Are widely used measurements in the human sciences (say happiness surveys or depression scales) quantitative or merely ordinal? If they are merely ordinal, could they be developed into quantitative measurements, just like in the progression from thermoscopes to thermometers? Taking inspiration from recent philosophy of measurement, some practitioners express optimism about future human science measurements. The so-called quantity objection stands out for having the only chance of settling the debate in favour of the pessimists. It claims that the (...) problem lies not with current, or likely future, measurement practices in the human sciences, but with human science attributes themselves—they just are not quantitative, but merely ordinal. Hence, they cannot not (thus will not) be measured quantitatively. The argument has a long and distinguished pedigree. This paper assesses old and recent versions of it, namely: the objection made originally to Fechner’s psychophysics by von Kries (among others) and Michell’s recent version of this objection. To do so, the paper first draws important distinctions between different versions of the argument that have been overlooked. Then, it argues that none of the versions of the quantity objection provide a good reason for the optimists to give up their optimism. In particular, Michell’s argument characterizes the measurand (that is, the attribute to be measured) in a way that optimists do not and need not accept. Yet the optimists’ defence articulated here brings with it serious burdens to discharge. The ball is in their court. (shrink)

This article focuses on the criticisms of current approaches in educational research methodology. Itsummarizes rationales for mixed methods and argues that the mixing quantitative paradigm andqualitative paradigm is problematic due to practical and philosophical arguments. It is alsoindicated that the current rise of mixed methods work has increased problems with quantitativeand qualitative methods. In this article we offer a different symbolic system, with differentlogical form for describing educational phenomena based on the philosophical assumptions andnew mathematical reasoning: para-quantitativism. Para-quantitative (...) theory is an approachwhich has been developed in respect to close relationship between paradigm and method, using apostpositivist transcendental realism as a philosophical beginning of the research methodology,taking Operational Logic System or Fuzzy Logic System (OLS/FLS) as logic of scientificresearch in education. (shrink)

In this work, we propose a definition of logical consequence based on the relation between the quantity of information present in a particular set of formulae and a particular formula. As a starting point, we use Shannon‟s quantitative notion of information, founded on the concepts of logarithmic function and probability value. We first consider some of the basic elements of an axiomatic probability theory, and then construct a probabilistic semantics for languages of classical propositional logic. We define the quantity (...) of information for the formulae of these languages and introduce the concept of informational logical consequence, identifying some important results, among them: certain arguments that have traditionally been considered valid, such as modus ponens, are not valid from the informational perspective; the logic underlying informational logical consequence is not classical, and is at the least paraconsistent sensu lato; informational logical consequence is not a Tarskian logical consequence. (shrink)

The paper explores the handling of singular analogy in quantitative inductive logics. It concentrates on two analogical patterns coextensive with the traditional argument from analogy: perfect and imperfect analogy. Each is examined within Carnap’s λ-continuum, Carnap’s and Stegmüller’s λ-η continuum, Carnap’s Basic System, Hintikka’s α-λ continuum, and Hintikka’s and Niiniluoto’s K-dimensional system. Itis argued that these logics handle perfect analogies with ease, and that imperfect analogies, while unmanageable in some logics, are quite manageable in others. The paper concludes (...) with a modification of the K-dimensional system that synthesizes independent proposals by Kuipers and Niiniluoto. (shrink)

We present an interdisciplinary approach to study systematic relations between logical form and attacks between claims in an argumentative framework. We propose to generalize qualitative attack principles by quantitative ones. Specifically, we use coherent conditional probabilities to evaluate the rationality of principles which govern the strength of argumentative attacks. Finally, we present an experiment which explores the psychological plausibility of selected attack principles.

Drawing on the epistemology of logic literature on anti-exceptionalism about logic, we set out to investigate the following metaphilosophical questions empirically: Is philosophy special? Are its methods (dis)continuous with science? More specifically, we test the following metaphilosophical hypotheses empirically: philosophical deductivism, philosophical inductivism, and philosophical abductivism. Using indicator words to classify arguments by type (namely, deductive, inductive, and abductive arguments), we searched through a large corpus of philosophical texts mined from the JSTOR database (N = 435,703) to find patterns of (...) argumentation. The results of our quantitative, corpus-based study suggest that deductive arguments are significantly more common than abductive arguments and inductive arguments in philosophical texts overall, but they are gradually and steadily giving way to non-deductive (i.e. inductive and abductive) arguments in academic philosophy. (shrink)

In recent decades, the analysis of phraseology has made use of the exploration of large corpora as a source of quantitative information about language. This paper intends to present the main lines of work in progress based on this empirical approach to linguistic analysis. In particular, we focus our attention on some problems relating to the morpho-syntactic annotation of corpora. The CORIS/CODIS corpus of contemporary written Italian, developed at CILTA – University of Bologna (Rossini Favretti 2000; Rossini Favretti, Tamburini, (...) De Santis in press), is a synchronic 100-million-word corpus and is being lemmatised and annotated with part-of-speech (POS) tags, in order to increase the quantity of information and improve data retrieval procedures (Tamburini 2000). The aim of POS tagging is to assign each lexical unit to the appropriate word class. Usually the set of tags is pre-established by the linguist, who uses his/her competence to identify the different word classes. The very first experiments we made revealed how the traditional part-of-speech distinctions in Italian (generally based on morphological and semantic criteria) are often inadequate to represent the syntactic features of words in context. It is worth noting that the uncertainties in categorisation contained in Italian grammars and dictionaries reflect a growing difficulty as they move from fundamental linguistic classes, such as nouns and verbs, to more complex classes, such as adverbs, pronouns, prepositions and conjunctions. This latter class, that groups together elements traditionally used to express connections between sentences, appears inadequate when describing cohesive relations in Italian. This phenomenon actually seems to involve other elements traditionally assigned to different classes, such as adverbs, pronouns and interjections. Recent studies proposed the class of ‘connectives’, grouping all words that, apart from their traditional word class, have the function of connecting phrases and contributing to textual cohesion. From this point of view, conjunctions can be considered as part of phrasal connectives, that can in turn be included in the wider category of textual connectives. The aim of this study is to identify elements that can be included in the class of phrasal connectives, using quantitative methods. According to Shannon and Weaver’s (1949) observation that words are linked by dependent probabilities, corroborated by Halliday’s (1991) argument that the grammatical “system” (in Firth’s sense of the term) is essentially probabilistic, quantitative data are introduced in order to provide evidence of relative frequencies. Section 2 presents a description of word-class categorisation from the point of view of grammars and dictionaries arguing that the traditional category of conjunctions is inadequate for capturing the notion of phrasal connective. Section 3 examines the notion of ‘connective’ and suggests a truth-function interpretation of connective behaviour. Section 4 describes the quantitative methods proposed for analysing the distributional properties of lexical units, and section 5 comments on the results obtained by applying such methods drawing some provisional conclusions. (shrink)

