An adequate semantics for generic sentences must stake out positions across a range of contested territory in philosophy and linguistics. For this reason the study of generic sentences is a venue for investigating different frameworks for understanding human rationality as manifested in linguistic phenomena such as quantification, classification of individuals under kinds, defeasible reasoning, and intensionality. Despite the wide variety of semantic theories developed for generic sentences, to date these theories have been almost universally model-theoretic and representational. This essay outlines (...) a range of proof-theoretic analyses for characterizing generics. Particular attention is given to an expressivist proof-theory that can be traced to 1) work on logical syntax that Carnap undertook prior to his turn toward truth-conditional model theory in the late 1930s, and 2) research on sequent calculi and natural deduction systems that originate in work from Gentzen and Prawitz.1. (shrink)

The so-called materially valid inferences have come to new prominence through the work of Robert Brandom. This paper introduces a fragment of a logic of concepts that does not reduce concepts to their extensions. Concept logic and ist semantics allow us to represent the conceptual knowledge used in material inferences and thus suggests a way to deal with them.

Inferences from the absence of evidence to something are common in ordinary speech, but when used in scientific argumentations are usually considered deficient or outright false. Yet, as demonstrated here with the help of various examples, archaeologists frequently use inferences and reasoning from absence, often allowing it a status on par with inferences from tangible evidence. This discrepancy has not been examined so far. The article analyses it drawing on philosophical discussions concerning the validity of inference from absence, using (...) probabilistic models that were originally developed to show that such inferences are weak and inconclusive. The analysis reveals that inference from absence can indeed be justified in many important situations of archaeological research, such as excavations carried out to explore the past existence and time-span of sedentary human habitation. The justification is closely related to the fact that archaeology explores the human past via its material remains. The same analysis points to instances where inference from absence can have comparable validity in other historical sciences, and to research questions in which archaeological inference from absence will be problematic or totally unwarranted. (shrink)

Academic institutions migrated to modular teaching-learning amid the COVID-19 pandemic. To ensure the quality of the pedagogical innovations employed, the study determined the students’ evaluation of the faculty prepared instructional modules for the courses they enrolled in during the first and second semesters of Academic Year 2020-2021. Employing a descriptive-correlational research design, the study was participated by 644 students from three colleges who were then available during the data gathering. Data gathered through online surveys were then analyzed using descriptive statistics (...) and Spearman's rank correlation coefficient utilizing jamovi software. Results revealed that the faculty-prepared instructional modules were acceptable and satisfactory to the students. Besides, the students' evaluation of the instructional modules was positively related to their level of satisfaction. Still, the students recommended that a review of the modules be done before sending the modules; a more extended time allotment is considered, and sufficient concrete examples are given in the modules. With this, the faculty concerned are encouraged to review the phases involved in the design, development, and distribution of the instructional modules to make them highly acceptable and very satisfactory to the students while maintaining the quality of both the content and aesthetics of the learning materials. Considering the study’s limitations, further endeavors may be carried out to validate this pedagogical innovation. (shrink)

Inferentialism is a theory in the philosophy of language which claims that the meanings of expressions are constituted by inferential roles or relations. Instead of a traditional model-theoretic semantics, it naturally lends itself to a proof-theoretic semantics, where meaning is understood in terms of inference rules with a proof system. Most work in proof-theoretic semantics has focused on logical constants, with comparatively little work on the semantics of non-logical vocabulary. Drawing on Robert Brandom’s notion of material inference (...) and Greg Restall’s bilateralist interpretation of the multiple conclusion sequent calculus, I present a proof-theoretic semantics for atomic sentences and their constituent names and predicates. The resulting system has several interesting features: (1) the rules are harmonious and stable; (2) the rules create a structure analogous to familiar model-theoretic semantics; and (3) the semantics is compositional, in that the rules for atomic sentences are determined by those for their constituent names and predicates. (shrink)

In his recent book, John Norton has created a theory of inference to the best explanation, within the context of his "material theory of induction". I apply it to the problem of scientific explanations that are false: if we want the theories in our explanations to be true, then why do historians and scientists often say that false theories explained phenomena? I also defend Norton's theory against some possible objections.

The paper defends a variant of the material implication approach to the meaning of conditional sentences against some arguments that are considered to be widely subscribed to and/or important in the philosophical, psychological and linguistic literature. These arguments are shown to be wrong, debatable, or to miss their aim if the truth conditions defining material implication are viewed as determining nothing but the denotation of conditional sentences and if the function of conditional sentences in deduction (logic) is focused (...) on rather than in inferencing (reasoning). It is shown that some ‘paradoxes of material implication’ are due to inconsistent premises of deductions introduced by semantic relations between clauses constituting the premises, a fact which does not invalidate the approach. Other ‘paradoxes’ are shown to arise because they are based on uninformative deductions, violating a basic pragmatic principle. In addition, the paper introduces the distinction between the set of possible states of a mental model of the actual world and of alternative worlds. It is argued that material implication determines the denotation of an indicative conditional as a subset of the former set and the denotation of a subjunctive conditional as a subset of the latter set, thus unifying these two types of conditionals. (shrink)

The chapter outlines an abstract theoretical framework that is currently (re-)emerging in the course of a theoretical convergence of several disciplines. In the first section, the fundamental problem of perception theory is formulated, namely, the generation, by the perceptual system, of meaningful categories from physicogeometric energy patterns. In the second section, it deals with basic intuitions and assumptions underlying what can be regarded as the current Standard Model of Perceptual Psychology and points out why this model is profoundly inadequate for (...) dealing with the fundamental problem of perception theory. In the third section, it discusses a level of analysis that promises to be fruitful for dealing, in conformity with established procedures of the natural sciences, with the problem of perceptual “meaning” and the problem of what constitutes a “perceptual object.” In the fourth section, it outlines a theoretical perspective on basic principles of the perceptual system which centers on the notions of complex data types and conceptual forms, and draws an entirely different theoretical picture of the role of the sensory input than traditional accounts. The final section focusses on the issue of material qualities and discusses, within the general theoretical framework outlined, some observations and results on the perception of certain material properties, namely, lustrous and glassy appearances. (shrink)

I argue against the skeptical epistemological view exemplified by the Groarkes that “all theories of informal argument must face the regress problem.” It is true that in our theoretical representations of reasoning, infinite regresses of self-justification regularly and inadvertently arise with respect to each of the RSA criteria for argument cogency (the premises are to be relevant, sufficient, and acceptable). But they arise needlessly, by confusing an RSA criterion with argument content, usually premise material.

