Axiomathes

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Article
We introduce and study some variants of a notion of canonical set theoretical truth. By this, we mean truth in a transitive proper class model M of ZFC that is uniquely characterized by some ∈\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\in$$\end{document}-formula. We show that there are interesting statements that hold in all such models, but do not follow from ZFC, such as the ground model axiom and the nonexistence of measurable cardinals. We also study a related concept in which we only require M to be fixed up to elementary equivalence. We show that this theory-canonicity also goes beyond provability in ZFC, but it does not rule out measurable cardinals and it does not fix the size of the continuum.
 
Article
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.
 
Article
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.
 
Article
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.
 
The graph representation of the SS-puzzle, Example 2, with three people
Graph representation of the SSW-puzzle of Example 4
The two non-isomorphic digraphs that are represented by K3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_{3}$$\end{document} with broken edges in the underlying undirected graph
a An example of the graph of a good puzzle with the maximum number of arcs which is 18, where we have 9 broken arcs and 9 solid arcs. b An example of graph of a good puzzle with minimum number of edges equals 3, where there is also the minimum number of broken arcs appears which is 1
Article
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.
 
Article
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.
 
Article
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.
 
A system with infinite components. Initial state
A system with infinite components. Final state
Article
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.
 
Article
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.
 
Article
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.
 
Article
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.
 
Article
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.
 
Article
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.
 
Article
A \emph{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 $\in$). Patrick Suppes (\cite{sup92}) 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 \emph{mathematicized}, one must specify the underlying \emph{applied mathematics base theory}, which the physical axioms live on top of. Second, such theories are typically \emph{geometric}, concerning quantities or trajectories in space/time: so, one must specify the underlying \emph{physical geometry}. Third, the differential equations involved generally refer to \emph{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 $\R$-valued quantities $Q$ (that is, scalar fields), defined on $n$ (``spatial'' or ``temporal'') dimensions, taken to be isomorphic to the usual Euclidean space $\R^n$. 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.
 
Article
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.
 
Article
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.
 
Compound optical microscope
Atomic force microscope
Article
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.
 
Article
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.
 
Article
A correction to this paper has been published: https://doi.org/10.1007/s10516-021-09562-7
 
The rectangle paradox
Article
The notion of indivisibles and atoms arose in ancient Greece. The continuum—that is, the collection of points in a straight line segment, appeared to have paradoxical properties, arising from the ‘indivisibles’ that remain after a process of division has been carried out throughout the continuum. In the seventeenth century, Italian mathematicians were using new methods involving the notion of indivisibles, and the paradoxes of the continuum appeared in a new context. This cast doubt on the validity of the methods and the reliability of mathematical knowledge which had been regarded as established by the axiomatic method in geometry expounded by Aristotle’s younger contemporary Euclid. The teaching of indivisibles was banned within the Society of Jesus, the Jesuits. In England, indivisibles were used by the mathematician John Wallis, and there was an acrimonious and extended feud between Wallis and the philosopher Thomas Hobbes over legitimate methods of argument in mathematics. Notions of the infinitesimal were used by Isaac Newton and Gottfried Leibniz, and were attacked by Bishop Berkeley for the vagueness of the concept and the illegitimate reasoning applied to it. This article discusses aspects of these events with reference to the book Infinitesimal by Amir Alexander and to other sources. Also discussed are wider issues arising from Alexander’s book including: the changes in cultural sensibility associated with the growth of new mathematical and scientific knowledge in the seventeenth century, the changes in language concomitant with these changes, what constitutes valid methods of enquiry in various contexts, and the question of authoritarianism in knowledge. More general aims of this article are to widen the immediate mathematical and historical contexts in Alexander’s book, to bridge a gap in conversations between mathematics and the humanities, and to relate mathematical ideas to wider human and contemporary issues.
 
Article
In this paper, I argue that the distinction between standard and non-standard pragmatic implications, originally used to differentiate among types of conversational implicatures, applies to the family of contents—traditionally referred to as ‘presuppositions’—that exhibit projective behaviour. Following the scholars working within the Question Under Discussion model of communication, I distinguish between two types of projective implications: suppositions and presuppositions narrowly construed. Next, I identify two rules of appropriateness that govern the use of, respectively, supposition-triggering and presupposition-triggering expressions. Finally, I argue that the ostentatious violation of the rules in question gives rise to non-standard projective implications, whereas their observance results in standard suppositions and presuppositions; I also use the idea of discourse coherence to develop a sketchy account of the mechanisms underlying the functioning of non-standard projective implications.
 
