the realities that confront and surround her/him. The tribalization and/or manufacture of "logics" is an unwholesome venture, and an unholy exercise which carries with it massive and catastrophic consequences identified within this work. (shrink)

It has been noticed by several authors that the colloquial understanding of anonymity as mere unknown-ness is insufficient. This common-sense notion of anonymity does not recognize the role of the goal for which the anonymity is sought. Starting with the distinction between the intentional and unintentional anonymity (which are usually taken to be the same) and the general concept of the non-coordinatability of traits, we offer a logical analysis of anonymity and identification (understood as de-anonymization). In our enquiry, (...) we focus on the intentional aspect of anonymity and develop a metaphor of “anonymity game” between “perpetrator” and “detective”. Beginning from common-sense intuitions, we provide a formalized, critical notion of anonymity. (shrink)

Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any advantages when dealing with the (...) so-called paradoxes of higher-order vagueness. We offer a proposal that makes strides on both issues. We argue that the intuitionist’s characteristic rejection of any third alethic value alongside true and false is best elaborated by taking the normal modal system S4M to be the sentential logic of the operator ‘it is clearly the case that’. S4M opens the way to an account of higher-order vagueness which avoids the paradoxes that have been thought to infect the notion. S4M is one of the modal counterparts of the intuitionistic sentential calculus and we use this fact to explain why IPC is the correct sentential logic to use when reasoning with vague statements. We also show that our key results go through in an intuitionistic version of S4M. Finally, we deploy our analysis to reply to Timothy Williamson’s objections to intuitionistic treatments of vagueness. (shrink)

This article provides an analysis of Johannes Clauberg’s intentions in writing his Logica vetus et nova (1654, 1658). Announced before his adherence to Cartesianism, his Logica was eventually developed in order to provide Cartesian philosophy with a Scholastic form, embodying a complete methodology for the academic disciplines based on Descartes’ rules and a medicina mentis against philosophical prejudices. However, this was not its only function: thanks to the rules for the interpretation of philosophical texts it encompassed, Clauberg’s Logica was (...) meant to provide a general hermeneutics designed to put an end to the quarrels raised by the dissemination of Cartesianism. Such quarrels, according to Clauberg, were caused by the misinterpretation of Descartes’ texts in Revius’ Methodi cartesianae consideratio theologica (1648) and Statera philosophiae cartesianae (1650) and in Lentulus’ Nova Renati Descartes sapientia (1651), which criticized the apparent lack of a logical theory in Descartes’ philosophy and its supposed inconsistencies. Clauberg answers their criticisms by giving a clear account of Descartes’ logical theory and by undermining the interpretative criteria they assumed, in light of a general theory of error. Polemics over Cartesian philosophy, in this way, favored the development of a comprehensive Cartesian methodology for academic disciplines and of the first hermeneutics for philosophical texts. (shrink)

Meaning without Analyticity draws upon the author’s essays and articles, over a period of 20 years, focused on language, logic and meaning. The book explores the prospect of a non-behavioristic theory of cognitive meaning which rejects the analytic-synthetic distinction, Quinean behaviorism, and the logical and social-intellectual excesses of extreme holism. Cast in clear, perspicuous language and oriented to scientific discussions, this book takes up the challenges of philosophical communication and evaluation implicit in the recent revival of the pragmatist tradition—especially (...) those arising from its relation to prior American analytic thought. This volume continues the work of Callaway’s 1993 book, Context for Meaning and Analysis, building on the “turn toward pragmatism.” . (shrink)

The verifiability principle was the characteristic claim of a group of thinkers who called themselves the Vienna Circle and who formed the philosophical movement now known as logical positivism. The verifiability principle is an empiricist criterion of meaning which declares that only statements that are verifiable by —i.e., logically deducible from— observational statements are cognitively meaningful. -/- This essay is a short introduction to the philosophical movement of logical positivism and its formulation of the verifiability principle. Its primary (...) aim is to provide students of philosophy with an accessible first overview of this philosophical movement. -/- After pointing out some aspects of the philosophical background of logical positivism (section 1), I will comment on the reasoning that lead these authors to formulate the verifiability principle (section 2), and I will analyse the debate about how to understand observational language and how observational statements (the so-called ‘protocol statements’) are verified (section 3). I will also comment on the two main consequences of accepting the verifiability principle: the conception of philosophy as the task of logical analysis and the project of unified science (section 4), and I will explain the different views on ethical language defended by logical positivists (section 5). I will end this essay by identifying the main problems of the verifiability principle and I will explain the core ideas of Carnap’s confirmability criterion, which attempts to resolve these problems (section 6 and 7). (shrink)