Sometimes we love and hate the same thing at the same time. Margaret Cavendish (1623-1673)—the maverick early modern materialist—appeals to this type of passionate conflict to argue that the mind is a material thing. When our passions conflict, the mind or reason conflicts with itself. From this Cavendish infers that the mind has parts and, therefore, is material. Cavendish says this argument is among the best proofs of the mind’s materiality. And yet, the existing scholarship on Cavendish lacks (...) the kind of detailed reconstruction required to evaluate this argument’s merits. In this paper, I provide just such a reconstruction. I also show that Cavendish’s argument is an effective intervention in her dispute with René Descartes and Henry More about the (im)materiality of the mind. (shrink)

Aristotle presents four causes in Posterior Analytics 2.11, but where we expect matter we find instead the confusing formula, ‘what things being the case, necessarily this is the case’, and an equally confusing example. Some commentators infer that Aristotle is not referring to matter, others that he is but in a non-standard way. I argue that APo. 94a20-34 presents not matter, but determination by general features or facts, including facts about something’s genus. The closest connection to matter is Aristotle’s view (...) that the relation between genus and species is analogous to that between matter and a hylomorphic compound. (shrink)

According to John D. Norton's Material Theory of Induction, all inductive inferences are justified by local facts, rather than their formal features or some grand principles of nature's uniformity. Recently, Richard Dawid (Found Phys 45(9):1101–1109, 2015) has offered a challenge to this theory: in an adaptation of Norton's own celebrated "Dome" thought experiment, it seems that there are certain inductions that are intuitively reasonable, but which do not have any local facts that could serve to justify them in accordance (...) with Norton's requirements. Dawid's suggestion is that “raw induction” might have a limited but important role for such inferences. I argue that the Material Theory can accommodate such inductions, because there are local facts concerning the combinatoric features of the induction’s target populations that can licence the inferences in an analogous way to existing examples of material induction. Since my arguments are largely independent of the details of the Dome, Norton's theory emerges as surprisingly robust against criticisms of excessive narrowness. (shrink)

This paper concerns the recent revival of entity realism. Having been started with the work of Ian Hacking, Nancy Cartwright and Ronald Giere, the project of entity realism has recently been developed by Matthias Egg, Markus Eronen, and Bence Nanay. The paper opens a dialogue among these recent views on entity realism and integrates them into a more advanced view. The result is an epistemological criterion for reality: the property-tokens of a certain type may be taken as real insofar as (...) only they can be materially inferred from the evidence obtained in a variety of independent ways of detection. (shrink)

We focus on issues of learning assessment from the point of view of an investigation of philosophical elements in teaching. We contend that assessment of concept possession at school based on ordinary multiple-choice tests might be ineffective because it overlooks aspects of human rationality illuminated by Robert Brandom’s inferentialism––the view that conceptual content largely coincides with the inferential role of linguistic expressions used in public discourse. More particularly, we argue that multiple-choice tests at schools might fail to accurately assess the (...) possession of a concept or the lack of it, for they only check the written outputs of the pupils who take them, without detecting the inferences actually endorsed or used by them. We suggest that school tests would acquire reliability if they enabled pupils to make the reasons of their answers or the inferences they use explicit, so as to contribute to what Brandom calls the game of giving and asking for reasons. We explore the possibility to put this suggestion into practice by deploying two-tier multiple-choice tests. (shrink)

Inferentialism, especially Brandom’s theory, is the project aimed at understanding meaning as determined by inferences, and language as a social practice governed by rational discursive norms. Discursive practice is thus understood as the basic rational practice, where commitments undertaken by participants are evaluated in terms of their being correct/incorrect. This model of explanation is also intended to rescue, by means of reasons, the commitments we undertake ourselves and assess the commitments we attribute to others, in an objective sense: starting from (...) our subjective normative and doxastic attitudes we should be able to use the normative discursive resources apt to assess our commitments, not only referring to what we take to be correct, but also referring to how things actually are.My hypothesis is that this objectivity is not achieved only on the basis of the rational structure of discursive practice. The main worry concerns the fact that material inferences, those responsible for the content of our concepts (and commitments), are in general non-monotonic. These inferences put experts in an advantageous position,namely as those capable of defeasible reasoning. I propose a view by which this asymmetry among language users is the crucial factor in assessing the objectivity of claims within discursive practice. (shrink)

This paper advances an approach to relevance grounded on patterns of material inference called argumentation schemes, which can account for the reconstruction and the evaluation of relevance relations. In order to account for relevance in different types of dialogical contexts, pursuing also non-cognitive goals, and measuring the scalar strength of relevance, communicative acts are conceived as dialogue moves, whose coherence with the previous ones or the context is represented as the conclusion of steps of material inferences. Such (...) inferences are described using argumentation schemes and are evaluated by considering 1) their defeasibility, and 2) the acceptability of the implicit premises on which they are based. The assessment of both the relevance of an utterance and the strength thereof depends on the evaluation of three interrelated factors: 1) number of inferential steps required; 2) the types of argumentation schemes involved; and 3) the implicit premises required. (shrink)

The aim of this paper is to address a longstanding concern about the linguistic ‘relativ- ity’ of ontological categories, and resulting limitations in the scope of ontological theo- ries. Given recent evidence on the influence of language on cognitive dispositions, do we have empirical reasons to doubt that there are ontological categories that have uni- versal scope across languages? I argue that this is the case, at least if we retain the stan- dard ‘inferential’ approach within analytical ontology, i.e., if (...) we evaluate ontological interpretations of L-sentences relative to certain material inferences in L. Research in linguistic typology suggests that types of entities postulated for the domain of Indo- European languages cannot capture the ontological commitments of the (much larger group of) non-Indo-European languages. Ontological category theory thus seems to have three options. The first option is to abandon the standard ‘inferential’ approach to ontological category theory. Alternatively, if we stay with the inferential approach, we face the following choice. Either ontology must let go of its ambitions to provide general domain descriptions for any language and settle for the more modest project of reconstructing the ontological commitments of a group of natural languages. Or else analytical ontologists should turn to linguistic typology in order to accommodate the diversity of inferential structures embedded in natural languages. I recommend and ex- plore this third option, illustrating a strategy for how to construct a domain theory that can be used across languages. In a first step I show how linguistic research on the se- mantics of verbs and nouns (studies on so-called “Aktionsarten” and “Seinsarten”) can be used to identify the inferential patterns of ten basic concepts of modes of existence in time and space. In a second step I show how these inferential data can be inter- preted ontologically within General Process Theory, an ontological framework based on nonparticular individuals (“dynamics”). -/- . (shrink)