Article
The morphological account of landscape aims to overcome the contrast between an objectivist/scientific account of space and the more qualitative/subjective account of place. It does so by actualizing the notion of landscape, which endows a materiality often overlooked in contemporary spatial theories. In this paper, I will discuss what has been called the ‘space-place conundrum’ by referring mostly to the human geography contemporary debate on space and place. In the following, I will retrieve Carl Sauer’s morphological conception of landscape as an alternative framework aimed at rephrasing both the concepts of space and place. Landscape must be freed from the cage of the aesthetic gaze so that it can be understood as a lived and dynamic complex of interacting forms that encompass the embodied subject. In the end, I will outline the main characteristics of a morphological conception of landscape, paving the way for further inquiries.
 
Article
In attempts to compare different distributions with regards to need, so-called "measures of need-based distributive justice" have emerged in recent years. Each of the proposed measures relies on a single dimension of need that is taken into account. This is shown to be problematic since humans experience different kinds of need that appear to be incommensurable. A strategy to deal with this problem is introduced by using multidimensional measures.
 
Article
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.
 
Article
The non-alethic systems N1 of da Costa and A of Grana are both paraconsistent and paracomplete. Based on them, a multi-agent doxastic logic NADK can be obtained by logical expansion. The soundness and completeness of NADK are proved and its special theorems are also presented. In this logic, the belief version of the laws of contradiction and excluded middle, as well as the principle of explosion are all invalid. Therefore, it may provide a reliable logical basis for any theory which has paraconsistent or paracomplete epistemic conflicts, such as true contradictions, true contrarieties, and belief paradoxes. We also explain in detail how a non-alethic doxastic logic provides a reliable logical basis for tolerating these three types of epistemic conflicts. The present paper is the deepening and development of system N1 and A.
 
Article
Some important and decisive observations allowed a widespread and almost unquestionable acceptance of the big bang cosmology, but we can admit and search other factors that have contributed and continue to contribute to the enormous acceptance and great popularity of this cosmological conception, not only inside but also outside of cosmology and even in numerous no scientific contexts. To find some of those factors, a case study was undertaken based on thematic analysis, an analytical tool which is based on the idea that the scientific activity, in addition to a theoretical and an experimental dimensions, has a third dimension with psychological and cultural elements called themata that strongly influence the construction of scientific theories and also their acceptance or rejection. This case study focused on the most important founding texts of big bang cosmology, namely articles and books of Alexandre Friedmann, Georges Lemaître, and George Gamow, covering three decades of important developments (1922–1952), and the founding texts of its great rival, the steady-state cosmology. This article presents a summary of the main results of this case study, which allowed to identify several themata with a very important role in the big bang cosmology: differentiation and unification (methodological themata); unity, creation, change, evolution, constancy (of mass/energy), simplicity, life cycle, circularity, and disorder (conceptual themata). All these themata form a methodological and conceptual matrix—with a triple dimension: historical, transversal/cultural, and psychological—that can help explain the acceptance and popularity of the big bang cosmology within and beyond its disciplinary boundaries.
 
Article
Many recently released Hollywood films feature superheroes like Superman, Ironman, the Hulk, Optimus Prime, and so on who possess amazing superpower and defeat supervillains with unassailable commitment to moral justice. Interestingly, different superheroes possess and exercise their superpower in very different fashions. What is more, this aspect of their difference is intimately related to an issue that is lately in intense debate among metaphysicians of powers and dispositions, the issue of the possibility of intrinsic interferers with dispositions. This paper will argue that a strong case can be made against this possibility when we give due weight to the commonsensical understanding of superheroes and their superpower. Whilst other arguments have been raised against the possibility of intrinsic interferers with dispositions in the latest literature, this will present further difficulties for those who accept it.
 
The syntactic tree of the sentence 'the waiter over there looks at my friend in fear and I do not know why'
The distinction between syntactic compositional structures and meaning relations (MR1…MR12): while MR7, MR8, MR5, MR2, MR1, MR9 can be derived in terms of relevant functions of syntactic composition, other MRs cannot
The preservation of truth via deductive inferences from more complex to less complex meaning relations
The inheritance of event structures, argument structures and qualia structures across types of meaning relations
Article
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.
 
