Recent academic fashions have posited visual images of colonial landscape space as forming part of a network of intellectual influences that promoted both a culture of imperialism and an imperial culture in the nineteenth century. Frequently these analyses concentrate on constructing an overarching socio-political interpretation into which to place this art, thereby ignoring the influence of artistic and aesthetic theory in the creation, assessment and reception of these images.

The study of biodiversity spans many disciplines and includes data pertaining to species distributions and abundances, genetic sequences, trait measurements, and ecological niches, complemented by information on collection and measurement protocols. A review of the current landscape of metadata standards and ontologies in biodiversity science suggests that existing standards such as the Darwin Core terminology are inadequate for describing biodiversity data in a semantically meaningful and computationally useful way. Existing ontologies, such as the Gene Ontology and others in the Open (...) Biological and Biomedical Ontologies (OBO) Foundry library, provide a semantic structure but lack many of the necessary terms to describe biodiversity data in all its dimensions. In this paper, we describe the motivation for and ongoing development of a new Biological Collections Ontology, the Environment Ontology, and the Population and Community Ontology. These ontologies share the aim of improving data aggregation and integration across the biodiversity domain and can be used to describe physical samples and sampling processes (for example, collection, extraction, and preservation techniques), as well as biodiversity observations that involve no physical sampling. Together they encompass studies of: 1) individual organisms, including voucher specimens from ecological studies and museum specimens, 2) bulk or environmental samples (e.g., gut contents, soil, water) that include DNA, other molecules, and potentially many organisms, especially microbes, and 3) survey-based ecological observations. We discuss how these ontologies can be applied to biodiversity use cases that span genetic, organismal, and ecosystem levels of organization. We argue that if adopted as a standard and rigorously applied and enriched by the biodiversity community, these ontologies would significantly reduce barriers to data discovery, integration, and exchange among biodiversity resources and researchers. (shrink)

Demonstratives seem to have posed a severe difficulty for Frege’s philosophy of language, to which his doctrine of incommunicable senses was a reaction. In “The Thought,” Frege briefly discusses sentences containing such demonstratives as “today,” “here,” and “yesterday,” and then turns to certain questions that he says are raised by the occurrence of “I” in sentences (T, 24-26). He is led to say that, when one thinks about oneself, one grasps thoughts that others cannot grasp, that cannot be communicated. However, (...) nothing could be more out of the spirit of Frege’s account of sense and thought than an incommunicable, private thought. In the first part of the paper, I explain the problem demonstratives pose for Frege, and explore three ways he might have dealt with it. I argue that none of these ways provides Frege with a solution to his problem consistent with his philosophy of language. The first two are plausible as solutions, but contradict his identification of the sense expressed by a sentence with a thought. The third preserves the identification, but is implausible. In the second part, I suggest that Frege was led to his doctrine of incommunicable senses as a result of some appreciation of the difficulties his account of demonstratives faces, for these come quickly to the surface when we think about “I.” I argue that incommunicable senses won’t help. I end by trying to identify the central problem with Frege’s approach, and sketching an alternative. (shrink)

This paper briefly describes process metaphysics, and argues that it is better suited for describing life than the more standard thing, or substance, metaphysics. It then explores the implications of process metaphysics for conceptualizing evolution. After explaining what it is for an organism to be a process, the paper takes up the Hull/Ghiselin thesis of species as individuals and explores the conditions under which a species or lineage could constitute an individual process. It is argued that only sexual species satisfy (...) these conditions, and that within sexual species the degree of organization varies. This, in turn, has important implications for species' evolvability. One important moral is that evolution will work differently in different biological domains. (shrink)

This paper critically evaluates the regress argument for infinitism. The dialectic is essentially this. Peter Klein argues that only an infinitist can, without being dogmatic, enhance the credibility of a questioned non-evident proposition. In response, I demonstrate that a foundationalist can do this equally well. Furthermore, I explain how foundationalism can provide for infinite chains of justification. I conclude that the regress argument for infinitism should not convince us.

ABSTRACT Drawing inspiration from Fred Dretske, L. S. Carrier, John A. Barker, and Robert Nozick, we develop a tracking analysis of knowing according to which a true belief constitutes knowledge if and only if it is based on reasons that are sensitive to the fact that makes it true, that is, reasons that wouldn’t obtain if the belief weren’t true. We show that our sensitivity analysis handles numerous Gettier-type cases and lottery problems, blocks pathways leading to skepticism, and validates (...) the epistemic closure thesis that correct inferences from known premises yield knowledge of the conclusions. We discuss the plausible views of Ted Warfield and Branden Fitelson regarding cases of knowledge acquired via inference from false premises, and we show how our sensitivity analysis can account for such cases. We present arguments designed to discredit putative counterexamples to sensitivity analyses recently proffered by Tristan Haze, John Williams and Neil Sinhababu, which involve true statements made by untrustworthy informants and strange clocks that sometimes display the correct time while running backwards. Finally, we show that in virtue of employing the paradox-free subjunctive conditionals codified by Relevance Logic theorists instead of the paradox-laden subjunctive conditionals codified by Robert Stalnaker and David Lewis. (shrink)