By a reasoned change in logic I mean a change in the logic with which you make inferences that is based on your evidence. An argument sourced in recently published material Kripke lectured on in the 1970s, and dubbed the Adoption Problem by Birman (then Padró) in her 2015 dissertation, challenges the possibility of reasoned changes in logic. I explain why evidentialists should be alarmed by this challenge, and then I go on to dispel it. The Adoption Problem rests (...) on a failure to distinguish between logical principles such as Universal Instantiation and Modus Ponens which might or might not govern your inferences with superficially similar laws which must govern your cognitive architecture. (shrink)

This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The probability bounds imposed (...) by the premises on the conclusion are derived on the basis of a few trivial principles such as "a part of the tank cannot contain more liquid than its capacity allows", or "if a part is empty, the other part contains all the liquid". This stems from the equivalence between the physical constraints imposed by the capacity of the tank and its subdivisions on the volumes of liquid, and the axioms and rules of probability. The device materializes de Finetti's coherence approach to probability. It also suggests a physical counterpart of Dutch book arguments to assess individuals' rationality in probability judgments in the sense that individuals whose degrees of belief in a conclusion are out of the bounds of coherence intervals would commit themselves to executing physically impossible tasks. (shrink)

This paper argues that two widely accepted principles about the indicative conditional jointly presuppose the falsity of one of the most prominent arguments against epistemological iteration principles. The first principle about the indicative conditional, which has close ties both to the Ramsey test and the “or‐to‐if” inference, says that knowing a material conditional suffices for knowing the corresponding indicative. The second principle says that conditional contradictions cannot be true when their antecedents are epistemically possible. Taken together, these principles (...) entail that it is impossible to be in a certain kind of epistemic state: namely, a state of ignorance about which of two partially overlapping bodies of knowledge corresponds to one's actual one. However, some of the more popular “margin for error” style arguments against epistemological iteration principles suggest that such states are not only possible, but commonplace. I argue that the tension between these views runs deep, arising just as much for non‐factive attitudes like belief, presupposition, and certainty. I also argue that this is worse news for those who accept the principles about the indicative conditional than it is for those who reject epistemological iteration principles. (shrink)

A ‘vestigial social practice' is a norm, convention, or social behavior that persists even when few endorse it or its original justifying rationale. Begby (2021) explores social explanations for the persistence of prejudice, arguing that even if we all privately disavow a stereotype, we might nevertheless continue acting as if it is true because we believe that others expect us to. Meanwhile the persistence of the practice provides something like implicit testimonial evidence for the prejudice that would justify it, making (...) it rational for members of the next generation to acquire the corresponding prejudiced beliefs. This paper distinguishes between three different types of vestigial social practice in terms of the underlying explanatory mechanisms, and argues that the persistence of prejudicial social stereotypes is most tightly linked not to others’ beliefs or expectations, but to the ways that material infrastructure constrains options shapes social outcomes. Given that, the persistence of a practice only provides grounds to infer that most people endorse the corresponding prejudiced belief only if we are in a position to dismiss relevant alternative explanations. (shrink)

Brogaard and Salerno (2008) argued that counter-examples to contraposition, strengthening the antecedent, and hypothetical syllogism involving subjunctive conditionals only seem to work because they involve a contextual fallacy where the context assumed in the premise(s) is illicitly shifted in the conclusion. To avoid such counter-examples they have proposed that the context must remain fixed when evaluating an argument for validity. That is the Brogaard-Salerno Stricture. Tristan Haze (2016), however, has recently objected that intuitively valid argumentative forms such as conjunction introduction (...) do not satisfy this constraint. This paper has two goals. First, it argues that the Brogaard-Salerno Stricture is not violated in Haze’s putative counter-example. Second, it argues that since this stricture blocks the usual counter-examples to instances of classical argumentative forms that involve indicative or subjunctive conditionals, it is reasonable to infer that indicative and subjunctive conditionals are material. (shrink)

This paper is a response to Anthony Brueckner's critique of my essay "The Self-Defeating Character of Skepticism," which appeared in Philosophy and Phenomenological Research in 1992. In this reply I contend that the three main avenues by which one might plausibly account for one's self-awareness are unavailable to an individual who is restricted to the skeptic's epistemic ground rules. First, all-encompassing doubt about the world cancels our "external" epistemic access via perception to ourselves as material individuals in the world. (...) Second, one does not have direct cpistemic access to one's substantial self through introspection, since the self as such is not a proper object of inner awareness. Third, we cannot claim, as Descartes did, that we have indirect epistemic access to the substantial self by inference from the occurrence of experiences.The summary conclusion for which I argue is that, if we are to account for our self-knowledge, we cannot adopt the purely subjective epistemological stance that is at the heart of global skepticism. (shrink)

Naive observers viewed a sequence of colored Mondrian patterns, simulated on a color monitor. Each pattern was presented twice in succession, first under one daylight illuminant with a correlated color temperature of either 16,000 or 4,000 K and then under the other, to test for color constancy. The observers compared the central square of the pattern across illuminants, either rating it for sameness of material appearance or sameness of hue and saturation or judging an objective property—that is, whether its (...) change of color originated from a change in material or only from a change in illumination. Average color constancy indices were high for material appearance ratings and binary judgments of origin and low for hue–saturation ratings. Individuals’ performance varied, but judgments of material and of hue and saturation remained demarcated. Observers seem able to separate phenomenal percepts from their ontological projections of mental appearance onto physical phenomena; thus, even when a chromatic change alters perceived hue and saturation, observers can reliably infer the cause, the constancy of the underlying surface spectral reflectance. (shrink)