It is often argued that the great quantity of evil in our world makes God’s existence less likely than a lesser quantity would, and this, presumably, because the probability that some evils are gratuitous increases as the overall quantity of evil increases. Often, an additive approach to quantifying evil is employed in such arguments. In this paper, we examine C. S. Lewis’ objection to the additive approach, arguing that although he is correct to reject this approach, there is a sense (...) in which he underestimates the quantity of pain. However, the quantity of pain in that sense does not significantly increase the probability that some pain is gratuitous. Therefore, the quantitative argument likely fails. (shrink)

While the empirical evidence pointing to a gender gap in professional, academic philosophy in the English-speaking world is widely accepted, explanations of this gap are less so. In this paper, we aim to make a modest contribution to the literature on the gender gap in academic philosophy by taking a quantitative, corpus-based empirical approach. Since some philosophers have suggested that it may be the argumentative, “logic-chopping,” and “paradox-mongering” nature of academic philosophy that explains the underrepresentation of women in the (...) discipline, our research questions are the following: Do men and women philosophers make different types of arguments in their published works? If so, which ones and with what frequency? Using data mining and text analysis methods, we study a large corpus of philosophical texts mined from the JSTOR database in order to answer these questions empirically. Using indicator words to classify arguments by type, we search through our corpus to find patterns of argumentation. Overall, the results of our empirical study suggest that women philosophers make deductive, inductive, and abductive arguments in their published works just as much as male philosophers do, with no statistically significant differences in the proportions of those arguments relative to each philosopher’s body of work. (shrink)

Blumenthal-Barby and her colleagues (2022) situate their discussion of philosophy and bioethics in the context of (reportedly) widely held assumption that, when compared to the early days of bioethics, the role of philosophy is now diminished across the field – the assumption we call the Disconnection Thesis. This assumption can be summarized, to use the authors’ own words, by the phrase “philosophy’s glory days in bioethics are over“. While in no place of the article they explicitly endorse the Disconnection Thesis, (...) at least some of the authors had previously endorsed it in print (Savulescu 2015). Such expressions of collective expert wisdom might be a valuable source of information on the discipline's history, but they should not be accepted uncritically. Given the explosion in the size and scope of bioethical research in recent decades, any scholar’s familiarity with the area is necessarily based on selective reading and might be biased. Hence, in this commentary, we examine what kind of more rigorous evidence could corroborate the Disconnection Thesis. In other words, if the role of philosophy in bioethics has been indeed diminishing, what kind of observable patterns should we expect to see? Drawing on our previous research (Bystranowski, Dranseika, Żuradzki 2022), here we focus on two useful perspectives: citation analysis and topic modeling. While the first approach allows us to indirectly measure the level of engagement of bioethicists with philosophical literature (by measuring the proportion of references from articles published in journals in bioethics that cite philosophy journals), the latter provides a window into the content and argumentative style of bioethical texts. (shrink)

The quantitative argument against the notion of a best possible world claims that, no matter how many worthwhile lives a world contains, another world contains more and is, other things being equal, better. Parfit’s ‘ Mere Addition Paradox ’ suggests that defenders of this argument must accept his ‘ Repugnant Conclusion ’ : that outcomes containing billions upon billions of lives barely worth living are better than outcomes containing fewer lives of higher quality. Several responses to the (...) Paradox are discussed and rejected as either inadequate or unavailable in a theistic context. The quantitative argument fails if some world is such that addition to it is not possible, i.e., if it is intensively infinite, as Liebniz claimed. If the notion of such a world is incoherent, then no world is quantitatively best and the quantitative argument succeeds, but only at the cost of embracing the Repugnant Conclusion. (shrink)

Contemporary mainstream economics cannot be seen as disconnected from philosophical concerns. On the contrary, it should be understood as a defence for a specific philosophy, namely, crude quantitative hedonism where money would measure pleasure and pain. Disguised among a great mathematical apparatus involving utility functions, supply, and demand, lies a specific hedonist philosophy that every year is lectured to thousands of economic and business students around the world. This hedonist philosophy is much less sophisticated than that in ancient hedonist (...) philosophers as Epicurus or Lucretius. Furthermore, it does not solve any of the systematic difficulties regularly faced by hedonist philosophy. However, the argument that economics is detached from philosophy works as a rhetorical artifice to protect its dominant underlying philosophy: Philosophical disputes would have to be addressed within the biased mathematical apparatus of quantitative hedonism. Economists and business students must learn to identify the underlying philosophy in mainstream economics and alternative philosophical systems. (shrink)

I show that in our theoretical representations of argument, vicious infinite regresses of self-reference may arise with respect to each of the three usual, informal criteria of argument cogency: the premises are to be relevant, sufficient, and acceptable. They arise needlessly, by confusing a cogency criterion with argument content. The three types of regress all are structurally similar to Lewis Carroll’s famous regress, which involves quantitative extravagance with no explanatory power. Most attention is devoted to the (...) sufficiency criterion, including its relation to the view au courant that inferring necessarily involves the thinker taking her premises to support her conclusion. I contend that this view is mistaken and likewise that arguments make no such assumption or inference claim as that the premises support the conclusion. The core of the positive alternative model I propose is that there is commitment to, but not claiming, the proposition that the premises support the conclusion. (shrink)

Inspired by the eminently successful physical theories and informed by commonplace experiences such as seeing a cat upon looking at a cat, conscious experience is thought of as a measurement or photocopy of given stimulus. Conscious experience, unlike a photocopy, is symbolic—like language—in that the relation between conscious experience and physical stimulus is analogous to that of the word "cat" and its meaning, i.e., arbitrary and yet systematic. We present arguments against the photocopy model and arguments for a symbolic conception (...) of conscious experience. Learning and the corresponding plasticity of the brain make a strong case for the symbolic conception of conscious experience, while many extra-ordinary conscious experiences argue against the formalisation of consciousness as a measuring device. The notions of place-value notation and grammar, which organise quantitative measurements and conscious experiences in the medium of numbers and language, respectively, are suggested as model systems for putting together a comprehensive theory of conscious experience. (shrink)

In the growing literature on decision-making under moral uncertainty, a number of skeptics have argued that there is an insuperable barrier to rational "hedging" for the risk of moral error, namely the apparent incomparability of moral reasons given by rival theories like Kantianism and utilitarianism. Various general theories of intertheoretic value comparison have been proposed to meet this objection, but each suffers from apparently fatal flaws. In this paper, I propose a more modest approach that aims to identify classes of (...) moral theories that share common principles strong enough to establish bases for intertheoretic comparison. I show that, contra the claims of skeptics, there are often rationally perspicuous grounds for precise, quantitative value comparisons within such classes. In light of this fact, I argue, the existence of some apparent incomparabilities between widely divergent moral theories cannot serve as a general argument against hedging for one's moral uncertainties. (shrink)