The A-theory and the B-theory advance competing claims about how time is grounded. The A-theory says that A-facts are more fundamental in grounding time than are B-facts, and the B-theory says the reverse. We argue that whichever theory is true of the actual world is also true of all possible worlds containing time. We do this by arguing that time is uniquely groundable: however time is actually grounded, it is necessarily grounded in that way. It follows that if either the (...) A-theory or the B-theory is actually false, then it is necessarily false. (shrink)

The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano’s second-order Induction Axiom is approximated by Herbrand’s Induction-Axiom (...) Schema [23]. Similarly, in first-order set theory, Zermelo’s second-order Separation Axiom is approximated by Fraenkel’s first-order Separation Schema [17]. In some of several closely related senses, a schema is a complex system having multiple components one of which is a template-text or scheme-template, a syntactic string composed of one or more “blanks” and also possibly significant words and/or symbols. In accordance with a side condition the template-text of a schema is used as a “template” to specify a multitude, often infinite, of linguistic expressions such as phrases, sentences, or argument-texts, called instances of the schema. The side condition is a second component. The collection of instances may but need not be regarded as a third component. The instances are almost always considered to come from a previously identified language (whether formal or natural), which is often considered to be another component. This article reviews the often-conflicting uses of the expressions ‘schema’ and ‘scheme’ in the literature of logic. It discusses the different definitions presupposed by those uses. And it examines the ontological and epistemic presuppositions circumvented or mooted by the use of schemata, as well as the ontological and epistemic presuppositions engendered by their use. In short, this paper is an introduction to the history and philosophy of schemata. (shrink)

In a recent very interesting and important challenge to tracking theories of knowledge, Williams & Sinhababu claim to have devised a counter-example to tracking theories of knowledge of a sort that escapes the defense of those theories by Adams & Clarke. In this paper we will explain why this is not true. Tracking theories are not undermined by the example of the backward clock, as interesting as the case is.

There is a growing sense of unease around algorithmic modes of governance ('algocracies') and their impact on freedom. Contrary to the emancipatory utopianism of digital enthusiasts, many now fear that the rise of algocracies will undermine our freedom. Nevertheless, there has been some struggle to explain exactly how this will happen. This chapter tries to address the shortcomings in the existing discussion by arguing for a broader conception/understanding of freedom as well as a broader conception/understanding of algocracy. Broadening the focus (...) in this way enables us to see how algorithmic governance can be both emancipatory and enslaving, and provides a framework for future development and activism around the creation of this technology. (shrink)

This article considers two related and fundamental issues about morality in a virtual world. The first is whether the anonymity that is a feature of virtual worlds can shed light upon whether people are moral when they can act with impunity. The second issue is whether there are any moral obligations in a virtual world and if so what they might be. -/- Our reasons for being good are fundamental to understanding what it is that makes us moral or indeed (...) whether any of us truly are moral. Plato grapples with this problem in book two of The Republic where Socrates is challenged by his brothers Adeimantus and Glaucon. They argue that people are moral only because of the costs to them of being immoral; the external constraints of morality. -/- Glaucon asks us to imagine a magical ring that enables its wearers to become invisible and capable of acting anonymously. The ring is in some respects analogous to the possibilities created by online virtual worlds such as Second Life, so the dialogue is our entry point into considering morality within these worlds. These worlds are three dimensional user created environments where people control avatars and live virtual lives. As well as being an important social phenomenon, virtual worlds and what people chose to do in them can shed light on what people will do when they can act without fear of normal sanction. -/- This paper begins by explaining the traditional challenge to morality posed by Plato, relating this to conduct in virtual worlds. Then the paper will consider the following skeptical objection. A precondition of all moral requirements is the ability to act. There are no moral requirements in virtual worlds because they are virtual and it is impossible to act in a virtual world. Because avatars do not have real bodies and the persons controlling avatars are not truly embodied, it is impossible for people to truly act in a virtual world. We will show that it is possible to perform some actions and suggest a number of moral requirements that might plausibly be thought to result. Because avatars cannot feel physical pain or pleasure these moral requirements are interestingly different from those of real life. Hume’s arguments for why we should be moral apply to virtual worlds and we conclude by considering how this explains why morality exists in these environments. (shrink)

We are much better equipped to let the facts reveal themselves to us instead of blinding ourselves to them or stubbornly trying to force them into preconceived molds. We no longer embarrass ourselves in front of our students, for example, by insisting that “Some Xs are Y” means the same as “Some X is Y”, and lamely adding “for purposes of logic” whenever there is pushback. Logic teaching in this century can exploit the new spirit of objectivity, humility, clarity, observationalism, (...) contextualism, and pluralism. Besides the new spirit there have been quiet developments in logic and its history and philosophy that could radically improve logic teaching. This lecture expands points which apply equally well in first, second, and third courses, i.e. in “critical thinking”, “deductive logic”, and “symbolic logic”. (shrink)

The outlines of a novel, fully naturalistic theory of perception are provided, that can explain perception of an object X by organism Z in terms of reflexive causality. On the reflexive view proposed, organism Z perceives object or property X just in case X causes Z to acquire causal dispositions reflexively directed back upon X itself. This broadly functionalist theory is potentially capable of explaining both perceptual representation and perceptual content in purely causal terms, making no use of informational concepts. (...) However, such a reflexive, naturalistic causal theory must compete with well entrenched, supposedly equally naturalistic theories of perception that are based on some concept of information, so the paper also includes some basic logical, naturalistic and explanatory criticisms of such informational views. (shrink)