Article
In this paper, I relate key features of Adolf Reinach’s abundant ontology of propositional states of affairs of his (1911) to Armstrong’s—or an Armstrongian—state of affairs ontology, with special regard to finding out how sparse or abundant the latter is with respect to negative states of affairs. After introducing the issue, I clarify the notion of a propositional state of affairs, paying special attention to the notion of abstract versus concrete. I show how Reinach’s states of affairs are propositional, and how they compare with Chisholm’s well-known propositional states of affairs. In the next section, I outline Reinach’s five roles for states of affairs and show that only one of them is relevant to Armstrongian state of affairs ontology. In the following section, I utilise this role to create a ranking of state of affairs ontologies according to how abundant (sparse) they are. It is, however, unclear which level Armstrongian state of affairs ontology is at, since it is unclear if, like Reinach’s ontology, it includes negative states of affairs. In the final section, I argue that the answer is a qualified ‘yes’, i.e. it does not occupy the sparsest level.
 
As later and later B-series times become from the future into the present and then into the past in the A-series, time goes on. This accords with experience
Earlier-to-later times become from the future (positive e) into the present (e around 0) and then into the past (negative e)
Article
There are long-standing questions about the Big Bang: What were its properties? Was there nothing before it? Was the universe always here? Many conceptual issues revolve around time. This paper gives a novel model based on McTaggart’s temporal distinction between the A-series (future-present-past) and B-series (earlier-times to later-times). These series are useful while situated in a Presentist and Fragmentalist account of quantum mechanics, one in which the consistency with the Special Relativity (in particular the relativity of simultaneity) will be made explicit (section 6). This allows us to make a fruitful distinction between two pertinent questions: what happens as we go to earlier times toward the Big Bang? And: what happens as we go further into the past toward the Big Bang?
 
Article
If we take the indexical, “I”, to be epistemologically identical across different contexts, as in, for example, it is the same “I” that at one moment observes, “I see a puddle of water on the floor”, and then, subsequently, exclaims, “I detect a leaking tap”, and, furthermore, we attribute not only self reference but self awareness in the use of the indexical, “I”, then a question arises as to how the “I” finds itself to be in reference to the speaker in one context and not another. We cannot look to the ingredients of the context that the “I” inhabits for the answer because, based upon the above assumptions, the identity, or character, of the “I” stands independently of the context of the speaker. The answer, I argue, requires both the admission of the unreality of space and time, as well as an explanation as to why we have a sense of the here and now despite space and time being unreal. To this end, I turn to the juxtaposition of Kant’s a priori forms of inner sense and outer sense to explain how the cognitive faculty arrives at a sense of time and place despite the declared unreality of time and space. To sustain this explanation in the face of the problem of localisation, I draw on the full implications of Kant’s transcendental idealism in which the properties of time and space are not only withdrawn from things as they exist externally to the mind but also from mental representations insofar as mental representations can be said to exist in themselves.
 
Practical disposition to accept ES, Næss replication study
Judgments of equivalence and difference for Q6–Q13
Article
There are many variants of deflationism about truth, but one of them, Paul Horwich’s minimalism, stands out because it accepts as axiomatic practical variants of the equivalence schema: 〈 p 〉 is true if and only if p . The equivalence schema is epistemologically fundamental. In this paper, I call upon empirical studies to show that practical variants of the equivalence schema are widely accepted by non-philosophers. While in the empirical data there is variation in how non-philosophers and philosophers talk about truth and how they judge that a proposition is true, a significant amount of data collected over the years reveal that the ordinary or folk view of truth is compatible with the epistemological fundamentality of alethic minimalism. This, I take it, suggests that people share in the same intuitions that form the bedrock of Horwich’s minimalism.
 
Article
The article discusses the enigmatic backtracking counterfactuals. It offers an explanation according to which in the case of the latter the negative time direction is due to their being abductive retrodictions, i.e. explanations of unreal effects by introducing possible causes while the conditions remain tacit or unexpressed. The counterfactual abductive retrodictions' backtracking time direction is in accordance with the postulating the positive time direction from cause to effect. Thus we demonstrate that in order to explain backtracking counterfactuals there is no need to consider the backtracking impact of the present on the past. Further, there is no need to violate natural laws or to have a special logic. What we need is to take into account the third parameter, i.e. a set of tacit or unexpressed additional propositions, as well as the principle of ceteris paribus as our background. When the power of logic is not overestimated, there is no need to change the direction of causality. And a correct analysis does not require any special logic. Last, but not least, we show, how to correctly make the abductive retrodiction by the contraposition of the deductive retrodiction. © 2018 Slovak Academy of Sciences - Inst of Philosophy. All Rights Reserved.
 