An organizing theme of the dissertation is the issue of how to make philosophical theories useful for scientific purposes. An argument for the contention is presented that it doesn’t suffice merely to theoretically motivate one’s theories, and make them compatible with existing data, but that philosophers having this aim should ideally contribute to identifying unique and hard to vary predictions of their theories. This methodological recommendation is applied to the ranking-theoretic approach to conditionals, which emphasizes the epistemic relevance and (...) the expression of reason relations as part of the semantics of the natural language conditional. As a first step, this approach is theoretically motivated in a comparative discussion of other alternatives in psychology of reasoning, like the suppositional theory of conditionals, and novel approaches to the problems of compositionality and accounting for the objective purport of indicative conditionals are presented. In a second step, a formal model is formulated, which allows us to derive quantitative predictions from the ranking-theoretic approach, and it is investigated which novel avenues of empirical research that this model opens up for. Finally, a treatment is given of the problem of logical omniscience as it concerns the issue of whether ranking theory (and other similar approaches) makes too idealized assumptions about rationality to allow for interesting applications in psychology of reasoning. Building on the work of Robert Brandom, a novel solution to this problem is presented, which both opens up for new perspectives in psychology of reasoning and appears to be capable of satisfying a range of constraints on bridge principles between logic and norms of reasoning, which would otherwise stand in a tension. (shrink)

What is the relationship between the world and logic, between intuition and language, between objects and their quantitative determinations? Rationalists, on the one hand, hold that the world is structured in a rational way. Representationalists, on the other hand, assume that language, logic, and mathematics are only the means to order and describe the intuitively given world. In World and Logic, Jens Lemanski takes up three surprising arguments from Arthur Schopenhauer’s hitherto undiscovered Berlin Lectures, which concern the philosophy of (...) language, logic, and mathematics. Based on these arguments, Lemanski develops a new position entitled ‘rational representationalism’: the world is always structured by human beings according to linguistic, logical, and mathematical principles, but the basic vocabulary of these structural descriptions already contains metaphors taken from the world around us. (shrink)

Although the concept of uncertainty is as old as Epicurus’s writings, and an excellent quantitative theory, with entropy as the measure of uncertainty having been developed in recent times, there has been little exploration of the qualitative theory. The purpose of the present paper is to give a qualitative axiomatization of uncertainty, in the spirit of the many studies of qualitative comparative probability. The qualitative axioms are fundamentally about the uncertainty of a partition of the probability space of events. (...) Of course, it is common to speak of the uncertainty, or randomness, of a random variable, but only the partition defined by the values of the random variable enter into the definition of uncertainty, not the actual values. It is straightforward to add axioms for decision making following the general line of Savage from the 1950s. Indeed, in the spirit of Epicurus, it is really our intuitive feeling about the uncertainty of the future that motivates much of our thinking about decisions. Here, the distinction between the concepts of probability and uncertainty can be made by citing many familiar examples. Without spelling out the technical details, the axiomatization of qualitative probability with uncertainty as the most important primitive concept, it is possible to raise a different kind of question about bounded rationality. This new question is whether or not one should bound the uncertainty in thinking and investigating any detailed framework of decision making. Discussion of this point is certainly different from the question of bounding rationality by not maximizing expected utility. In practice, we naturally bound uncertainty in our analysis of decision-making problems. As in the case of formulating an alternative for maximizing expected utility, so is the case of rational alternatives to maximizing uncertainty. There are several issues to consider. In the spirit of my other work in qualitative probability, I explore alternatives rather than attempt to give a definitive argument for one single solution. (shrink)

In 2009, we celebrated the bicentennial of the birth of Charles Darwin and the sesquicentennial of the publication of his book The Origin of Species. This seems to be a good opportunity to evaluate the importance of Darwin’s work for the social sciences, mainly for philosophical anthropology. The aim of this paper is to discuss the traditional anthropocentric conceptions of man, which consider our biological species to be exceptional – qualitatively higher than other living organisms. Over the course of the (...) 20th century, philosophers have argued for the claim in a number of ways: man is supposed to be the only animal capable of laughter, love, thought or language. It has also been claimed that only members of Homo sapiens have free will, morality or religion. The paper refutes these arguments on the basis of contemporary studies by M. Davila Ross, H. Fischer, K. Arnold, K. Zuberbühler, G. Konopka, B. Libet, F. De Waal, M. Bekoff, P. Boyer, B. Hood, G. Paul and others. The author argues that the only differences between man and other animals are quantitative, and therefore the nature of humans should be studied using the methods of naturalized philosophy, with respect to the natural sciences. (shrink)

In his latest attack, even though he claims to be a practitioner of “close reading” (Wills 2018b, 34), it appears that Wills still has not bothered to read the paper in which I defend the thesis he seeks to attack (Mizrahi 2017a), or any of the papers in my exchange with Brown (Mizrahi 2017b; 2018a), as evidenced by the fact that he does not cite them at all. This explains why Wills completely misunderstands Weak Scientism and the arguments for the (...) quantitative superiority (in terms of research output and research impact) as well as qualitative superiority (in terms of explanatory, predictive, and instrumental success) of scientific knowledge over non-scientific knowledge. (shrink)

In economics, thought experiments are frequently justified by the difficulty of conducting controlled experiments. They serve several functions, such as establishing causal facts, isolating tendencies, and allowing inferences from models to reality. In this paper, I argue that thought experiments served a further function in economics: facilitating the quantitative definition and measurement of the theoretical concept of utility, thereby bridging the gap between theory and statistical data. I support my argument by a case study, the “hypothetical experiments” of (...) the Norwegian economist Ragnar Frisch (1895-1973). Frisch aimed to eliminate introspection and a subjective concept of utility from economic reasoning. At the same time, he sought behavioral foundations for economic theory that enabled quantitative reasoning. By using thought experiments to justify his set of choice axioms and facilitating the operationalization of utility, Frisch circumvented the problem of observing utility via actual experiments without eliminating the concept of utility from economic theory altogether. As such, these experiments helped Frisch to empirically support the theory’s most important results, such as the laws of demand and supply, without the input of new empirical findings. I suggest that Frisch’s experiments fulfill the main characteristics of thought experiments. (shrink)

How ought you to evaluate your options if you're uncertain about what's fundamentally valuable? A prominent response is Expected Value Maximisation (EVM)—the view that under axiological uncertainty, an option is better than another if and only if it has the greater expected value across axiologies. But the expected value of an option depends on quantitative probability and value facts, and in particular on value comparisons across axiologies. We need to explain what it is for such facts to hold. Also, (...) EVM is by no means self-evident. We need an argument to defend that it’s true. This book introduces an axiomatic approach to answer these worries. It provides an explication of what EVM means by use of representation theorems: intertheoretic comparisons can be understood in terms of facts about which options are better than which, and mutatis mutandis for intratheoretic comparisons and axiological probabilities. And it provides a systematic argument to the effect that EVM is true: the theory can be vindicated through simple axioms. The result is a formally cogent and philosophically compelling extension of standard decision theory, and original take on the problem of axiological or normative uncertainty. (shrink)