One routinely undergoes a noetic feeling (also called “metacognitive feeling” or “epistemic feeling”), the so-called “feeling of knowing”, whenever trying to recall a person’s name. One feels the name is known despite being unable to recall it. Other experiences also fall under this category, e.g., the tip-of-the-tongue experience, the feeling of confidence. A distinguishing characteristic of noetic feelings is how they are crucially related to the facts we know, so much so that the activation of semantic memory can easily result (...) in the production of noetic feelings – a regularity that memory research has often exploited. And yet little is known about the mechanism that produces noetic feelings. Is it solely brain-based or does it depend upon the extracerebral body for its production of feelings? To arrive at an answer, various studies in metamemory research will be analyzed to determine what ought to be made of the mechanism responsible for noetic feelings. I argue that evidence suggests that it relies upon extracerebral processes, in particular cardiovascular processes, the result being support for an embodied view of metacognition. (shrink)

The artefacts produced by artists during their creation of works of art are very various: paintings, writings, musical scores, and so on. I have a general thesis to offer about the relations of artefacts and artworks, but within the confines of this article I shall mainly discuss cases drawn from the art of painting, central specimens of which seem to be autographic in Nelson Goodman's sense, namely such that even the most exact duplication of them does not count as producing (...) the same work of art. My view will be that an artwork (such as a painting) and its associated artefact are not identical, and nor is the artefact in any sense part of the painting in question,2 but that nevertheless it is still possible to maintain the view that paintings are autographic (which view I shall call l the autographic thesis). I shall proceed initially through presentation of some counter-examples to common assumptions as to the relations of artefacts and artworks, and then present an alternative 'representational' theory of their relations. (shrink)

The field of machine perception is based on standard informational and computational approaches to perception. But naturalistic informational theories are widely regarded as being inadequate, while purely syntactic computational approaches give no account of perceptual content. Thus there is a significant need for a novel, purely naturalistic perceptual theory not based on informational or computational concepts, which could provide a new paradigm for mechanistic perception. Now specifically evolutionary naturalistic approaches to perception have been—perhaps surprisingly—almost completely neglected for this purpose. Arguably (...) perceptual mechanisms enhance evolutionary fitness by facilitating sensorily mediated causal interactions between an organism Z and items X in its environment. A ‘reflexive’ theory of perception of this kind is outlined, according to which an organism Z perceives an item X just in case X causes a sensory organ zi of Z to cause Z to acquire a disposition toward the very same item X that caused the perception. The rest of the paper shows how an intuitively plausible account of mechanistic perception can be developed and defended in terms of the reflexive theory. Also, a compatibilist option is provided for those who wish to preserve a distinct informational concept of perception. (shrink)

I argue that the physical marks on a canvas resulting from an artist's intentional, stylistic and expressive acts cannot themselves be the artist's expression, but instead they serve to signify or indicate those acts. Thus there is a kind of indicative content associated with a picture that is distinct from its subject matter (or 'representational content'). I also argue that this kind of indicative content is closely associated with the specific artistic medium chosen by the artist as her expressive medium, (...) for which reason I call this kind of content medium content (or medium-related content). (shrink)

Clearly we can perceive both objects, and various aspects or appearances of those objects. But how should that complexity of perceptual content be explained or analyzed? I argue that perceptual representations normally have a double or two level nested structure of content, so as to adequately incorporate information both about contextual aspects Y(X) of an object X, and about the object X itself. On this double content (DC) view, perceptual processing starts with aspectual data Y?(X?) as a higher level of (...) content, which data does not itself provide lower level X-related content, but only an aspectually encoded form of such data. Hence the relevant perceptual data Y?(X?) must be. (shrink)

A revisionist account of how philosophical induction was conceived in the ancient world and how that conception was transmitted, altered, and then rediscovered. I show how philosophers of late antiquity and then the medieval period came step-by-step to seriously misunderstand Aristotle’s view of induction and how that mistake was reversed by humanists in the Renaissance and then especially by Francis Bacon. I show, naturally enough then, that in early modern science, Baconians were Aristotelians and Aristotelians were Baconians.

Misinformation can have significant societal consequences. For example, misinformation about climate change has confused the public and stalled support for mitigation policies. When people lack the expertise and skill to evaluate the science behind a claim, they typically rely on heuristics such as substituting judgment about something complex (i.e. climate science) with judgment about something simple (i.e. the character of people who speak about climate science) and are therefore vulnerable to misleading information. Inoculation theory offers one approach to effectively neutralize (...) the influence of misinformation. Typically, inoculations convey resistance by providing people with information that counters misinformation. In contrast, we propose inoculating against misinformation by explaining the fallacious reasoning within misleading denialist claims. We offer a strategy based on critical thinking methods to analyse and detect poor reasoning within denialist claims. This strategy includes detailing argument structure, determining the truth of the premises, and checking for validity, hidden premises, or ambiguous language. Focusing on argument structure also facilitates the identification of reasoning fallacies by locating them in the reasoning process. Because this reason-based form of inoculation is based on general critical thinking methods, it offers the distinct advantage of being accessible to those who lack expertise in climate science. We applied this approach to 42 common denialist claims and find that they all demonstrate fallacious reasoning and fail to refute the scientific consensus regarding anthropogenic global warming. This comprehensive deconstruction and refutation of the most common denialist claims about climate change is designed to act as a resource for communicators and educators who teach climate science and/or critical thinking. (shrink)

This is an encyclopedia article about epistemic closure principles. The article explains what they are, their various philosophical uses, how they are argued for or against, and provides an overview of the related literature.

