Subjects -> PHILOSOPHY (Total: 762 journals)
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 AxiomathesJournal Prestige (SJR): 0.184 Number of Followers: 6      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1122-1151 - ISSN (Online) 1572-8390 Published by Springer-Verlag  [2469 journals]
• Muslim Philosophers on Affirmative Judgement with Negative Predicate

Abstract: Abstract According to Aristotelian logic, in categorical logic, there are three kinds of judgements (qaḍīyya): affirmative, negative, and metathetic (ma‘dūla). Khūnajī, a famous Muslim logician in the 13th century, introduces a different judgement (or statement) entitled “affirmative judgement with the negative predicate” (mūjiba al-sāliba al-maḥmūl; henceforth, ANP judgement). Although in the Arabic language, formally, ANP judgement is similar to definite negative (sāliba muḥaṣṣala) and also metathetic judgements, the way of its construction is different from both of them and its truth conditions are different from metathetic ones. From a modern logic viewpoint, ANP may indicate equality judgement; however, attributing it to Muslim logicians is questionable, although some of their wordings may implicitly show it. According to Ḥāʾirī, an Iranian contemporary philosopher and logician, the new judgement is supposed to solve some problems, especially logical explanation of the division of modalities into necessity, impossibility, and contingency (imkān khāṣṣ). However, Ṭabāṭabāʾī, another Iranian contemporary philosopher, disagrees with Ḥāʾirī and regards ANP judgement the same as an affirmative metathetic one. In this paper, while examining Ṭabāṭabāʾī’s and Ḥāʾirī’s reasons, by using some insights into modern logic, I will try to strengthen Ṭabāṭabāʾī’s views, although it may be confronted with some questions or deficiencies.
PubDate: 2022-08-01

• Undeformable Bodies that are Not Rigid Bodies: A Philosophical Journey

Abstract: Abstract There is broad consensus (both scientific and philosophical) as to what a rigid body is in classical mechanics. The idea is that a rigid body is an undeformable body (in such a way that all undeformable bodies are rigid bodies). In this paper I show that, if this identification is accepted, there are therefore rigid bodies which are unstable. Instability here means that the evolution of certain rigid bodies, even when isolated from all external influence, may be such that their identity is not preserved over time. The result is followed by analyzing supertasks that are possible in infinite systems of rigid bodies. I propose that, if we wish to preserve our original intuitions regarding the necessary stability of rigid bodies, then the concept of rigid body must be clearly distinguished from that of undeformable body. I therefore put forward a new definition of rigid body. Only the concept of undeformable body is holistic (every connected part of an undeformable body is not always an undeformable body) and every connected part of a rigid body in this new sense is always a rigid body in this new sense. Finally, I briefly discuss the connection between this conceptual distinction and the dimensionality of space, thereby enabling it to be supported from a new and interesting perspective.
PubDate: 2022-08-01

• Motivating Emotions: Emotionism and the Internalist Connection

Abstract: Abstract I outline a theory of moral motivation which is compatible with the metaphysical claims of strong emotionism—a sentimentalist account of morality first outlined by Jesse Prinz (The emotional construction of morals, Oxford University Press, Oxford, 2007) and supported by myself (Bartlett in Axiomathes, 2020. https://doi.org/10.1007/s10516-020-09524-5) which construes moral concepts and properties as a subset of emotion-dispositional properties. Given these claims, it follows that sincere moral judgements are necessarily motivating in virtue of their emotional constitution. I defend an indefeasible version of judgement motivational internalism which takes into consideration both positively and negatively valenced affective states and how they promote both approach and avoidance motivation, respectively. On this view, in making sincere moral judgements agents are antecedently motivated by standing Desires to avoid or approach the stimuli picked out by their judgements. I also defend internalism against the objections from defeating circumstances and amoralists. As regards the former, I claim that the tendency of philosophers to frame the motivation debate in terms of positive moral judgements makes the argument from defeating circumstances appear more plausible than it is; as regards the latter, I claim the amoralist argument only has force if it is empirically well supported and that psychological data has hitherto been unconvincing.
PubDate: 2022-08-01