While the term “reactivity” has come to be associated with specific phenomena in the social sciences, having to do with subjects’ awareness of being studied, this paper takes a broader stance on this concept. I argue that reactivity is a ubiquitous feature of the psychological subject matter and that this fact is a precondition of experimental research, while also posing potential problems for the experimenter. The latter are connected to the worry about distorted data and experimental artifacts. But what are (...) experimental artifacts and what is the most productive way of dealing with them? In this paper, I approach these questions by exploring the ways in which experimenters in psychology simultaneously exploit and suppress the reactivity of their subject matter in order to produce experimental data that speak to the question or subject matter at hand. Highlighting the artificiality of experimental data, I raise the question of what distinguishes a genuine experimental result from an experimental artifact. My analysis construes experimental results as the outcomes of inferences from the data that take material background assumptions as auxiliary premises. Artifacts occur when one or more of these background assumptions are false, such that the data do not reliably serve the purposes they were generated for. I conclude by laying out the ways in which my analysis of data quality is relevant to, and informed by, recent debates about the replicability of experimental results. (shrink)

Thirteen meanings of 'implication' are described and compared. Among them are relations that have been called: logical implication, material implication,deductive implication, formal implication, enthymemic implication, and factual implication. In a given context, implication is the homogeneous two-place relation expressed by the relation verb 'implies'. For heuristic and expository reasons this article skirts many crucial issues including use-mention, the nature of the entities that imply and are implied, and the processes by which knowledge of these relations are achieved. This paper (...) is better thought of as an early stage of a dialogue than as a definitive treatise. (shrink)

I offer a meta-level analysis of realist arguments for the reliability of ampliative reasoning about the unobservable. We can distinguish form-driven and content-driven arguments for realism: form-driven arguments appeal to the form of inductive inferences, whilst content-driven arguments appeal to their specific content. After regimenting the realism debate in these terms, I will argue that the content-driven arguments are preferable. Along the way I will discuss how my analysis relates to John Norton’s recent, more general thesis that the grounds for (...) licit induction are always material. (shrink)

A recent surge of work on prediction-driven processing models--based on Bayesian inference and representation-heavy models--suggests that the material basis of conscious experience is inferentially secluded and neurocentrically brain bound. This paper develops an alternative account based on the free energy principle. It is argued that the free energy principle provides the right basic tools for understanding the anticipatory dynamics of the brain within a larger brain-body-environment dynamic, viewing the material basis of some conscious experiences as extensive--relational and (...) thoroughly world-involving. (shrink)

● Any given placement (e.g. Sun in Taurus; Mars in Capricorn; Mercury in the third house) is necessarily common to tens of thousands of people. Saturn in the ninth house, for example, will not behave the same or produce the same effects in the twenty or one hundred charts in which we find it there. In each case Saturn will behave in accordance with the rest of the astrographic/chart composition (as if we stayed in the same hotel in different epochs (...) or different people contracted the same disease; our stay will be different each time, according to the epoch, and each person’s symptoms will too, be different, according to their individual biochemistry; not to mention that each chart or astrography, like each genetic code or sequence, is unrepeatable). Certainly, “no planet can produce, on its own, what only the combined or concerted action of all can” (BUSTAMANTE, 2023, SPICA magazine, pp. 93-111). Hence the synergistic nature of the interpretative exercise (i.e., the whole is greater than all its parts). The fundamental component of the mathematical expression of the interpretive exercise is: astrological triangulation, the functional denomination for what we know as synthesis (WEISS, 1946; LEO, 1983, HAND, 1981). In order to demonstrate its usefulness, as well as the convenience of its mathematical expression, we have chosen two individuals (JEFFREY DAHMER, STEVEN SPIELBERG) whose astrographies do not—according to the community—explain their lives. The rest of the astrographies correspond to those of serial killers JOHN WAYNE GACY, DAVID CARPENTER, and TED BUNDY. ● We explain, by means of algebraic notations, the synthesis and the functional values that make up the synthesis. ● We take the Moon and Neptune as relevant bodies for the purpose of diagnosing or studying endocrine or neurohormonal issues, and Mars, Pluto, and Saturn as relevant planets for the purpose of inferring violence or sinister behaviour, upon the case, and quadratures or oppositions—and conjunctions—between Venus and the Moon, the Moon and Neptune, and the Sun or Venus and Neptune or Uranus as indicators of neurohormonal disorders and/or sexual deviance (APA definition) . ● We consider quadratures (90º) or oppositions (180º)—and conjunctions—between Mercury or the Moon and Saturn, or between Mars or the Moon and Saturn, Uranus, Neptune, and/or Pluto as powerful indications of violence or mental disorders, upon the case. ● We have also regarded Sagittarius as a sign as expansive and abundant as its ruler, Jupiter, according to the best of its characterisations (or as an exceptionally swift and wild sign, according to other characterisations), and the fifth region of a natal chart as one closely related to fortune in a broad sense (material and immaterial). ● Because we advocate the idea that orbs should be predicated of the planet (size, speed), not the aspect itself, the gas giants (Jupiter, Saturn, Uranus, and Neptune) and the Sun have been granted up to 10º of orb (or 12º, in the case of broad influence ). We understand aspectual relationships as angular relationships held between two or more celestial bodies placed in signs with at least one property in common (according to our molecular theory of the ecliptic, compatible with the optical theory of the aspects from the Hellenistic tradition). (shrink)