Article
I focus on the commonly shared view that Hume’s monetary theory is inconsistent. I review several attempts to solve the alleged inconsistency in Hume’s monetary theory, including the consensus interpretation according to which Hume was committed to the neutrality of money only in the long run, while he conceded that money can be non-neutral in the short run. Then, building on a monetary version of the logical fallacy of monotonic counterfactuals in the essay Of the Balance of Trade , I argue for the consistency of Hume’s theory of money by ascribing to Hume a distinction between money as collectively neutral and distributively non-neutral.
 
Article
The significance of Max Black’s indistinguishable spheres for the nature of particles in quantum mechanics is discussed, focusing in particular on the use of the idea of weak indiscernibility. It is argued that there can be four such Black spheres but that five are impossible. It follows from this that Black’s example cannot serve as a model for indistinguishability in physics. But Black’s discussion of his spheres gave rise to the idea of weak discernibility and it is argued that such predicates are unsatisfiable in the way intended. The underlying problem with weak discernibility spreads out to also undermine the whole notion that indistinguishability rests on a notion of the permutation invariance of particles. A better foundation is indicated.
 
Article
Seungbae Park argues that Bas van Fraassen’s rejection of inference to the best explanation (IBE) is problematic for his contextual theory of explanation because van Fraassen uses IBE to support the contextual theory. This paper provides a defense of van Fraassen’s views Park’s objections. I point out three weaknesses of Park’s objection against van Fraassen. First, van Fraassen may be perfectly content to accept the implications that Park claims to follow from his views. Second, even if van Fraassen rejects IBE he may still endorse particular arguments that instantiate IBE. Third, van Fraassen does not, in fact, use IBE to support his contextual theory.
 
Article
How can we acquire knowledge of metaphysical modality? How can someone come to know that he could have been elsewhere right now, or an accountant rather than a philosophy teacher, but could not have been a turnip? Jago proposes an account of a route to knowledge of the way things could have been and must be. He argues that we can move to knowledge of metaphysical modality from knowledge about essence. Curtis rejects Jago’s explanation. It cannot, he argues, explain our knowledge of de re necessity. We agree. But there is more to be said. To give an account of our knowledge of metaphysical necessity is part of the task Jago set himself. But another part is to give an account of the knowledge of the (non-actual) possibilities accorded to particular objects. And prior to both what is needed, and something Jago attempts to supply, is an account of how ordinary knowers can come to have knowledge of an individual’s essential properties. We argue that Jago’s accounts of both these additional matters are also unsatisfactory. This is important because the thought that our knowledge of metaphysical modality has its source in our knowledge of essence is currently an attractive one and Jago has set out very clearly what must be done to justify the thought. The flaws in his proposal thus indicate the work needed if the attractive thought is to be accepted.
 
Article
A debated issue in the mathematical foundations in at least the last two decades is whether one can plausibly argue for the merits of treating undecidable questions of mathematics, e.g., the Continuum Hypothesis (CH), by relying on the existence of a plurality of set-theoretical universes except for a single one, i.e., the well-known set-theoretical universe V associated with the cumulative hierarchy of sets. The multiverse approach has some varying versions of the general concept of multiverse yet my intention is to primarily address ontological multiversism as advocated, for instance, by Hamkins or Väätänen, precisely for the reason that they proclaim, to the one or the other extent, ontological preoccupations for the introduction of respective multiverse theories. Taking also into account Woodin’s and Steel’s multiverse versions, I take up an argumentation against multiversism, and in a certain sense against platonism in mathematical foundations, mainly on subjectively founded grounds, while keeping an eye on Clarke-Doane’s concern with Benacerraf’s challenge. I note that even though the paper is rather technically constructed in arguing against multiversism, the non-negligible philosophical part is influenced to a certain extent by a phenomenologically motivated view of the matter.
 
Article
It has been argued that Humean Supervenience (HS) is threatened by the existence of quantum entanglement relations. The most conservative strategy for defending HS is to add the problematic entanglement relations to the supervenience basis, alongside spatiotemporal relations. In this paper, I’m going to argue against this strategy by showing how certain particular cases of tripartite entanglement states – i.e. GHZ states – posit some crucial problems for this amended version of HS. Moreover, I will show that the principle of free recombination – which is strictly linked to HS – is severely undermined if we add entanglement relations to the supervenience basis. I conclude that the conservative move is very unappealing, and therefore the defender of HS should pursue other, more controversial, strategies (e.g. committing to the nomological interpretation of the wave function).
 