• Neyman-Pearson Hypothesis Testing, Epistemic Reliability and Pragmatic

Abstract: Abstract We show that if among the tested hypotheses the number of true hypotheses is not equal to the number of false hypotheses, then Neyman-Pearson theory of testing hypotheses does not warrant minimal epistemic reliability (the feature of driving to true conclusions more often than to false ones). We also argue that N-P does not protect from the possible negative effects of the pragmatic value-laden unequal setting of error probabilities on N-P’s epistemic reliability. Most importantly, we argue that in the case of a negative impact no methodological adjustment is available to neutralize it, so in such cases the discussed pragmatic-value-ladenness of N-P inevitably compromises the goal of attaining truth.
PubDate: 2022-08-01

• Crazy Truth-Teller–Liar Puzzles

Abstract: Abstract In this manuscript, we define and discuss a new type of logical puzzles. These puzzles are based on the simplest truth-teller and liar puzzles. Graphs are used to represent graphically the puzzles. (The solution of) these logical puzzles contain three types of people. Strong Truth-tellers who can say only true statements, Strong Liars who can make only false statements and Weak Crazy people who must make at least one self-contradicting statement if he/she says anything. Self-contradicting statements are related to the Liar paradox, such that, there is no Truth-teller or a Liar could say “I am a Liar”. In any good puzzle there is a unique solution, while the puzzle is clear if only the people of the puzzle and their statements are given to solve the puzzle. It is well-known that there is no good and clear SS-puzzle (Strong Truth-teller-Strong Liar puzzle). However, in this paper, we show that there are clear and good SSW-puzzles. Characteristics of the newly investigated type of people, the ‘Weak Crazy’ people, has also been studied. Some statistical results about the new type of puzzles and a comparison with other types of puzzles are also shown: the number of solvable and also the number of good puzzles is much larger than in the previously known SS-puzzles.
PubDate: 2022-08-01

• Is so-called Phenomenal Intentionality Real Intentionality'

Abstract: Abstract This paper addresses the title question and provides an argument for the conclusion that so-called phenomenal intentionality, in both its relational and non-relational construals, cannot be identified with intentionality meant as the property for a mental state to be about something. A main premise of the argument presented in support of that conclusion is that a necessary requirement for a property to be identified with intentionality is that it satisfy the features taken to be definitory of it, namely: the possible non-existence of the intentional object (the fact that an intentional state may be directed towards something that does not exist) and aspectuality (the fact that what is intended is always intended in some way, under some specific aspect, from a particular perspective). By taking this premise on board, I attempt to show that phenomenal intentionality cannot be identified with intentionality because, appearances notwithstanding, it ultimately satisfies neither of the two above mentioned features.
PubDate: 2022-08-01

• Mathesis Universalis and Husserl’s Phenomenology

Abstract: Abstract The paper’s central theme is the link between phenomenology and the notion of the mathesis universalis, a link articulated by Husserl in the third volume of the Ideas: “My way to phenomenology was essentially determined by the mathesis universalis (Bolzano did not see anything of this).” The paper suggests three interpretations of the phenomenology—mathesis universalis nexus: the first is related to the development of Husserl’s conception of the foundations of arithmetic; the second is based on the role of the theory of manifolds in Husserl’s Logical Investigations; and the third reflects the importance of the distinction between “generalization” and “formalization” for phenomenology. After examining these interpretations, the paper explores which is most helpful for understanding why Husserl distanced himself from Bolzano, arguing that the third interpretation provides the most edifying answer.
PubDate: 2022-08-01

• Husserl’s Arguments for Psychologism

Abstract: Abstract The question of the psychologism of the theory of number developed by Husserl in his Philosophy of Arithmetic has long been debated, but it cannot be considered fully resolved. In this paper, I address the issue from a new point of view. My claim is that in the Philosophy of Arithmetic, Husserl made, albeit indirectly, a series of arguments that are worth reconstructing and clarifying since they are useful in shedding some light on the psychologism issue. More specifically, I maintain that the clarification of these arguments, along with other arguments that Husserl presented against alternative theories of number as well as with some contemporary distinctions concerning the notion of ontological dependence, allows us to determine that Husserl’s theory of number is psychologistic in a minimal and precise sense: it entails a generic ontological dependence of numbers upon the mind.
PubDate: 2022-08-01

• How Do You Apply Mathematics'