The article discusses the varying conceptions of the faculty of ‘the understanding’ in 18th-century British philosophy and logic. Topics include the distinction between the understanding and the will, the traditional division of three acts of understanding and its critics, the naturalizing of human understanding, conceiving of the limits of human understanding, British innatism and the critique of empiricist conceptions of the understanding, and reconceiving the understanding and the elimination of scepticism. Authors discussed include Richard Price, James Harris, Zachary Mayne, Edward (...) Bentham, Isaac Watts, Dugald Stewart, John Norris—as well as Locke, Berkeley, Hume and Reid. (shrink)

The category of works of fiction is a very broad and heterogeneous one. I do have a general thesis in mind about such works, namely, that they themselves are fictional, in much the same way as are the fictional events or entities that they are about. But a defense of such a broad thesis would provide an intractably complex topic for an introductory essay, so I shall here confine myself to a presentation of a similar thesis for narrative theatrical works (...) or plays, performances of which are naturally regarded as involving, or evoking, a “fictional world” whose fictional characters and events are what the work in question is about. Another reason for initially focusing on such narrative plays is because performances of them provide a rich source of epistemic issues about evidence for artistic authenticity or correctness of artworks, which will turn out to be of integral importance to my fictionalist account of plays. (shrink)

What is the relation between a perceptual experience of an object X as being red, and one's belief, if any, as to the nature of that experience? A traditional Cartesian view would be that, if indeed object X does seem to be red to oneself, then one's resulting introspective belief about it could only be a _conforming _belief, i.e., a belief that X perceptually seems to be _red _to oneself--rather than, for instance, a belief that X perceptually seems to be (...) green to oneself instead. On such a Cartesian view, our introspective certainly about our own thoughts extends also to our perceptual experiences as to how things seem to be to us, so that our resulting introspective beliefs about our phenomenal states also count as knowledge of them. (shrink)

A novel semantic naturalization program is proposed. Its three main differences from informational semantics approaches are as follows. First, it makes use of a perceptually based, four-factor interactive causal relation in place of a simple nomic covariance relation. Second, it does not attempt to globally naturalize all semantic concepts, but instead it appeals to a broadly realist interpretation of natural science, in which the concept of propositional truth is off-limits to naturalization attempts. And third, it treats all semantic concepts as (...) being purely abstract, so that concrete cognitive states are only indexed by them rather than instantiating them. (shrink)

FEEL FREE TO CITE - IGNORE IN-PDF REQUEST The eight year gap between the publication of Volume I (1976) of The History of Sexuality and Volumes II and III (1984) has provoked a fair amount of debate within scholarly circles. Does it represent a fundamental rethinking of the analysis of power and knowledge begun in Volume I, or is something else at stake? And what does the shift in emphasis regarding power and resistance after these eight years ultimately entail? James (...) Miller’s influential, if often flawed, biography of Foucault has provided one of the leading interpretations of this gap in Foucault’s publishing career. On Miller’s account, the turn towards governmentality and technologies of the self represents something of a tacit admission of failure on Foucault’s part regarding his Volume I rendering of power and resistance.1 Now, it seems to me that there is something right about this reading – we can map a shift in Foucault’s consideration of power and resistance in this period, culminating in the 1982 essay, “The Subject and Power,” which it seems to me can be read as a perverse re-writing of the themes of Volume I. However, the idea that this eight year period represents a ‘hard break,’ or an introduction of an incommensurability between resistance as tactical reversal (Volume I) and resistance as.. (shrink)

This work treats the correlative concepts knowledge and opinion, in various senses. In all senses of ‘knowledge’ and ‘opinion’, a belief known to be true is knowledge; a belief not known to be true is opinion. In this sense of ‘belief’, a belief is a proposition thought to be true—perhaps, but not necessarily, known to be true. All knowledge is truth. Some but not all opinion is truth. Every proposition known to be true is believed to be true. Some but (...) not every proposition believed to be true is known to be true. Our focus is thus on propositional belief (“belief-that”): the combination of propositional knowledge (“knowledge-that”) and propositional opinion (“opinion-that”). Each of a person’s beliefs, whether knowledge or opinion, is the end result of a particular thought process that continued during a particular time interval and ended at a particular time with a conclusive act—a judgment that something is the case. This work is mainly about beliefs in substantive informative propositions—not empty tautologies. We also treat objectual knowledge (knowledge of objects in the broadest sense, or “knowledge-of”), operational knowledge (abilities and skills, “knowledge-how-to”, or “know-how”), and expert knowledge (expertise). Most points made in this work have been made by previous writers, but to the best of our knowledge, they have never before been collected into a coherent work accessible to a wide audience. -/- Key words: belief, knowledge/opinion, propositional, operational, objectual, cognition, . (shrink)