Revelation, or the view that the essence of phenomenal properties is presented to us, is as intuitively attractive as it is controversial. It is notably at the core of defences of anti-physicalism. I propose in this paper a new argument against Revelation. It is usually accepted that low-level sensory phenomenal properties, like phenomenal red, loudness or brightness, stand in relation of similarity and quantity. Furthermore, these similarity and quantitative relations are taken to be internal, that is, to be (...) fixed by what their relata are. I argue that, under some plausible additional premises, no account of what grounds these relations in the essence of their relata is consistent with Revelation, at least if we take common phenomenological descriptions for granted. As a result, the plausibility of Revelation is undermined. One might however resist this conclusion by weakening the epistemic relation postulated between subjects and their phenomenal properties. (shrink)

Pascal Engel défend explicitement le purisme (ou l’intellectualisme). Selon la version générale de cette thèse, les facteurs qui déterminent si une croyance est justifiée, ou si elle est une connaissance, ne concernent que la vérité. Ils sont totalement indépendants des désirs ou des préférences du sujet, ainsi que des conséquences pratiques potentielles du fait de posséder ces croyances. Dans son article « Pragmatic Encroachment and Epistemic Value » (2009), P. Engel concède que des facteurs pratiques peuvent déterminer la quantité de (...) données (ou la justification) dont on a besoin pour savoir ou croire, tout en maintenant que cela n’affecte pas le purisme épistémique (dans sa version évidentialiste) sur les notions de donnée ou de degré de justification. Mais cela ne revient-il pas tout simplement à concéder l’impurisme épistémique au moins à propos de la connaissance ou de la justification simpliciter des croyances ? Dans cet article, j’examine en détails la position de P. Engel. Je montre que, correctement comprise, elle est intégralement puriste. En considérant le principe connaissance-action, je soulève néanmoins un dilemme pour son approche, jetant ainsi un doute sur le potentiel qu’elle aurait à fournir une réponse puriste satisfaisante à l’argument fondamental motivant l’impurisme épistémique. (shrink)

It is often thought that sensible qualities such as colours do not exist as properties of physical objects. Focusing on the case of colour, I discuss two views: the Galilean view, according to which colours do not exist as qualities of physical objects, and the naive view, according to which colours are, as our perception presents them to be, qualities instantiated by physical objects. I argue that it is far from clear that the Galilean view is better than the naive (...) view. Given the arguments in this paper, the naive view ought to be taken seriously. The discussion here appeals especially to theorists who, like Goff, are already convinced that the quantitative language of physical science fails to capture all qualities. (shrink)

This paper strengthens and defends the pluralistic implications of Einstein's successful, quantitative predictions of Brownian motion for a philosophical dispute about the nature of scientific advance that began between two prominent philosophers of science in the second half of the twentieth century (Thomas Kuhn and Paul Feyerabend). Kuhn promoted a monistic phase-model of scientific advance, according to which a paradigm driven `normal science' gives rise to its own anomalies, which then lead to a crisis and eventually a scientific revolution. (...) Feyerabend stressed the importance of pluralism for scientific progress. He rejected Kuhn's model arguing that it fails to recognize the role that alternative theories can play in identifying exactly which phenomena are anomalous in the first place. On Feyerabend's account, Einstein's predictions allow for a crucial experiment between two incommensurable theories, and are an example of an anomaly that could refute the reigning paradigm only after the development of a competitor. Using Kuhn's specification of a disciplinary matrix to illustrate the incommensurability between the two paradigms, we examine the different research strategies available in this peculiar case. On the basis of our reconstruction, we conclude by rebutting some critics of Feyerabend's argument. (shrink)

Many metaphysicians often appeal to Hume’s dictum (HD), according to which there are no necessary connections between distinct entities (or states of entities), in order to resist theories that commit us to such connections. Some have argued that HD is an unsupported dogma of metaphysics. But theories that commit us to necessary connections between distinct goings-on can also be resisted by invoking a normative twist on HD, which I call the Humean Solvent (HS): “Do not connect distinct entities (or states (...) of entities) beyond necessity”. HS is a principle of structural parsimony – assuming that a theory is structurally more parsimonious than another when the latter is committed to a more connected ontology than the former is. Just as Ockham’s ‘razor’ encourages us to cut down superfluous ontological commitments, the Humean ‘solvent’ encourages us to dissolve dispensable metaphysical glue: we ought not to glue elements of our ontology beyond necessity. HS has both a qualitative and a quantitative dimension: qualitatively, it encourages us to avoid using metaphysical glues that are unnecessarily strong, the strongest of which being metaphysically necessary connections; quantitatively, it encourages us not to metaphysically glue things that need no gluing. Thus, given HS, other things being equal, what is worst is a theory that entails that everything is metaphysically necessarily connected to anything else and what is best is a theory that leaves all things loose and separable. In this paper, I will first compare HD and HS as grounds for paradigmatic Humean doctrines in contemporary metaphysics, then I will argue that structural parsimony is neither a variety of ontological nor of ideological parsimony; finally, I will offer an argument for HS. (shrink)

In Science Without Numbers (1980), Hartry Field defends a theory of quantity that, he claims, is able to provide both i) an intrinsic explanation of the structure of space, spacetime, and other quantitative properties, and ii) an intrinsic explanation of why certain numerical representations of quantities (distances, lengths, mass, temperature, etc.) are appropriate or acceptable while others are not. But several philosophers have argued otherwise. In this paper I focus on arguments from Ellis and Milne to the effect that (...) one cannot provide an account of quantity in ''purely intrinsic'' terms. I show, first, that these arguments are confused. Second, I show that Field's treatment of quantity can provide an intrinsic explanation of the structure of quantitative properties; what it cannot do is provide an intrinsic explanation of why certain numerical representations are more appropriate than others. Third, I show that one could provide an intrinsic explanation of this sort if one modified Field's account in certain ways. (shrink)

In his book Modal Logic as Metaphysics, Timothy Williamson defends first-order necessitism using simplicity as a powerful argument. However, simplicity is decomposed into two different, even antagonistic, sides: elegance and parsimony. On the one hand, elegance is the property of theories possessing few and simple principles that allow them to deploy all their theoretical power; on the other hand, parsimony is the property of theories having the fair and necessary number of ontological entities that allow such theories give an (...) account of themselves. Since necessitism endorses Barcan Formulae for the sake of elegance, it is committed to a vast number of contingently non-concrete objects, so one may think that it is not qualitatively parsimonious. I argue that necessitism could be viewed as an additive case in the sense that Alan Baker characterizes the adjective so quantitative parsimony should be considered when it comes to necessitism instead of qualitative parsimony. (shrink)