Abstract: Abstract As far as disputes in the philosophy of pure mathematics goes, these are usually between classical mathematics, intuitionist mathematics, paraconsistent mathematics, and so on. My own view is that of a mathematical pluralist: all these different kinds of mathematics are equally legitimate. Applied mathematics is a different matter. In this, a piece of pure mathematics is applied in an empirical area, such as physics, biology, or economics. There can then certainly be a disputes about what the correct pure mathematics to apply is. Such disputes may be settled by the standard criteria of scientific theory selection (adequacy of empirical predications, simplicity, etc.) But what, exactly is it to apply a piece of pure mathematics' How is mathematics applied' By and large, philosophers of mathematics have cared more about pure mathematics than applied mathematics, and not a lot of thought has gone into this question. In this paper I will address the issue and some of its implications.
PubDate: 2022-07-20

• On the Epistemological Relevance of Social Power and Justice in
Mathematics

Abstract: Abstract In this paper we argue that questions about which mathematical ideas mathematicians are exposed to and choose to pay attention to are epistemologically relevant and entangled with power dynamics and social justice concerns. There is a considerable body of literature that discusses the dissemination and uptake of ideas as social justice issues. We argue that these insights are also relevant for the epistemology of mathematics. We make this visible by a journalistic exploration of relevant cases and embed our insights into the larger question how mathematical ideas are taken up in mathematical practices. We argue that epistemologies of mathematics ought to account for questions of exposure to and choice of attention to mathematical ideas, and remark on the political relevance of such epistemologies.
PubDate: 2022-07-16

• How’s Everything'

Abstract: Abstract After a critical presentation of the debate between absolutists and relativists regarding generality where I show that the debate is framed in a way that is bound to be harmful to the relativist’s position, I examine critically one of the customary arguments advanced against the relativist: the expressibility objection (according to which the relativist would be logically unable to express her own position). I then propose a radical way out of this debate-usually centered on semantic paradoxes-by arguing that it rests on an unintelligible notion of “object”. I finally introduce a useful distinction between omnis and totus to elucidate the notions in play.
PubDate: 2022-07-16

• ‘None Enters Here Unless He is a Geometer’: Simone Weil on the
Immorality of Algebra

Abstract: Abstract The French philosopher Simone Weil (1909-1943) thought of geometry and algebra not as complementary modes of mathematical investigation, but rather as constituting morally opposed approaches: whereas geometry is the sine qua non of inquiry leading from ruthless passion to temperate perception, in accord with the human condition, algebra leads in the reverse direction, to excess and oppression. We explore the constituents of this argument, with their roots in classical Greek thought, and also how Simone Weil came to qualify it following her exchange with her brother, the mathematician André Weil.
PubDate: 2022-07-13

• Standard Formalization

Abstract: Abstract A standard formalization of a scientific theory is a system of axioms for that theory in a first-order language (possibly many-sorted; possibly with the membership primitive $$\in$$ ). Suppes (in: Carvallo M (ed) Nature, cognition and system II. Kluwer, Dordrecht, 1992) expressed skepticism about whether there is a “simple or elegant method” for presenting mathematicized scientific theories in such a standard formalization, because they “assume a great deal of mathematics as part of their substructure”. The major difficulties amount to these. First, as the theories of interest are mathematicized, one must specify the underlying applied mathematics base theory, which the physical axioms live on top of. Second, such theories are typically geometric, concerning quantities or trajectories in space/time: so, one must specify the underlying physical geometry. Third, the differential equations involved generally refer to coordinate representations of these physical quantities with respect to some implicit coordinate chart, not to the original quantities. These issues may be resolved. Once this is done, constructing standard formalizations is not so difficult—at least for the theories where the mathematics has been worked out rigorously. Here we give what may be claimed to be a simple and elegant means of doing that. This is for mathematicized scientific theories comprising differential equations for $$\mathbb{R}$$ -valued quantities Q (that is, scalar fields), defined on n (“spatial” or “temporal”) dimensions, taken to be isomorphic to the usual Euclidean space $$\mathbb{R}^n$$ . For illustration, I give standard (in a sense, “text-book”) formalizations: for the simple harmonic oscillator equation in one-dimension and for the Laplace equation in two dimensions.
PubDate: 2022-07-08

• On Thought Experiments, Theology, and Mathematical Platonism

Abstract: Abstract In our contribution to this special issue on thought experiments and mathematics, we aim to insert theology into the conversation. There is a very long tradition of substantial inquiries into the relationship between theology and mathematics. Platonism has been provoking a consolidation of that tradition to some extent in recent decades. Accordingly, in this paper we look at James R. Brown’s Platonic account of thought experiments. Ultimately, we offer an analysis of some of the merits and perils inherent in framing the use of thought experiments in mathematics and theology in terms of Platonism.
PubDate: 2022-07-06