This study posits ecological communion as the integration of facilitative learning through community engagements leading to an ecological conversion. Employing the interpretive phenomenological method, it examined how educational institutions in the CICM Philippine Schools’ Network (CICM-PSN) integrate the ecological principles of Pope Francis’ Laudato Si in terms of religious instruction, community engagement, and campus ministry program. Through a semi-structured interview with the participants, the study revealed three themes that illustrate the CICM educational institutions' efforts in bringing the Laudato Si’ teachings (...) to the level of practice and reflection. First, pedagogical integration denotes the challenge of integrating integral ecology in instruction. Second, community engagement shows the effort of the academic community to practice ecological principles through extension programs. Third, ecological conversion aims to internalize the ecological values taught through instruction and practiced through community service. Taken as a unified whole, the three themes mentioned form the Transformative Interpretative Pedagogical Model to consolidate the framework for the CICM-Philippine Schools Network. Furthermore, this model may guide the concrete articulation and application of ecological communion in their religious instruction, community extension and social action programs, and campus ministry activities. (shrink)

The logical form of a discourse—such as a proposition, a set of propositions, an argument, or an argumentation—is obtained by abstracting from the subject-matter of its content terms or by regarding the content terms as mere place-holders or blanks in a form. In a logically perfect language the logical form of a proposition, a set of propositions, an argument, or an argumentation is determined by the grammatical form of the sentence, the set of sentences, the argument-text, or the argumentation-text expressing (...) it. Two such discourse-texts are said to have the same grammatical form, in this sense, if a uniform one-one substitution of content words transforms the one exactly into the other. The sentence ‘Abe properly respects every agent who respects himself’ may be regarded as having the same grammatical form as the sentence ‘Ben generously assists every patient who assists himself’. (shrink)

This paper corrects a mistake I saw students make but I have yet to see in print. The mistake is thinking that logically equivalent propositions have the same counterexamples—always. Of course, it is often the case that logically equivalent propositions have the same counterexamples: “every number that is prime is odd” has the same counterexamples as “every number that is not odd is not prime”. The set of numbers satisfying “prime but not odd” is the same as the set of (...) numbers satisfying “not odd but not not-prime”. The mistake is thinking that every two logically-equivalent false universal propositions have the same counterexamples. Only false universal propositions have counterexamples. A counterexample for “every two logically-equivalent false universal propositions have the same counterexamples” is two logically-equivalent false universal propositions not having the same counterexamples. The following counterexample arose naturally in my sophomore deductive logic course in a discussion of inner and outer converses. “Every even number precedes every odd number” is counterexemplified only by even numbers, whereas its equivalent “Every odd number is preceded by every even number” is counterexemplified only by odd numbers. Please let me know if you see this mistake in print. Also let me know if you have seen these points discussed before. I learned them in my own course: talk about learning by teaching! (shrink)

Are universities justified in trying to regulate student use of cognitive enhancing drugs? In this article I argue that they can be, but that the most appropriate kind of regulatory intervention is likely to be voluntary in nature. To be precise, I argue that universities could justifiably adopt a commitment contract system of regulation wherein students are encouraged to voluntarily commit to not using cognitive enhancing drugs. If they are found to breach that commitment, they should be penalized by, for (...) example, forfeiting a number of marks on their assessments. To defend this model of regulation, I adopt a recently-proposed evaluative framework for determining the appropriateness of enhancement in specific domains of activity, and I focus on particular existing types of cognitive enhancement drugs, not hypothetical or potential forms. In this way, my argument is tailored to the specific features of university education, and common patterns of usage among students. It is not concerned with the general ethical propriety of using cognitive enhancing drugs. (shrink)

The representational content or subject matter of a picture is normally distinguished from various non-representational components of meaning involved in artworks, such as expressive, stylistic or intentional factors. However, I show how such non subject matter components may themselves be analyzed in content terms, if two different categories of representation are recognized--aspect indication for stylistic etc. factors, and normal representation for subject matter content. On the account given, the relevant kinds of content are hierarchically structured, with relatively unconceptualized lower level (...) aspectual contents encoding or symbolizing higher level conceptualized representational subject matter. Such an account is strongly supported by the latest findings of cognitive science regarding levels of conceptualization. The paper also demonstrates how the account given is compatible with the actual pictorial competence of normal viewers of visual artworks. (shrink)

Since at least late antiquity, Aristotle’s Prior Analytics B 23 has been misread. Aristotle does not think that an induction is a syllogism made good by complete enumeration. The confusion can be eliminated by considering the nature of the surviving text and watching very closely Aristotle’s moving back and forth between “induction” and “syllogism from induction.” Though he does move freely between them, the two are not synonyms.