Article
There is a robust tendency within the contemporary feminist mainstream to argue against and ultimately reject the so-called ‘dualising or dualist philosophy’ (associated historically with the thoughts of Plato and Descartes, though from different perspectives) since it is the supportive paradigm background for any gender discrimination originated from (and it also admits of) the hegemonic sovereignty of masculinity over femininity. In this paper, having dived deeper into the feminist critical depiction of the logical binarist foundation on which the dualising philosophy is said to be well-grounded, I will proceed to portray and examine a sequence of doctrines that feminist philosophers have developed to shed light on the fact that the hegemonic sovereignty of masculinity over femininity has been theoretically initiated from the logical disjunction 'p or not p' (p v ~ p) to masculinity essentialism. Finally, I will end by pointing to a tension between underlying assumptions of the feminist sequentialist approach and what feminists themselves claim to adhere to as the highest ideal: non-naturalising gender differences.
 
Classes of states of things
Three kinds of sequences (based on NEM 4:127, 1897–8)
Conic sections in projective geometry (adapted from Matsko 2017)
Mapping a circle to a line (R 427:122[113], 1902)
Mapping portions of a circle to parallel lines
Article
Charles Sanders Peirce is best known as the founder of pragmatism, but the name that he preferred for his overall system of thought was “synechism” because the principle of continuity was its central thesis. He considered time to be the paradigmatic example and often wrote about its various aspects while discussing other topics. This essay draws from many of those widely scattered texts to formulate a distinctively Peircean philosophy of time, incorporating extensive quotations into a comprehensive and coherent synthesis. Time is not an existential subject with past, present, and future as its incompatible predicates, but rather a real law enabling things to possess contrary qualities at its different determinations, and Peirce identifies four classes of such states based on when and how they are realized. Because time is continuous, it is not composed of instants, and even the present is an indefinite lapse during which we are directly aware of constant change. The accomplished past is perpetually growing as the possibilities and conditional necessities of the future are actualized at the present, and the entire universe evolves from being utterly indeterminate toward being absolutely determinate. Nevertheless, time must return into itself even if events are limited to only a portion of it, a paradox that is resolved with the aid of projective geometry. Temporal synechism thus touches on a broad spectrum of philosophical issues including mathematics, phenomenology, logic, and metaphysics.
 
A Spectrum Case with two aspects. The aspects are based on the same dimension, but Aspect 1 constitutes a qualitatively new subvalue that outranks Aspect 2. For illustration, items are mapped from the (unsorted) left hand side to the relation domains on the right hand side, where items higher in the R-boxes are better than lower items
Multidimensional parity based on top-distance. Items a4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_4$$\end{document} and b2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_2$$\end{document} are on a par with respect to aspects 1 and 2, where the threshold δ=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta =1$$\end{document}. Also on a par are a1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_1$$\end{document} and b8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_8$$\end{document}, a1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_1$$\end{document} and b3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_3$$\end{document}, a1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_1$$\end{document} and b5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_5$$\end{document}, a4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_4$$\end{document} and b3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_3$$\end{document}, and so forth
Article
According to the mixed lexicographic/additive account of ‘better than’ and similar aggregative value comparatives like ‘healthier than’, values are multidimensional and different aspects of a value are aggregated into an overall assessment in a lexicographic way, based on an ordering of value aspects. It is argued that this theory can account for an acceptable definition of Chang’s notion of parity and that it also offers a solution to Temkin’s and Rachels’s Spectrum Cases without giving up the transitivity of overall betterness. Formal details and proofs are provided in an “Appendix”.
 
Article
One of the reasons for relativistic attitudes toward science is the impossibility of justifying scientists’ decisions in the face of alternative theories. According to this paper, an alternative theory can challenge scientific rationality only if the conditions of “methodological shortcomings of scientists” and the “existence of alternative theories” are met at a specific time. A commonly used technique to counter relativism is to try to supplement and equip scientists’ methodologies when confronted with alternative theories. However, this paper focuses on evaluating the possibility of “existence an alternative theory.” To this end, by referring to the different definitions of being alternative, we try to show that only “after the decision” and “the conversion of the scientific community” can a theory be considered justifiably “alternative.” Therefore, the relativistic claim is inconsistent because relativists must first accept the validity of scientists’ decisions to attribute being alternative to a theory. In this work, we provide evidence for our claim using a historical example. We also defend conservatism as a corollary of our discussion.
 