• Contextual Causal Dependence and Causal Contrastivism

Abstract: Abstract This work presents a defense of causal contrastivism based on causal contexualism. As argued, our proposal on causal contextualism is compatible with both causal contrastivism and causal binarism, including explanations of why and in which sense secondary counterfactuals are relevant.
PubDate: 2022-06-29

• Extended Cognition and Constructive Empiricism

Abstract: Abstract According to constructive empiricists, accepting a scientific theory involves belief only that it is true of the observable world, where observability is defined in terms of what is detectable by the unaided senses. On this view, scientific instruments are machines that generate new observable data, but this data need not be interpreted as providing access to a realm of phenomena beyond what is revealed by the senses. A recent challenge to the constructive empiricist account of instruments appeals to the extended mind thesis, according to which cognitive processes are sometimes constituted not just by brain activity, but can extend into the rest of the body and the surrounding environment. If this is right, scientific instruments may, in the right circumstances, literally become part of our perceptual processes. In this article, I examine this extended perception argument, and I find that it fails for the vast majority of scientific instruments. Even if the extended mind thesis is accepted, the constructive empiricist can draw a line between observables and unobservables that makes very few concessions to the realist.
PubDate: 2022-06-25

• Proof, Semiotics, and the Computer: On the Relevance and Limitation of
Thought Experiment in Mathematics

Abstract: Abstract This contribution defends two claims. The first is about why thought experiments are so relevant and powerful in mathematics. Heuristics and proof are not strictly and, therefore, the relevance of thought experiments is not contained to heuristics. The main argument is based on a semiotic analysis of how mathematics works with signs. Seen in this way, formal symbols do not eliminate thought experiments (replacing them by something rigorous), but rather provide a new stage for them. The formal world resembles the empirical world in that it calls for exploration and offers surprises. This presents a major reason why thought experiments occur both in empirical sciences and in mathematics. The second claim is about a looming aporia that signals the limitation of thought experiments. This aporia arises when mathematical arguments cease to be fully accessible, thus violating a precondition for experimenting in thought. The contribution focuses on the work of Vladimir Voevodsky (1966–2017, Fields medalist in 2002) who argued that even very pure branches of mathematics cannot avoid inaccessibility of proof. Furthermore, he suggested that computer verification is a feasible path forward, but only if proof is not modeled in terms of formal logic.
PubDate: 2022-06-20

• Correction to: Standard and Non‑standard Suppositions and
Presuppositions

Abstract: A correction to this paper has been published: https://doi.org/10.1007/s10516-021-09562-7
PubDate: 2022-06-01
DOI: 10.1007/s10516-021-09562-7

• A Taxonomy of Noncanonical Uses of Interrogatives

Abstract: Abstract The aims of this paper are (i) to provide a detailed taxonomy of noncanonical uses of interrogative sentences, i.e. when they are used not to ask a question but to convey some information, or to ask a question albeit not that expressed by the interrogative sentence exploited in the act, (ii) to identify properties of circumstances where an interrogative sentence is being used in this way, and (iii) to propose some maxims that govern the rational use of questions. Four main categories of such cases are presented, and a few further subclasses are differentiated. I show how these types are interrelated, and what logical features differentiate them. I also propose a hypothesis for when an interrogative sentence is not being used in its primary mode. Studies on circumstances in which questions are used in other ways can shed light on maxims that govern asking and questioning in a rational conversation; therefore, some possible maxims of this kind are proposed.
PubDate: 2022-06-01
DOI: 10.1007/s10516-021-09536-9

• Meaning Relations, Syntax, and Understanding

Abstract: Abstract This paper revisits the conception of intelligence and understanding as embodied in the Turing Test. It argues that a simple system of meaning relations drawn from words/lexical items in a natural language and framed in terms of syntax-free relations in linguistic texts can help ground linguistic inferences in a manner that can be taken to be 'understanding' in a mechanized system. Understanding in this case is a matter of running through the relevant inferences meaning relations allow for, and some of these inferences are plain deductions and some can serve to act as abductions. Understanding in terms of meaning relations also supervenes on linguistic syntax because such understanding cannot be simply reduced to syntactic relations. The current approach to meaning and understanding thus shows that this is one way, if not the only way, of (re)framing Alan Turing's original insight into the nature of thinking in computing systems.
PubDate: 2022-06-01
DOI: 10.1007/s10516-021-09534-x

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