The aim of this article is to address the issue of measuring radio audience from a methodological perspective. Although our approach is contextualized, the case study of radio audience measurement in Romania is relevant to a large number of EU countries, in which scholars and practitioners use Day-After-Recall technique. Considering the size of the radio advertising market, as well as the number of radio listeners (about 90% in EU), it is crucial for both radio broadcasters and advertisers to measure radio (...) audience with high accuracy. First, we briefly review the main definitions of key concepts used in radio audience evaluation: audience, listener, rating, market share, daily-reach, or time spent listening. Next, we discuss two paradigms of audience and two theoretical models of mass communication used as a framework for measuring radio audience. Further, we briefly approach the issue of potential sources of error in rating data, by focusing on response error. Next, we emphasize the advantages and disadvantages of each quantitative method utilized in radio audience measurement, and present the case study of radio audience measurement in Romania. Based on a methodological critical review, we outline challenges and potential solutions for assessing more accurately radio audience. Finally, we reflect on the future of radio in digital era, and refer to new perspectives of upgrading existing research techniques. (shrink)

In this paper I argue that Nietzsche’s rejection of egalitarianism depends on equivocation between distinct conceptions of power and equality. When these distinct views are disentangled, Nietzsche’s arguments succeed only against a narrow sense of equality as qualitative similarity (die Gleichheit as die Ähnlichkeit), and not against quantitative forms that promote equality not as similarity but as multiple, proportional resistances (die Gleichheit as die Veilheit and der Widerstand). I begin by distinguishing the two conceptions of power at play in (...) Nietzsche’s arguments, power as quantitative superiority of ability and as qualitative feeling of power (das Gefühl der Macht), an affective state that does not directly correlate with quantitative ability and, because based in resistance (der Widerstand), requires relative equality as its condition. Nietzsche presents four principal arguments against egalitarianism, each concluding that equality harms the flourishing of humanity’s highest individuals. First, equality directly promotes qualitative similarity (die Ähnlichkeit) at the expense of multiplicity (die Vielheit). Second, because material inequalities ground the ‘pathos of distance’ (the recognition of spiritual inequality), equality indirectly undermines the desire for self-development. Third, because it opposes aristocratic conditions, egalitarianism promotes a form of liberalism that removes conditions of constraint necessary to human development. Finally, equality is a less efficient means to human enhancement, which is best promoted through unequal distribution of resources to the most able individuals. I argue that in each case Nietzsche’s argument succeeds only if interpreted according to the quantitative conception of power as superiority, but fails when we also consider the qualitative conception of power as feeling. For the promotion of an individual’s qualitative power is compatible with quantitative power equality. Moreover, because power is felt only in resistance, the feeling of power requires relative equality as its precondition—an alternate sense of equality construed, not as qualitative similarity, but as quantitative resistance from proportional counter-powers. I conclude that Nietzsche’s commitment to the promotion of humanity’s highest individuals does not entail the rejection of moral egalitarianism in every form and even supports certain forms. (shrink)

Recently there have been several attempts in formal epistemology to develop an adequate probabilistic measure of coherence. There is much to recommend probabilistic measures of coherence. They are quantitative and render formally precise a notion—coherence—notorious for its elusiveness. Further, some of them do very well, intuitively, on a variety of test cases. Siebel, however, argues that there can be no adequate probabilistic measure of coherence. Take some set of propositions A, some probabilistic measure of coherence, and a probability distribution (...) such that all the probabilities on which A’s degree of coherence depends (according to the measure in question) are defined. Then, the argument goes, the degree to which A is coherent depends solely on the details of the distribution in question and not at all on the explanatory relations, if any, standing between the propositions in A. This is problematic, the argument continues, because, first, explanation matters for coherence, and, second, explanation cannot be adequately captured solely in terms of probability. We argue that Siebel’s argument falls short. (shrink)

Twitter is an instrument used not only for sharing public or personal information, but also for persuading the audience. While specific platforms and software have been developed for analyzing macro-analytical data, and specific studies have focused on the linguistic dimension of the tweets, the argumentative dimension of the latter is unexplored to this date. This paper intends to propose a method grounded on the tools advanced in argumentation theory for capturing, coding, and assessing the different argumentative dimensions of the messages (...) posted on Twitter, focusing on the types of argument communicated, the quality of their premises, and the fallacies committed – including the use of unshared presuppositions and emotive words. This method is applied to a corpus of 843 tweets published by the Italian Minister of the Interior, Mr. Matteo Salvini, from the date of his appointment to the beginning of his campaign for the European elections. The quantitative data provide general indications for detecting the strategies that characterize the argumentative profile of Salvini, which are then analyzed qualitatively. (shrink)

Hermann von Helmholtz (1821-1894) established results both controversial and enduring: analysis of mixed colors and of combination tones, arguments against nativism, and the analysis of sensation and perception using the techniques of natural science. The paper focuses on Helmholtz’s account of sensation, perception, and representation via “physiological psychology”. Helmholtz emphasized that external stimuli of sensations are causes, and sensations are their effects, and he had a practical and naturalist orientation toward the analysis of phenomenal experience. However, he argued as well (...) that sensation must be interpreted to yield representation, and that representation is geared toward objective representation (the central thesis of contemporary intentionalism). The interpretation of sensation is based on “facts” revealed in experiment, but extends to the analysis of the quantitative, causal relationships between stimuli and responses. A key question for Helmholtz’s theory is the extent to which mental operations are to be ascribed a role in interpreting sensation. (shrink)