We introduce the notion of complexity, first at an intuitive level and then in relatively more concrete terms, explaining the various characteristic features of complex systems with examples. There exists a vast literature on complexity, and our exposition is intended to be an elementary introduction, meant for a broad audience. -/- Briefly, a complex system is one whose description involves a hierarchy of levels, where each level is made of a large number of components interacting among themselves. The time evolution (...) of such a system is of a complex nature, depending on the interactions among subsystems in the next level below the one under consideration and, at the same time, conditioned by the level above, where the latter sets the context for the evolution. Generally speaking, the interactions among the constituents of the various levels lead to a dynamics characterized by numerous characteristic scales, each level having its own set of scales. What is more, a level commonly exhibits ‘emergent properties’ that cannot be derived from considerations relating to its component systems taken in isolation or to those in a different contextual setting. In the dynamic evolution of some particular level, there occurs a self-organized emergence of a higher level and the process is repeated at still higher levels. -/- The interaction and self-organization of the components of a complex system follow the principle commonly expressed by saying that the ‘whole is different from the sum of the parts’. In the case of systems whose behavior can be expressed mathematically in terms of differential equations this means that the interactions are nonlinear in nature. -/- While all of the above features are not universally exhibited by complex systems, these are nevertheless indicative of a broad commonness relative to which individual systems can be described and analyzed. There exist measures of complexity which, once again, are not of universal applicability, being more heuristic than exact. The present state of knowledge and understanding of complex systems is itself an emerging one. Still, a large number of results on various systems can be related to their complex character, making complexity an immensely fertile concept in the study of natural, biological, and social phenomena. -/- All this puts a very definite limitation on the complete description of a complex system as a whole since such a system can be precisely described only contextually, relative to some particular level, where emergent properties rule out an exact description of more than one levels within a common framework. -/- We discuss the implications of these observations in the context of our conception of the so-called noumenal reality that has a mind-independent existence and is perceived by us in the form of the phenomenal reality. The latter is derived from the former by means of our perceptions and interpretations, and our efforts at sorting out and making sense of the bewildering complexity of reality takes the form of incessant processes of inference that lead to theories. Strictly speaking, theories apply to models that are constructed as idealized versions of parts of reality, within which inferences and abstractions can be carried out meaningfully, enabling us to construct the theories. -/- There exists a correspondence between the phenomenal and the noumenal realities in terms of events and their correlations, where these are experienced as the complex behavior of systems or entities of various descriptions. The infinite diversity of behavior of systems in the phenomenal world are explained within specified contexts by theories. The latter are constructs generated in our ceaseless attempts at interpreting the world, and the question arises as to whether these are reflections of `laws of nature' residing in the noumenal world. This is a fundamental concern of scientific realism, within the fold of which there exists a trend towards the assumption that theories express truths about the noumenal reality. We examine this assumption (referred to as a ‘point of view’ in the present essay) closely and indicate that an alternative point of view is also consistent within the broad framework of scientific realism. This is the view that theories are domain-specific and contextual, and that these are arrived at by independent processes of inference and abstractions in the various domains of experience. Theories in contiguous domains of experience dovetail and interpenetrate with one another, and bear the responsibility of correctly explaining our observations within these domains. -/- With accumulating experience, theories get revised and the network of our theories of the world acquires a complex structure, exhibiting a complex evolution. There exists a tendency within the fold of scientific realism of interpreting this complex evolution in rather simple terms, where one assumes (this, again, is a point of view) that theories tend more and more closely to truths about Nature and, what is more, progress towards an all-embracing ‘ultimate theory’ -- a foundational one in respect of all our inquiries into nature. We examine this point of view closely and outline the alternative view -- one broadly consistent with scientific realism -- that there is no ‘ultimate’ law of nature, that theories do not correspond to truths inherent in reality, and that successive revisions in theory do not lead monotonically to some ultimate truth. Instead, the theories generated in succession are incommensurate with each other, testifying to the fact that a theory gives us a perspective view of some part of reality, arrived at contextually. Instead of resembling a monotonically converging series successive theories are analogous to asymptotic series. -/- Before we summarize all the above considerations, we briefly address the issue of the complexity of the {\it human mind} -- one as pervasive as the complexity of Nature at large. The complexity of the mind is related to the complexity of the underlying neuronal organization in the brain, which operates within a larger biological context, its activities being modulated by other physiological systems, notably the one involving a host of chemical messengers. The mind, with no materiality of its own, is nevertheless emergent from the activity of interacting neuronal assemblies in the brain. As in the case of reality at large, there can be no ultimate theory of the mind, from which one can explain and predict the entire spectrum of human behavior, which is an infinitely rich and diverse one. (shrink)

There are no established conventions for, and few examples of, indexing visual material on the basis of its form. Most image databases use keywords to describe the form or function, and access data by text-based retrieval of these keywords. An image-based approach would order the data by appearance, e.g. Shepherd (1971) and Dreyfuss (1972). A taxonomy must be created in order to apply this technique to a new data set. Previous applications have been aided by certain limiting factors on (...) the possible range of images indexed thus providing the key to a taxonomy, e.g. international pictorial signs in Dreyfuss. A fundamental principle which may be inferred from these studies is that the taxonomy needs to be related to the needs of the user, and not solely to abstract features of design. This is reflected in guidelines issued by the UK organisation The Society of Indexers. The studies also suggest the need for several approaches to classification within the same data set, e.g Dreyfuss, in which signs are located under more than one heading. (shrink)

Unger has recently argued that if you are the only thinking and experiencing subject in your chair, then you are not a material object. This leads Unger to endorse a version of Substance Dualism according to which we are immaterial souls. This paper argues that this is an overreaction. We argue that the specifically Dualist elements of Unger’s view play no role in his response to the problem; only the view’s structure is required, and that is available to Unger’s (...) opponents. We outline one such non-Dualist view, suggest how to resolve the dispute, respond to some objections, and argue that ours is but one of many views that survive Unger’s challenge. All these views are incompatible with microphysicalism. So Unger’s discussion does contain an insight: if you are the only conscious subject in your chair, then microphsyicalism is false. Unger’s mistake was to infer Substance Dualism from this; for microphysicalism is not the only alternative to Dualism. (shrink)

In the first of the Insolubles in Chapter 8 of his Sophismata, Buridan contends that the inference Omnis propositio est affirmativa; ergo, nulla propositio est negativa (PS) is valid, even though it appeals to the self-reference in the conclusion to show that what we (following Read 2001) call the classical conception of validity (CCV) fails. This requires that we accept that there are good inferences in which a false conclusion follows from true premises. Partially following Hughes’ proposal (1982), we (...) argue that the First Sophism (PS) involves three different notions of validity. Two of them correspond to the ones described by Hughes (1982, 80–86), who calls them Theory A and Theory B. The third one—that will we call Theory C—is not mentioned by Hughes; instead, it is suggested by Buridan himself in the first three arguments in favor of the validity of PS. We show that: a) from what Buridan says in his Theory C it follows that PS is a formal and material consequence, and hence, a valid one. Then we show that: b) the rejection of CCV and the acceptance of Nulla propositio est negativa (NPN) as a (formal) consequence of Omnis propositio est affirmativa (OPA) leads to a paradox that bears similarities with the one put forward by Pseudo Scotus—which has been studied by Read (2001) and is related to Curry’s paradox. However, there are enough differences to merit considering this paradox separately, especially in relation to the so-called validity paradoxes. Interestingly, our work suggests that Buridan was aware of these problems, which explains why he introduced a new criterion for validity, one that is not based on truth-preservation but on what Spade (1988) calls firmness, and Klima (2016) correspondence. (shrink)