Formalizing Euclid’s first axiom. Bulletin of Symbolic Logic. 20 (2014) 404–5. (Coauthor: Daniel Novotný) -/- Euclid [fl. 300 BCE] divides his basic principles into what came to be called ‘postulates’ and ‘axioms’—two words that are synonyms today but which are commonly used to translate Greek words meant by Euclid as contrasting terms. -/- Euclid’s postulates are specifically geometric: they concern geometric magnitudes, shapes, figures, etc.—nothing else. The first: “to draw a line from any point to any point”; the last: the (...) parallel postulate. -/- Euclid’s axioms are general principles of magnitude: they concern geometric magnitudes and magnitudes of other kinds as well even numbers. The first is often translated “Things that equal the same thing equal one another”. -/- There are other differences that are or might become important. -/- Aristotle [fl. 350 BCE] meticulously separated his basic principles [archai, singular archê] according to subject matter: geometrical, arithmetic, astronomical, etc. However, he made no distinction that can be assimilated to Euclid’s postulate/axiom distinction. -/- Today we divide basic principles into non-logical [topic-specific] and logical [topic-neutral] but this too is not the same as Euclid’s. In this regard it is important to be cognizant of the difference between equality and identity—a distinction often crudely ignored by modern logicians. Tarski is a rare exception. The four angles of a rectangle are equal to—not identical to—one another; the size of one angle of a rectangle is identical to the size of any other of its angles. No two angles are identical to each other. -/- The sentence ‘Things that equal the same thing equal one another’ contains no occurrence of the word ‘magnitude’. This paper considers the problem of formalizing the proposition Euclid intended as a principle of magnitudes while being faithful to the logical form and to its information content. (shrink)

Information-theoretic approaches to formal logic analyze the "common intuitive" concepts of implication, consequence, and validity in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; one given proposition is a consequence of a second if the latter contains all of the information contained by the former; an argument is valid if the conclusion contains no information beyond that of the premise-set. This (...) paper locates information-theoretic approaches historically, philosophically, and pragmatically. Advantages and disadvantages are identified by examining such approaches in themselves and by contrasting them with standard transformation-theoretic approaches. Transformation-theoretic approaches analyze validity (and thus implication) in terms of transformations that map one argument onto another: a given argument is valid if no transformation carries it onto an argument with all true premises and false conclusion. Model-theoretic, set-theoretic, and substitution-theoretic approaches, which dominate current literature, can be construed as transformation-theoretic, as can the so-called possible-worlds approaches. Ontic and epistemic presuppositions of both types of approaches are considered. Attention is given to the question of whether our historically cumulative experience applying logic is better explained from a purely information-theoretic perspective or from a purely transformation-theoretic perspective or whether apparent conflicts between the two types of approaches need to be reconciled in order to forge a new type of approach that recognizes their basic complementarity. (shrink)

In its strongest, unqualified form the principle of wholistic reference is that each and every proposition refers to the whole universe of discourse as such, regardless how limited the referents of its non-logical or content terms. Even though Boole changed from a monistic fixed-universe framework in his earlier works of 1847 and 1848 to a pluralistic multiple-universe framework in his mature treatise of 1854, he never wavered in his frank avowal of the principle of wholistic reference, possibly in a slightly (...) weaker form. Indeed, he took it as an essential accompaniment to his theory of concept formation and proposition formation. Similar views are found in later logicians, and some of the most recent formulations of standard, one-sorted first-order logic seem to be in accord with a form of it, if they do not actually imply the principle itself. (shrink)

2006. George Boole. Encyclopedia of Philosophy. 2nd edition. Detroit: Macmillan Reference USA. -/- George Boole (1815-1864), whose name lives among modern computer-related sciences in Boolean Algebra, Boolean Logic, Boolean Operations, and the like, is one of the most celebrated logicians of all time. Ironically, his actual writings often go unread and his actual contributions to logic are virtually unknown—despite the fact that he was one of the clearest writers in the field. Working with various students including Susan Wood and Sriram (...) Nambiar, I have written several publications trying to set the record straight—but so far to little avail. This encyclopedia entry is one more attempt to set the record straight in a way that can be appreciated by non-experts.Also see https://www.academia.edu/10161999/Booles_criteria_of_validity_and_invalidity . (shrink)

Volume 19, Issue 7, July 2019, Page 16-18.

Excerpts and paraphrases of this memoir appeared in 2008 and 2009. I posted it in full here in happy memory of Peter Hare and my joyful years with him. -/- 2008. Remembering Peter Hare 1935–2008. Philosophy Now. Co-authors: T. Madigan and A. Razin. Issue 66 March/April 2008. Pages 50–2. PDF -/- 2009. Remembering My Life with Peter Hare. Remembering Peter Hare 1935–2008. Ed. J. Campbell. Society for the Advancement of American Philosophy. pp. 9–16. http://american-philosophy.org/documents/RememberingPeterHare_final.pdf -/- Peter H. Hare, Distinguished Professor (...) Emeritus of Philosophy at the University of Buffalo (SUNY at Buffalo), died peacefully in his sleep on Thursday, January 3, 2008. I would like to share my memories of my life with him. Others have eulogized him, enumerated his virtues and accomplishments, and written his obituaries. I am revisiting my personal relationship with him. These memories are as much about me as about him. (shrink)

Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are devoted. (...) At the time of the first edition, 1920, the editor was apparently not acquainted with the secondary literature on Logica demonstrativa which continued to grow in the period preceding the second edition \ref[see D. J. Struik, in Dictionary of scientific biography, Vol. 12, 55--57, Scribner's, New York, 1975]. Of special interest in this connection is a series of three articles by A. F. Emch [Scripta Math. 3 (1935), 51--60; Zbl 10, 386; ibid. 3 (1935), 143--152; Zbl 11, 193; ibid. 3 (1935), 221--333; Zbl 12, 98]. (2) It seems curious that modern writers believe that demonstration of the "nondeducibility" of the parallel postulate vindicates Euclid whereas at first Saccheri seems to have thought that demonstration of its "deducibility" is what would vindicate Euclid. Saccheri is perfectly clear in his commitment to the ancient (and now discredited) view that it is wrong to take as an "axiom" a proposition which is not a "primal verity", which is not "known through itself". So it would seem that Saccheri should think that he was convicting Euclid of error by deducing the parallel postulate. The resolution of this confusion is that Saccheri thought that he had proved, not merely that the parallel postulate was true, but that it was a "primal verity" and, thus, that Euclid was correct in taking it as an "axiom". As implausible as this claim about Saccheri may seem, the passage on p. 237, lines 3--15, seems to admit of no other interpretation. Indeed, Emch takes it this way. (3) As has been noted by many others, Saccheri was fascinated, if not obsessed, by what may be called "reflexive indirect deductions", indirect deductions which show that a conclusion follows from given premises by a chain of reasoning beginning with the given premises augmented by the denial of the desired conclusion and ending with the conclusion itself. It is obvious, of course, that this is simply a species of ordinary indirect deduction; a conclusion follows from given premises if a contradiction is deducible from those given premises augmented by the denial of the conclusion---and it is immaterial whether the contradiction involves one of the premises, the denial of the conclusion, or even, as often happens, intermediate propositions distinct from the given premises and the denial of the conclusion. Saccheri seemed to think that a proposition proved in this way was deduced from its own denial and, thus, that its denial was self-contradictory (p. 207). Inference from this mistake to the idea that propositions proved in this way are "primal verities" would involve yet another confusion. The reviewer gratefully acknowledges extensive communication with his former doctoral students J. Gasser and M. Scanlan. ADDED 14 March 14, 2015: (1) Wikipedia reports that many of Saccheri's ideas have a precedent in the 11th Century Persian polymath Omar Khayyám's Discussion of Difficulties in Euclid, a fact ignored in most Western sources until recently. It is unclear whether Saccheri had access to this work in translation, or developed his ideas independently. (2) This book is another exemplification of the huge difference between indirect deduction and indirect reduction. Indirect deduction requires making an assumption that is inconsistent with the premises previously adopted. This means that the reasoner must perform a certain mental act of assuming a certain proposition. It case the premises are all known truths, indirect deduction—which would then be indirect proof—requires the reasoner to assume a falsehood. This fact has been noted by several prominent mathematicians including Hardy, Hilbert, and Tarski. Indirect reduction requires no new assumption. Indirect reduction is simply a transformation of an argument in one form into another argument in a different form. In an indirect reduction one proposition in the old premise set is replaced by the contradictory opposite of the old conclusion and the new conclusion becomes the contradictory opposite of the replaced premise. Roughly and schematically, P,Q/R becomes P,~R/~Q or ~R, Q/~P. Saccheri’s work involved indirect deduction not indirect reduction. (3) The distinction between indirect deduction and indirect reduction has largely slipped through the cracks, the cracks between medieval-oriented logic and modern-oriented logic. The medievalists have a heavy investment in reduction and, though they have heard of deduction, they think that deduction is a form of reduction, or vice versa, or in some cases they think that the word ‘deduction’ is the modern way of referring to reduction. The modernists have no interest in reduction, i.e. in the process of transforming one argument into another having exactly the same number of premises. Modern logicians, like Aristotle, are concerned with deducing a single proposition from a set of propositions. Some focus on deducing a single proposition from the null set—something difficult to relate to reduction. (shrink)

1971. Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value, Journal of Structural Learning 3, #2, 1–16. REPRINTED 1976. Structural Learning II Issues and Approaches, ed. J. Scandura, Gordon & Breach Science Publishers, New York, MR56#15263. -/- This is the second of a series of three articles dealing with application of linguistics and logic to the study of mathematical reasoning, especially in the setting of a concern for improvement of (...) mathematical education. The present article presupposes the previous one. Herein we develop our ideas of the purposes of a theory of proof and the criterion of success to be applied to such theories. In addition we speculate at length concerning the specific kinds of uses to which a successful theory of proof may be put vis-a-vis improvement of various aspects of mathematical education. The final article will deal with the construction of such a theory. The 1st is the 1971. Discourse Grammars and the Structure of Mathematical Reasoning I: Mathematical Reasoning and Stratification of Language, Journal of Structural Learning 3, #1, 55–74. https://www.academia.edu/s/fb081b1886?source=link . (shrink)

CORCORAN REVIEWS THE 4 VOLUMES OF TARSKI’S COLLECTED PAPERS Alfred Tarski (1901--1983) is widely regarded as one of the two giants of twentieth-century logic and also as one of the four greatest logicians of all time (Aristotle, Frege and Gödel being the other three). Of the four, Tarski was the most prolific as a logician. The four volumes of his collected papers, which exclude most of his 19 monographs, span over 2500 pages. Aristotle's writings are comparable in volume, but most (...) of the Aristotelian corpus is not about logic, whereas virtually everything written by Tarski concerns logic more or less directly. There is no doubt that Tarski wrote more on logic than any other author; he started publishing on logic in 1921 at the age of 20 and continued until his death at the age of 82. (shrink)