In situations of information overload, where cases of garbage-in-garbage-out are commonplace, it is necessary to sort out important and appropriate data for one’s specific purposes. A deluge of seemingly interrelated or interconnected data may lead us from one analytic moment to another without consideration for the credibility of our sources. Since people generally tend to be on one side of an issue rather than the other, information exploration and gathering can become a quantitative rather than qualitative exercise, as we (...) are commonly inclined to feed and reinforce our opinion and argument with one-sided information, to the neglect of necessary and vital points in the opposite argument. Unilateral information, which could at worst come from spurious and unreliable sources, appropriated to beef up a stand on a certain issue, can never lead to a meaningful understanding of reality. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Newton's Metaphysics: Essays by Eric SchliesserMarius StanEric Schliesser. Newton's Metaphysics: Essays. Oxford: Oxford University Press, 2021. Pp. 328. Hardback, $99.90.Newton owes his high regard to the quantitative science he left us, but his overall picture of the world had some robustly metaphysical threads woven in as well. Posthumous judgment about the value of these threads has varied wildly. Christian Wolff thought him a metaphysical rustic, as did (...) Hans Reichenbach some two centuries later ("Die Bewegungslehre bei Newton, Leibniz und Huygens," Kant-Studien 29 [1924]: 416–38). In the 1960s, the tide would turn, as Howard Stein and James Edward McGuire separately began to show that Newton's metaphysics was not just sophisticated, but often more compelling than its early modern alternatives (see respectively "Newtonian Spacetime," Texas Quarterly 10 [1967]: 174–200; and Tradition and Innovation: Newton's Metaphysics of Nature [Dordrecht: Kluwer Academic Publishers, 1995]). Eric Schliesser's book unfolds in that same register of appreciative, high scholarship, and it attests to the enduring attraction of its subject.The book grew out of previous discrete papers, to which he added a few more for this occasion. Accordingly, it does not come with a master argument. Rather, it is an in-depth exploration of some key metaphysical themes in Newton. As such, it befits its subject figure, who reflected on themes and concepts while stopping short of working out systems.The first major theme is Newton and Spinozism. The latter does not denote Spinoza's metaphysics. In fact, Schliesser explains, Newton shared with Spinoza some weighty commitments, for example, to space being actually infinite, and to substance monism: "for Newton, there is strictly speaking only one genuine substance," namely, God (33). Rather, "Spinozism" is an interpreter's category for a bundle of three theses: identifying God and nature; denying final causation in the physical world; and the assumption of "blind" metaphysical necessity. Some counted Hobbes and John Toland as Spinozist in this sense, and even Epicurus, avant la lettre. Newton and his followers argued vehemently against this package, as Schliesser shows in chapters 4, 5, and 8. Their chief complaint was that Spinozism is unable to account for the "origin of motion," for a certain type of order, and for the stability of cosmological structure—and to do so in a way that "meets the standards of Newtonian mechanics" (122). This interpretive lens allows Schliesser to draw Kant in, by reading his youthful Theory of Heaven as a possible Spinozist reply to their objections (chapter 3). [End Page 157]A second theme is the metaphysics of mechanics, where Schliesser weaves together several strands. One is the ontology of gravity, for which he offers a novel construal: for Newton, gravity counts as real, but in a qualified sense. Namely, it is not essential and not intrinsic: "even after creation, a lonely partless particle of matter in the universe would not be said to gravitate." And gravity is relational: a "shared quality" of two or more bits of matter, which obtains in virtue of their sharing a nature (19). Another strand is Newton's ontology of time—really, a subtle, difficult topic long neglected. Famously, Newton in Principia defends absolute, true, and mathematical time. The question is what these three qualifiers denote, and whether Newton thought they were synonymous. Schliesser in chapter 7 argues for the provocative view that "absolute" and "true" time are not identical concepts; rather, they pick out different entities. These entities share a common structure, namely, metric and topological. That makes them species of "mathematical" time (179). But, Schliesser contends, Newton has unequal warrant for his two concepts of time.Yet another theme is formal causation. It comes to the fore in chapter 5, which grapples with Newton's opaque idea that space is an "emanative effect." Schliesser explains that here, "emanation picks out a species of formal causation" (147), but in a novel, early modern sense that comes from Bacon, not Aristotle. If space has a formal cause, then so has its twin brother, time, the topic of chapter 7. God is their common formal cause. Then in chapter 6 (coauthored with Zvi Biener) Schliesser adds that, for Newton, laws... (shrink)

Although there is increasing recognition that theory and practice in science are often inseparably intertwined, discussions of scientific controversies often continue to focus on theory, and not practice or methodologies. As a contribution to constructing a framework towards understanding controversies linked to scientific practices, we introduce the notion of borrowed epistemic credibility, to describe the situation in which scientists exploit fallacious similarities between accepted tenets in other fields to garner support for a given position in their own field. Our proposal (...) is based on the analysis of a recent controversy in phylogeography, a biological subdiscipline concerned with the study of the historical causes of variation in genetic diversity within species in concrete biogeographical locations. Through a review of the arguments that support the two conflicting phylogeographic schools, we show that ‘theory’ plays essentially no role as a foundation of the controversy, whereas both sides borrow epistemic credibility from sources such as formal logic, similarity of results to those in other scientific areas, the authority of prominent scientists, or the presumed superiority of quantitative vs. verbal reasoning. Our case study underscores the indivisibility of theory and practice and provide a means to re-examine important philosophical issues such as the meaning of inference, rationality, justification, and objectivity in scientific practice. (shrink)

Bacon’s philosophy had a wide dissemination in Dutch Seventeenth Century context. This can be explained by the coeval diffusion of Cartesianism. Bacon’s project of a reformation of science was deemed by Heereboord and De Raey as the manifesto of a new philosophy. Along with Geulincx, moreover, De Raey borrowed Bacon’s arguments on the causes of error and on the replacement of Aristotelian natural history, aimed at integrating Descartes’s physics. Also in logic Bacon’s influence was noticeable, as the development of a (...) new Organon had its accomplishment in the Cartesian logic of Clauberg and of De Raey himself. In theology, Heidanus relied on Bacon in order to confute Socinianism. The fortune of Dutch Baconianism had its end with the rise of Newtonianism: as a quantitative, experimental philosophy arose, Bacon’s works were no more regarded as a valuable source of arguments. (shrink)

In recent years, some authors have proposed quantitative measures of the coherence of sets of propositions. Such probabilistic measures of coherence (PMCs) are, in general terms, functions that take as their argument a set of propositions (along with some probability distribution) and yield as their value a number that is supposed to represent the degree of coherence of the set. In this paper, I introduce a minimal constraint on PMC theories, the weak stability principle, and show that any (...) correct, coherent, and complete PMC cannot satisfy it. As a matter of fact, the argument offered in this paper can be applied to any coherence theory that uses a priori procedures. I briefly explore some consequences of this fact. (shrink)

This article presents a theodicy based on a revision of the popular concept of God’s benevolence. If we follow the Protestant tradition by assuming that God is the exclusive source of virtue, the benevolence of God has to be radically different from the benevolence of a human being. A benevolent and almighty God who wishes to reward virtue and punish evil would design the world order similar to that in the allegory of the long spoons. Divine punishment is unforgiving, merciless, (...) individually non-retributive, holistically retributive, and quantitatively unpredictable. All sufferings are divine punishment. Several popular arguments from evil, including animal suffering, victims of evil deeds, natural disasters, and children’s diseases, can be resolved within this framework. (shrink)