What the world needs now is another theory of vagueness. Not because the old theories are useless. Quite the contrary, the old theories provide many of the materials we need to construct the truest theory of vagueness ever seen. The theory shall be similar in motivation to supervaluationism, but more akin to many-valued theories in conceptualisation. What I take from the many-valued theories is the idea that some sentences can be truer than others. But I say very different things to (...) the ordering over sentences this relation generates. I say it is not a linear ordering, so it cannot be represented by the real numbers. I also argue that since there is higher-order vagueness, any mapping between sentences and mathematical objects is bound to be inappropriate. This is no cause for regret; we can say all we want to say by using the comparative truer than without mapping it onto some mathematical objects. From supervaluationism I take the idea that we can keep classical logic without keeping the familiar bivalent semantics for classical logic. But my preservation of classical logic is more comprehensive than is normally permitted by supervaluationism, for I preserve classical inference rules as well as classical sequents. And I do this without relying on the concept of acceptable precisifications as an unexplained explainer. The world does not need another guide to varieties of theories of vagueness, especially since Timothy Williamson (1994) and Rosanna Keefe (2000) have already provided quite good guides. I assume throughout familiarity with popular theories of vagueness. (shrink)

Picturing is a poorly understood element of Sellars’s philosophical project. We diagnose the problem with picturing as follows: on the one hand, it seems that it must be connected with action in order for it to do its job. On the other hand, the representational states of a picturing system are characterized in descriptive and seemingly static terms. How can static terms be connected with action? To solve this problem, we adopt a concept from recent work in Sellarsian metaethics: the (...) idea of a material practical inference, which (we argue) features centrally in how we picture. The key distinction is that the picturing of nonhuman animals involves only Humean material practical inference, in which representational states are corrected only by feedback from the environment and not from discursive interactions. The resulting view shows that Sellars’s contributions to practical philosophy (especially theory of action and metaethics) cannot be separated from his contributions to philosophy of mind, language, and cognitive science. Further, the view makes it clear that picturing is neither a version of the Given, nor is it a fifth wheel to inferential role in explaining representation, but is essential to Sellars’s model of how animals—including humans—represent their environment. (shrink)

Contemporary reasoning about health is infused with the work products of experts, and expert reasoning about health itself is an active site for invention and design. Building on Toulmin’s largely undeveloped ideas on field-dependence, we argue that expert fields can develop new inference rules that, together with the backing they require, become accepted ways of drawing and defending conclusions. The new inference rules themselves function as warrants, and we introduce the term “warranting device” to refer to an assembly (...) of the rule plus whatever material, procedural, and institutional resources are required to assure its dependability. We present a case study on the Cochrane Review, a new method for synthesizing evidence across large numbers of scientific studies. After reviewing the evolution and current structure of the device, we discuss the distinctive kinds of critical questions that may be raised around Cochrane Reviews, both within the expert field and beyond. Although Toulmin’s theory of field-dependence is often criticized for its relativism, we find that, as a matter of practical fact, field-specific warrants do not enjoy immunity from external critique. On the contrary, they can be opened to evaluation and critique from any interested perspective. (shrink)

The semantics of our event talk is a complex affair. What is it that we are talking about when we speak of Brutus’s stabbing of Caesar? Exactly where and when did it take place? Was it the same event as the killing of Caesar? Some take questions such as these to be metaphysical questions. I think they are questions of semantics—questions about the way we talk and about what we mean. And I think that this conflict between metaphysic and semantic (...) concerns is indicative of a “deep indeterminacy” (Bennett’s phrase) in our event concept. We do talk about events; but what events a statement is about is not something that can be inferred from the event names we use; it depends heavily (more heavily than with ordinary material objects) on local context and unprincipled intuitions. This paper illustrates this view in connection with two examples: the phenomenon of vagueness and the dispute over identity statements. (shrink)

This dissertation is devoted to empirically contrasting the Suppositional Theory of conditionals, which holds that indicative conditionals serve the purpose of engaging in hypothetical thought, and Inferentialism, which holds that indicative conditionals express reason relations. Throughout a series of experiments, probabilistic and truth-conditional variants of Inferentialism are investigated using new stimulus materials, which manipulate previously overlooked relevance conditions. These studies are some of the first published studies to directly investigate the central claims of Inferentialism empirically. In contrast, the Suppositional Theory (...) of conditionals has an impressive track record through more than a decade of intensive testing. The evidence for the Suppositional Theory encompasses three sources. Firstly, direct investigations of the probability of indicative conditionals, which substantiate “the Equation” (P(if A, then C) = P(C|A)). Secondly, the pattern of results known as “the defective truth table” effect, which corroborates the de Finetti truth table. And thirdly, indirect evidence from the uncertain and-to-if inference task. Through four studies each of these sources of evidence are scrutinized anew under the application of novel stimulus materials that factorially combine all permutations of prior and relevance levels of two conjoined sentences. The results indicate that the Equation only holds under positive relevance (P(C|A) – P(C|¬A) > 0) for indicative conditionals. In the case of irrelevance (P(C|A) – P(C|¬A) = 0), or negative relevance (P(C|A) – P(C|¬A) < 0), the strong relationship between P(if A, then C) and P(C|A) is disrupted. This finding suggests that participants tend to view natural language conditionals as defective under irrelevance and negative relevance (Chapter 2). Furthermore, most of the participants turn out only to be probabilistically coherent above chance levels for the uncertain and-to-if inference in the positive relevance condition, when applying the Equation (Chapter 3). Finally, the results on the truth table task indicate that the de Finetti truth table is at most descriptive for about a third of the participants (Chapter 4). Conversely, strong evidence for a probabilistic implementation of Inferentialism could be obtained from assessments of P(if A, then C) across relevance levels (Chapter 2) and the participants’ performance on the uncertain-and-to-if inference task (Chapter 3). Yet the results from the truth table task suggest that these findings could not be extended to truth-conditional Inferentialism (Chapter 4). On the contrary, strong dissociations could be found between the presence of an effect of the reason relation reading on the probability and acceptability evaluations of indicative conditionals (and connate sentences), and the lack of an effect of the reason relation reading on the truth evaluation of the same sentences. A bird’s eye view on these surprising results is taken in the final chapter and it is discussed which perspectives these results open up for future research. (shrink)