Article
This work draws an analogical defence of strong emotionism—the metaethical claim that moral properties and concepts consist in the propensity of actions to elicit emotional responses from divergent emotional perspectives. I offer a theory that is in line with that of Prinz (The emotional construction of morals. Oxford University Press, Oxford, 2007). I build an analogy between moral properties and what I call emotion-dispositional properties. These properties are picked out by predicates such as ‘annoying’, ‘frightening’ or ‘deplorable’ and appear to be uncontroversial and frequent cases of attribution error—the attributing of subjective emotional states as mind-independent properties. I present a linguistic analysis supporting the claim that moral properties and their related concepts are reducible to a subset of emotiondispositional properties and concepts. This is grounded in the observation that utterances featuring moral predicates function linguistically and conceptually in analogous ways to emotion-dispositional predicates. It follows from this view that asserted moral utterances are truth-apt relative to ethical communities, but that speakers misconceive the extensions of predicates. I show how the framework of Cognitive Linguistics allows us to explain this error. Further analysis of moral and non-moral utterances exposes the deeper conceptual schemas structuring language through cognitive construal processes. An understanding of these processes, coupled with an emotionist elucidation of moral properties and concepts, makes the attribution error an expected upshot of the emotionist thesis, rather than an uncomfortable consequence. See the full article here: https://rdcu.be/b8F08
 
Article
Strict finitism is a minority view in the philosophy of mathematics. In this paper, we develop a strict finite axiomatic system for geometric constructions in which only constructions that are executable by simple tools in a small number of steps are permitted. We aim to demonstrate that as far as the applications of synthetic geometry to real-world constructions are concerned, there are viable strict finite alternatives to classical geometry where by one can prove analogs to fundamental results in classical geometry. We consider this as one of many early steps investigating the extent to which strict finite foundations can be developed for the application of mathematics to the real-world.
 
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This paper is an attempt to construct a bridge between dialectics and mathematics, to interpret main dialectical laws in terms of the theory of dynamical systems. Negation is interpreted as a discrete shift along the dynamical system trajectory. For conservative systems, double negation law is trivial as in formal logic; for non-conservative systems, this law means slow evolution of the system under consideration. There are also mathematical interpretations for the transition from quantity to quality and interconnection between opposites.
 
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The Minimal Theory of Causation, presented in Graßhoff and May, 2001, aspires to be a version of a regularity analysis of causation able to correctly predict our causal intuitions. In my article, I will argue that it is unsuccessful in this respect. The second aim of the paper will be to defend Hitchcock’s proposal concerning divisions of causal relations (presented in Hitchcock, 2001) against criticism made, in Jakob, 2006 on the basis of the Minimal Theory of Causation.
 
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The supporters of Indeterminate Futurism Theory [IFT] suggest three different reasons for preferring their view over Growing Block Theory [GBT]. If compared to GBT, IFT offers a better account for the open future problem, our cognitive attitudes towards future contingents, and how open the future is. Michael Tze-Sung Longenecker disagrees with them, stating that the advantages suggested by IFT's supporters are not advantages at all and/or can be accommodated by GBT. This means that, if he is right, there is no reason to prefer IFT over GBT. However, if we prove the feasibility of (at least) one of the supposed advantages of IFT, Longenecker should admit that the game between IFT and GBT could still be open. Here, we focus on our cognitive attitudes towards future, with the aim of showing that the explanation of such attitudes may be a string to IFT's bow, as Ross Cameron suggests.
 
Article
Two opposing uses of the term ‘Scientific Ontology’ reflect attitudes towards the relation between (empirical) science and philosophical ontology. On the one side we can try to understand the broader picture by looking at the empirical details. On the other side we can try to find overarching principles that explain our observations. I am deeply aware of the history of this subject but—as we all know—history repeats itself. Perhaps it is time now for, actually, deduction to take more place in science. Perhaps—which of course is my own belief—we have reached the end of the road of so much depending on empirical observations. The natural sciences have reached beyond what is possible to empirically detect. My own research is an attempt to redefine our ontological starting point and to really test if the world only is physical. In this Reply I put Tambassi’s reply in the explicit context of my definition of scientific ontology. The outcome is that scientific ontology cannot settle the debate in the geographical sciences as to whether the geographical world is mind-dependent or not, but that the geographical universe, in that case, as a universe, belongs to the domain of scientific ontology.
 
Top-cited authors
Roberto Poli
  • Università degli Studi di Trento
Carita Paradis
  • Lund University
Mark Bickhard
  • Lehigh University
George Georgescu
  • University of Bucharest
Mark Reybrouck
  • KU Leuven and Ghent University