Given a subject so imbued with contention and conflicting theoretical stances, it is remarkable that automated instruments ever came to replace the human eye as sensitive arbiters of color specification. Yet, dramatic shifts in assumptions and practice did occur in the first half of the twentieth century. How and why was confidence transferred from careful observers to mechanized devices when the property being measured – color – had become so closely identified with human physiology and psychology? A fertile perspective on (...) the problem is via the history of science and technology, paying particular attention to social groups and disciplinary identity to determine how those factors affected their communities’ cognitive territory. There were both common and discordant threads motivating the various technical groups that took on the problems of measuring light and color from the late nineteenth century onwards, and leading them towards the development of appropriate instruments for themselves. The transition from visual to photoelectric methods could be portrayed as a natural evolution, replacing the eye by an alternative roviding more sensitivity and convenience – indeed, this is the conventional positivist view propounded by technical histories. However, the adoption of new measurement technologies seldom is simple, and frequently has a significant cultural component. Beneath this slide towards automation lay a raft of implicit assumptions about objectivity, the nature of the observer, the role of instruments, and the trade-offs between standardization and descriptive power. While espousing rational arguments for a physical detector of color, its proponents weighted their views with tacit considerations. The reassignment of trust from the eye to automated instruments was influenced as much by the historical context as by intellectual factors. I will argue that several distinct aspects were involved, which include the reductive view of color provided by the trichromatic theory; the impetus provided by its association with photometry; the expanding mood for a quantitative and objective approach to scientific observation; and, the pressures for commercial standardization. As suggested by these factors, there was another shift of authority at play: from one technical specialism to another. The regularization of color involved appropriation of the subject by a particular set of social interests: communities of physicists and engineers espousing a ‘physicalist’ interpretation, rather than psychologists and physiologists for whom color was conceived as a more complex phenomenon. Moreover, the sources for automated color measurement, and instrumentation for measuring color, were primarily from the industrial sphere rather than from academic science. To understand these shifts, then, this chapter explores differing views of the importance of observers, machines and automation. (shrink)

A simple interpretation of quantity calculus is given. Quantities are described as two-place functions from objects, states or processes (or some combination of them) into numbers that satisfy the mutual measurability property. Quantity calculus is based on a notational simplification of the concept of quantity. A key element of the simplification is that we consider units to be intentionally unspecified numbers that are measures of exactly specified objects, states or processes. This interpretation of quantity calculus combines all the advantages of (...) calculating with numerical values (since the values of quantities are numbers, we can do with them everything we do with numbers) and all the advantages of calculating with standardly conceived quantities (calculus is invariant to the choice of units and has built-in dimensional analysis). This also shows that the standard metaphysics and mathematics of quantities and their magnitudes is not needed for quantity calculus. At the end of the article, arguments are given that the concept of quantity as defined here is a pivotal concept in understanding the quantitative approach to nature. As an application of this interpretation of quantity calculus, an easy proof of dimensional homogeneity of physical laws is given. (shrink)

Le présent travail s'inscrit à l'intersection de deux problèmes épistémologiques majeurs. D'une part, le problème de la démarcation scientifique, qui consiste à identifier ce qui distingue intrinsèquement un système (un énoncé, une théorie, ...) scientifique d'un système non scientifique ou pseudo-scientifique. D'autre part, le problème de l'unité épistémologique des sciences, qui consiste à se demander si toutes les disciplines à vocation scientifique peuvent être vues comme des instanciations d'une notion unique de la scientificité. Ces deux problèmes ont soulevé de nombreux (...) débats ayant mis en évidence un ensemble important de difficultés. Le terme « scientifique » désigne en effet des méthodes empiriques, des constructions théoriques et des pratiques de recherche si hétérogènes qu’il semble voué à l’échec d’en chercher une définition aisée à circonscrire. De plus, les objets des disciplines scientifiques sont eux-mêmes de natures très diverses, ce qui semble rendre pareillement caduque toute recherche d’un concept unique de science qui pourrait s’appliquer indépendamment de la discipline en question. Dans cette thèse, je me propose de prendre à contre-pied cet état de fait en soutenant la possibilité et la pertinence d'un modèle unitaire de la scientificité, tout en me restreignant à une approche épistémologique comparée entre les sciences physiques et les sciences sociales. Pour défendre mon propos, j’ai mobilisé deux types de réponses pouvant être opposées au constat présenté plus haut. D’une part, des réponses de principe, où j’examine et m’oppose à des arguments théoriques soutenant l’impossibilité ou en tout cas la difficulté de définir la scientificité en général, et la nécessité pour les sciences sociales de jouir d’une définition à part. D’autre part, je mobilise également des réponses par l’exemple. J’étudie alors plus en détail l’approche dite « analytique » en sociologie. Ce courant a cela d’intéressant pour mon propos qu’il ne semble pas nécessiter d’épistémologie alternative à celle ayant cours, par exemple, en physique ou en biologie, tout en prétendant bien produire des connaissances sur le monde social. Il s’agit donc d’un contre-exemple concret et manifeste de la thèse soutenant que la sociologie ne peut pas jouir du même type d’épistémologie que les autres disciplines. Plus concrètement, j’élabore un (méta-)modèle unitaire de la scientificité en me concentrant sur une unité d’analyse bien circonscrite : les modèles. Je distingue chez ses derniers, classiquement, deux composantes principales : une composante empirique, qui a pour vocation à identifier des régularités dans le réel auquel on a accès à travers des données, et une composante théorique, à visée explicative et classificatoire. Je propose alors de construire formellement un degré de scientificité global dans lequel se combinent la maximisation d’une certaine quantité d’information définie sur la composante empirique et un critère d’invariance structurelle défini sur la composante théorique. Ces diverses constructions, bien que formelles, permettent d’éclairer efficacement les questions épistémologiques que je me suis données au départ de mon travail, ce dernier ayant vocation à constituer une étape supplémentaire vers un modèle unitaire de la scientificité. (shrink)

The environmental costs and energy constraints have become emerging issues for the future development of Machine Learning (ML) and Artificial Intelligence (AI). So far, the discussion on environmental impacts of ML/AI lacks a perspective reaching beyond quantitative measurements of the energy-related research costs. Building on the foundations laid down by Schwartz et al., 2019 in the GreenAI initiative, our argument considers two interlinked phenomena, the gratuitous generalisation capability and the future where ML/AI performs the majority of quantifiable inductive (...) inferences. The gratuitous generalisation capability refers to a discrepancy between the cognitive demands of a task to be accomplished and the performance (accuracy) of a used ML/AI model. If the latter exceeds the former because the model was optimised to achieve the best possible accuracy, it becomes inefficient and its operation harmful to the environment. The future dominated by the non-anthropic induction describes a use of ML/AI so all-pervasive that most of the inductive inferences become furnished by ML/AI generalisations. The paper argues that the present debate deserves an expansion connecting the environmental costs of research and ineffective ML/AI uses (the issue of gratuitous generalisation capability) with the (near) future marked by the all-pervasive Human-Artificial Intelligence Nexus. (shrink)