In §12 of his 1837 magnum opus, the Wissenschaftslehre, Bolzano remarks that “In the new logic textbooks one reads almost constantly that ‘in logic one must consider not the material of thought but the mere form of thought, for which reason logic deserves the title of a purely formal science’” (WL §12, 46).1 The sentence Bolzano quotes is his own summary of others’ philosophical views; he goes on to cite Jakob, Hoffbauer, Metz, and Krug as examples of thinkers who (...) held that logic abstracts from the matter of thought and considers only its form. Although Bolzano does not mention Kant by name here, Kant does of course hold that “pure general logic”, what Bolzano would consider logic in the traditional sense (the theory of propositions, representations, inferences, etc.), is formal. As Kant remarks in the Introduction to the 2nd edition of Kritik der reinen Vernunft , (pure general) logic is “justified in abstracting – is indeed obliged to abstract – from all objects of cognition and all of their differences; and in logic, therefore, the understanding has to do with nothing further than itself and its own form” (KrV, Bix).2. (shrink)

One’s constitution—whether one is generous or miserly, temperate or intemperate, kind or mean, etc.—is beyond one’s control in significant respects. Yet one’s constitution affects how one acts. And how one acts affects one’s moral standing. The counterintuitive inference—the so-called problem of constitutive moral luck—is that one’s moral standing is, to some significant extent, beyond one’s control. This article grants the premises but resists the inference. It argues that one’s constitution should have no net impact on one’s moral standing. (...) While a bad constitution lowers the chance that one will act morally, it offers significant gains to moral standing should that chance materialize. A good constitution increases one’s chance of performing good acts but for correspondingly more modest gains. This effect should smooth out, and possibly eliminate, the expected impact of constitution on moral standing. (shrink)

Many epistemologists hold that an agent can come to justifiably believe that p is true by seeing that it appears that p is true, without having any antecedent reason to believe that visual impressions are generally reliable. Certain reliabilists think this, at least if the agent’s vision is generally reliable. And it is a central tenet of dogmatism (as described by Pryor (2000) and Pryor (2004)) that this is possible. Against these positions it has been argued (e.g. by Cohen (2005) (...) and White (2006)) that this violates some principles from probabilistic learning theory. To see the problem, let’s note what the dogmatist thinks we can learn by paying attention to how things appear. (The reliabilist says the same things, but we’ll focus on the dogmatist.) Suppose an agent receives an appearance that p, and comes to believe that p. Letting Ap be the proposition that it appears to the agent that p, and → be the material implication, we can say that the agent learns that p, and hence is in a position to infer Ap → p, once they receive the evidence Ap.1 This is surprising, because we can prove the following. (shrink)

There is widespread recognition at universities that a proper understanding of science is needed for all undergraduates. Good jobs are increasingly found in fields related to Science, Technology, Engineering, and Medicine, and science now enters almost all aspects of our daily lives. For these reasons, scientific literacy and an understanding of scientific methodology are a foundational part of any undergraduate education. Recipes for Science provides an accessible introduction to the main concepts and methods of scientific reasoning. With the help of (...) an array of contemporary and historical examples, definitions, visual aids, and exercises for active learning, the textbook helps to increase students’ scientific literacy. The first part of the book covers the definitive features of science: naturalism, experimentation, modeling, and the merits and shortcomings of both activities. The second part covers the main forms of inference in science: deductive, inductive, abductive, probabilistic, statistical, and causal. The book concludes with a discussion of explanation, theorizing and theory-change, and the relationship between science and society. The textbook is designed to be adaptable to a wide variety of different kinds of courses. In any of these different uses, the book helps students better navigate our scientific, 21st-century world, and it lays the foundation for more advanced undergraduate coursework in a wide variety of liberal arts and science courses. Selling Points Helps students develop scientific literacy—an essential aspect of _any_ undergraduate education in the 21 st century, including a broad understanding of scientific reasoning, methods, and concepts Written for all beginning college students: preparing science majors for more focused work in particular science; introducing the humanities’ investigations of science; and helping non-science majors become more sophisticated consumers of scientific information Provides an abundance of both contemporary and historical examples Covers reasoning strategies and norms applicable in all fields of physical, life, and social sciences, _as well as_ strategies and norms distinctive of specific sciences Includes visual aids to clarify and illustrate ideas Provides text boxes with related topics and helpful definitions of key terms, and includes a final Glossary with all key terms Includes Exercises for Active Learning at the end of each chapter, which will ensure full student engagement and mastery of the information include earlier in the chapter Provides annotated ‘For Further Reading’ sections at the end of each chapter, guiding students to the best primary and secondary sources available Offers a Companion Website, with: For Students: direct links to many of the primary sources discussed in the text, student self-check assessments, a bank of exam questions, and ideas for extended out-of-class projects For Instructors: a password-protected Teacher’s Manual, which provides student exam questions with answers, extensive lecture notes, classroom-ready Power Point presentations, and sample syllabi Extensive Curricular Development materials, helping any instructor who needs to create a Scientific Reasoning Course, ex nihilo. (shrink)

Presumption is a complex concept in law, affecting the dialogue setting. However, it is not clear how presumptions work in everyday argumentation, in which the concept of “plausible argumentation” seems to encompass all kinds of inferences. By analyzing the legal notion of presumption, it appears that this type of reasoning combines argument schemes with reasoning from ignorance. Presumptive reasoning can be considered a particular form of reasoning, which needs positive or negative evidence to carry a probative weight on the conclusion. (...) For this reason, presumptions shift the burden of providing evidence or explanations onto the interlocutor. The latter can provide new information or fail to do so: whereas in the first case the new information rebuts the presumption, in the second case, the absence of information that the interlocutor could reasonably provide strengthen the conclusion of the presumptive reasoning. In both cases the result of the presumption is to strengthen the conclusion of the reasoning from lack of evidence. As shown in the legal cases, the effect of presumption is to shift the burden of proof to the interlocutor; however, the shift a presumption effects is only the shift of the evidential burden, or the burden of completing the incomplete knowledge from which the conclusion was drawn. The burden of persuasion remains on the proponent of the presumption. On the contrary, reasoning from definition in law is a conclusive proof, and shifts to the other party the burden to prove the contrary. This crucial difference can be applied to everyday argumentation: natural arguments can be divided into dialectical and presumptive arguments, leading to conclusions materially different in strength. -/- . (shrink)