Copernican reasoning involves considering ourselves, in the absence of other information, to be randomly selected members of a reference class. Consider the reference class intelligent observers. If there are extraterrestrial intelligences (ETIs), taking ourselves to be randomly selected intelligent observers leads to the conclusion that it is likely the Earth has a larger population size than the typical planet inhabited by intelligent life, for the same reason that a randomly selected human is likely to come from a more populous country. (...) The astrophysicist Fergus Simpson contends that this reasoning supports the claims that the typical planet inhabited by ETIs is smaller than Earth (radius about 5,000km; cf. Earth's radius = 6,371km) and that the typical ETI is significantly larger than us about 314kg, the size of an adult male grizzly bear). Simpson's applications of Copernican reasoning are novel and exciting. They should be of interest to philosophers concerned with Richard Gott's delta t argument, the N=1 problem in astrobiology, limited principles of indifference, and probabilistic epistemology in general. While we agree with Simpson about the qualitative direction of his conclusions, we take issue with his presentation of precise quantitative results because his methods (1) display bias, (2) ignore other variables contributing to population size, (3) commit an equivocation, and (4) conceal their dependence on arbitrary assumptions. (shrink)

The discussion in Perspectives on Psychological Science about criteria for scholarly merit shows a potential bias of quantitative measurements compared with informed judgments of scholarly merits. This comment argues for a selection procedure that is open for qualitative arguments.

This study assessed the partial as well as the collaborative impact of age and gender on academic staff preparedness to adopt Internet tools for research sharing in African universities during Covid-19. Although evidence abounds in the literature on gender and age as they affect relatively, scholars’ utilisation of digital tools for research communication, such studies did not examine scholars’ preparedness to adopt from a broad perspective of Africa. This study was conducted based on the argument that the preparedness of (...) scholars may affect their future interest to utilize digital tools for research sharing. A quantitative method, based on the descriptive survey research design, was adopted to provide answers to four prevailing research questions. The examination focused on a populace of 8,591 staff in African universities, nonetheless, information was gathered from 1,977 of them, who deliberately took part from 24 African nations. A validated electronic rating scale, which was mailed/posted to targeted participants, was used as the instrument for data collection. Gender and age significantly affected academic staff preparedness to adopt Internet tools for research sharing partially and interactively in African Universities during Covid-19. Female staff were more prepared than males to adopt internet tools for research sharing during the pandemic. Older lecturers reported a higher rate of preparedness than their younger colleagues to adopt Internet tools for research sharing during Covid-19. In light of these proofs, ramifications and proposals for future exploration are discussed. (shrink)

When experimental participants are given the chance to reflect and revise their initial judgments in a dynamic conversational context, do their responses to philosophical scenarios differ from responses to those same scenarios presented in a traditional static survey? In three experiments comparing responses given in conversational contexts with responses to traditional static surveys, we find no consistent evidence that responses differ in these different formats. This aligns with recent findings that various manipulations of reflectiveness have no effect on participants’ judgments (...) about philosophical scenarios. Although we did not find a consistent quantitative effect of format (conversation vs. static survey), conversational experiments still provide qualitative insights into debates about how participants are understanding (or misunderstanding) the scenarios they read in experimental studies, whether they are replacing difficult questions with questions that are more easily answered, and how participants are imagining the scenarios they read in ways that differ from what is explicitly stated by experimenters. We argue that conversational experiments—"Socratic questionnaires"—help show what is going on “under the hood” of traditional survey designs in the experimental investigation of philosophical questions. (shrink)

The Logic of Analogy is a study of the valid logical forms of qualitative and quantitative analogical argument, and the rules pertaining to them. It investigates equally valid conflicting arguments, statistics-based arguments and their utility in science, arguments from precedent used in law-making or law-application, and examines subsumption in analogical terms. Included for purposes of illustration is a large section on Talmudic use of analogical reasoning.

This study is about the Quality. Here I have dealt with the quality that differs significantly from the common understanding of quality /as determined quality/ that arise from the law of dialectics. This new quality is the quality of the quantity /quality of the quantitative changes/, noticed in philosophy by Plato as “quality of numbers”, and later developed by Hegel as “qualitative quantity. The difference between the known determined quality and qualitative quantity is evident in the exhibit form of (...) these two qualities. The exhibit form of the known determined quality from the law of dialectics /or it transformation/ is related with discreteness and abrupt changes. The exhibit form of the qualitative quantity /and it transformation/ is related with the continuity and gradual transition from one condition, to a different condition, without any abrupt changes. In my paper “Quality of the quantity”, I have argued that one of the most ancient implementation of quality of the number can be found in the dimensional mathematical model of point – line – surface – figure - introduced by Plato. The most whole presentation of the idea of quality of number in Plato is embeded in his teaching about the "eidical number". The quality of the quantity emerges as criteria for recognizing the difference between the eidical numbers and natural arithmetical number. The thesis concerning Plato is based on the The Unwritten Doctrine of Plato and one of the most original works in the history of philosophy written in the 20th century - “Arete bei Platon und Aristoteles” – “Arete in Plato and Aristotle” /Heidelberg 1959/ written by Hans Joachim Krämer. The new quality as the quality of the quantity /quality of the quantitative changes/, first noticed in philosophy by Plato as “quality of numbers” was developed in Hegel as “qualitative quantity”. Hegel proclaimed the Qualitative quantity, or Measure in the both of his Logics -The Science of Logic / the Greater Logic/ and The Lesser Logic/ Part One of the Encyclopedia of Philosophical Sciences: The Logic. In my paper I have offered the arguments that the concept of quality of the quantity should be enhanced with the adopted methodological approach of analogy with an implementation in the field of the Topology - Analysis Situs, developed by the Jules Henri Poincare. In the topology we could see homeomorphism as exhibit form of Quality on the Quantity. The explicit form of the quality of the quantity transformation is the continuous deformation – typically known in topology as homeomorphism. The concept of qualitative quantity is linked with the concept “structural stability” and nonequilibrum phase transition. The concept of structural stability is related with the topological homeomorphism. In his book “Synergetics: Introduction and Advanced Topics” /Springer, ISBN 3-540-40824/, in the Chapter 1.13. Qualitative Changes: General approach, p. 434-435, Hermann Haken explores and illustrate the structural stability with an example /figure 1.13, p.434/ given by of D'Arcy W. Thompson, the Scottish biologist, mathematician and classics scholar and pioneering mathematical biologist, Nobel Laureate in Medicine /1960/, the author of the book, On Growth and Form, /1917/. The quality of the quantity could be seen in the Herman Haken’s citation on the D'Arcy W. Thompson. My thesis is that the topological homeomorphism is the explicit form of the quality of the quantity transformation. The qualitative quantity change which becomes phenomenon, according to Émile Boutroux, is the subject of study in Cultural Phenomenology of Qualitative quantity. Our approach to this subject is Poincaré Model of the Subconscious Mind in Mathematics, which is the most suitable tool to unfold the arhetype of qualitative quantity. (shrink)