There is widespread agreement that while on a Dummettian theory of meaning the justified logic is intuitionist, as its constants are governed by harmonious rules of inference, the situation is reversed on Huw Price's bilateralist account, where meanings are specified in terms of primitive speech acts assertion and denial. In bilateral logics, the rules for classical negation are in harmony. However, as it is possible to construct an intuitionist bilateral logic with harmonious rules, there is no formal argument against (...) intuitionism from the bilateralist perspective. Price gives an informal argument for classical negation based on a pragmatic notion of belief, characterised in terms of the differences they make to speakers' actions. The main part of this paper puts Price's argument under close scrutiny by regimenting it and isolating principles Price is committed to. It is shown that Price should draw a distinction between A or ¬A making a difference. According to Price, if A makes a difference to us, we treat it as decidable. This material allows the intuitionist to block Price's argument. Abandoning classical logic also brings advantages, as within intuitionist logic there is a precise meaning to what it might mean to treat A as decidable: it is to assume A ∨ ¬A. (shrink)

Coordination in thought is the treatment of beliefs by the believer as being about the same thing. Such treatment can be indirect, via an identity belief, or direct. Direct coordination presents a problem concerning how this treatment is justified. Dickie accounts for the justification of coordination in terms of aptness to a motivational state: coordination serves to fulfil a need to represent things outside the mind. I argue that this account gets the problem coordination presents wrong, and so does not (...) present an adequate solution. While the material of that account may be reconfigured to provide a more promising proposal, I argue that this depends on a specious psychology of belief, and will anyway end up being circular. I propose an account that, while similar in some ways, improves on both the official and reconfigured Dickie-style accounts, and points to some broader conclusions about the nature of rational cognition. (shrink)

The question of whether we have free will is a longstanding philosophical debate that has led to divided fronts and interpretations. The first ambiguity arises due to a misconception about the relation between causal determinism, as formulated in classical physics, and the notion of free will, which, once clarified, undermines not only compatibilism but also naïve formulations of libertarianism. We show that either one maintains a material monistic physical causal determinism and must give up free will, or one must (...) give up determinism and embrace metaphysical ontologies. Moreover, with the advent of modern neuroscientific investigations, the questions surrounding our freedom of choice have received renewed attention but, so far, lead to several inconclusive findings. In fact, the issue is far from settled and no resolution is in sight. We contend that an exclusively third-person approach that abstracts from the deeper complexities of the human psychological nature and resists a first-person inquiry has led to a much too simplistic and superficial understanding of the problem and is affected by fallacious inferences and unwarranted conclusions. Meanwhile, an introspective approach easily reveals that our identity can't be reduced to a single personality whose choice-making is determined by a unique agency and volition. Our nature is much more complex than that. Therefore, every analysis involving propositions about free will requires more careful articulation. One cannot meaningfully answer the question of free will if it is not clear (1) what determinism is in physical sciences, (2) who is supposed to be free from what and (3) what will is. Here, we show that the question regarding free will isn't meaningful in the first place unless cleared from conceptual conflations and that it is unlikely it will ever be answered by a binary ‘yes’ or ‘no’ statement. (shrink)

This short paper grew out of an observation—made in the course of a larger research project—of a surprising convergence between, on the one hand, certain themes in the work of Mary Hesse and Nelson Goodman in the 1950/60s and, on the other hand, recent work on the representational resources of science, in particular regarding model-based representation. The convergence between these more recent accounts of representation in science and the earlier proposals by Hesse and Goodman consists in the recognition that, in (...) order to secure successful representation in science, collective representational resources must be available. Such resources may take the form of (amongst others) mathematical formalisms, diagrammatic methods, notational rules, or—in the case of material models—conventions regarding the use and manipulation of the constituent parts. More often than not, an abstract characterization of such resources tells only half the story, as they are constituted equally by the pattern of (practical and theoretical) activities—such as instances of manipulation or inference—of the researchers who deploy them. In other words, representational resources need to be sustained by a social practice; this is what renders them collective representational resources in the first place. (shrink)

According to Brandom’s conceptual role semantics, to grasp a concept involves a commitment to drawing certain inferences. This is a consequence of the inferentialist thesis that the meaning of a term is given by its justification through assertibility conditions. Inferential commitments come out from a material notion of inference which underwrites human rational discourse and activity. In this paper I discuss a problem of Brandom’s semantics allegedly exposed in an argument by Paul Boghossian against Dummett’s and Brandom’s substantive (...) conception of meaning. I contend that Boghossian’s analysis is dubious because it overlooks an important difference between Dummett’s and Brandom’s positions related respectively to a monotonic and a non-monotonic view of the norm underwriting meaning. (shrink)

How to say no less, no more about conditional than what is needed? From a logical analysis of necessary and sufficient conditions (Section 1), we argue that a stronger account of conditional can be obtained in two steps: firstly, by reminding its historical roots inside modal logic and set-theory (Section 2); secondly, by revising the meaning of logical values, thereby getting rid of the paradoxes of material implication whilst showing the bivalent roots of conditional as a speech-act based on (...) affirmations and rejections (Section 3). Finally, the two main inference rules for conditional, viz. Modus Ponens and Modus Tollens, are reassessed through a broader definition of logical consequence that encompasses both a normal relation of truth propagation and a weaker relation of falsity non-propagation from premises to conclusion (Section 3). (shrink)

In this paper, building on recent and longstanding work (Warren 2001, Friedman 2013, Glezer 2018), I investigate how the account of the essences or natures of material substances in the Metaphysical Foundations is related to Kant’s demand for the completeness of the system of nature. We must ascribe causal powers to material substances for the properties of those substances to be observable and knowable. But defining those causal powers requires admitting laws of nature, taken as axioms or principles (...) of natural science, which govern anything that can be constructed mathematically or “given as an object of experience” (MAN, 4:474–75). Presenting a complete system of nature requires adumbrating the properties of material substances that can be objects of experience. But it is not possible to show how those properties are involved in explanations of the phenomena without involving the laws that govern interactions between material substances. For Kant, or so I will argue, it is not possible to account for the natures of things, or for the features of laws of nature, independently of each other. The paper will substantiate the Finitist Account (FA) of Kant on laws. The Finitist Account has it that modal judgments about the possible proofs that can be made, or interactions that can be explained, are (1) based on concrete intuitive reasoning and motivated by the desire to avoid appeal to the actual infinite, (2) grounded in finite decision procedures, which are (3) based on reliable systems of axioms or rules of inference. (shrink)