The expressions ‘form’, ‘structure’, ‘schema’, ‘shape’, ‘pattern’, ‘figure’, ‘mold’, and related locutions are used in logic both as technical terms and in metaphors. This paper juxtaposes, distinguishes, and analyses uses of [FOR these PUT such] expressions by logicians. No [FOR such PUT similar] project has been attempted previously. After establishing general terminology, we present a variant of traditional usage of the expression ‘logical form’ followed by a discussion of the usage found in the two-volume Chateaubriand book Logical Forms (2001 and (...) 2005)—the most comprehensive work on the subject ever written and in many ways the focus of this paper. Key Words: morphology, character, sense, sentence, proposition, form, structure, schema, alternative constituent, type, token . (shrink)

Iffication, Preiffication, Qualiffication, Reiffication, and Deiffication. -/- Roughly, iffication is the speech-act in which—by appending a suitable if-clause—the speaker qualifies a previous statement. The clause following if is called the qualiffication. In many cases, the intention is to retract part of the previous statement—called the preiffication. I can retract part of “I will buy three” by appending “if I have money”. This initial study focuses on logical relations among propositional contents of speech-acts—not their full conversational implicatures, which will be treated (...) elsewhere. The modified statement—called the iffication—is never stronger than the preiffication. A degenerate iffication is one logically equivalent to its preiffication. There are limiting cases of degenerate iffications. In one, the qualiffication is tautological, as “I will buy three if three is three”. In another, the negation of the qualiffication implies the preiffication, as “I will buy three if I will not buy three”. Reiffication is iffication of an iffication. “I will buy three if I have money” is reifficated by appending “if there are three left”. Deiffication is the speech-act in which—by appending a suitable and-clause—the effect of an iffication is cancelled so that the result implies the preiffication. “I will buy three if I have money” is deifficated by appending “and I have money”. All further examples come from standard (one-sorted, tenseless, non-modal) first-order arithmetic. All theorems are about first-order arithmetic propositions. An easy theorem, hinted above, is that an iffication is degenerate if and only if the negation of the qualiffication implies the preiffication. The iffication of a conjunction using one of the conjuncts as qualiffication need not imply the other conjunct: “Two is an even square if two is square” does not imply “Two is even”. END OF PRINTED ABSTRACT. -/- Some find that the last statement provides a surprise in logic. https://www.academia.edu/s/a5a4386b75?source=link Acknowledgements: Robert Barnes, William Frank, Amanda Hicks, David Hitchcock, Leonard Jacuzzo, Edward Keenan, Mary Mulhern, Frango Nabrasa, and Roberto Torretti. (shrink)

Moti Mizrahi argues that Gettier cases are unsuccessful counterexamples to the traditional analysis of knowledge (TAK) because such cases inadequately reveal epistemic failures of justified true belief (JTB); and because Gettier cases merely demonstrate semantic inadequacy, the apparent epistemic force of Gettier cases is misleading. Although Mizrahi claims to have deflated the epistemic force of Gettier cases, I will argue that the presence of semantic deficiency in Gettier cases neither requires nor indicates the denial of the epistemic force of those (...) cases. I will provide an extracted version of Mizrahi’s argument, which I believe to be most charitable to his motivation. Then I will offer a counterexample to a pivotal premise in Mizrahi’s argument, ultimately rendering the argument unsound. Finally, upon the examination of a plausible objection, I conclude that Gettier cases are epistemically sustained. (shrink)

This paper will annoy modern logicians who follow Bertrand Russell in taking pleasure in denigrating Aristotle for [allegedly] being ignorant of relational propositions. To be sure this paper does not clear Aristotle of the charge. On the contrary, it shows that such ignorance, which seems unforgivable in the current century, still dominated the thinking of one of the greatest modern logicians as late as 1831. Today it is difficult to accept the proposition that Aristotle was blind to the fact that, (...) for example, incommensurability is a relation and not a property: that the proposition “In every square, the diagonals are incommensurable with the sides” is relational and not categorical. This paper asks the reader to do something more difficult: to accept the proposition that as late as 1831 De Morgan was blind to the same fact. This paper shows conclusively that in 1831, De Morgan was still in the grips of the allegedly Aristotelian paradigm. (shrink)

A truth-preservation fallacy is using the concept of truth-preservation where some other concept is needed. For example, in certain contexts saying that consequences can be deduced from premises using truth-preserving deduction rules is a fallacy if it suggests that all truth-preserving rules are consequence-preserving. The arithmetic additive-associativity rule that yields 6 = (3 + (2 + 1)) from 6 = ((3 + 2) + 1) is truth-preserving but not consequence-preserving. As noted in James Gasser’s dissertation, Leibniz has been criticized for (...) using that rule in attempting to show that arithmetic equations are consequences of definitions. -/- A system of deductions is truth-preserving if each of its deductions having true premises has a true conclusion—and consequence-preserving if, for any given set of sentences, each deduction having premises that are consequences of that set has a conclusion that is a consequence of that set. Consequence-preserving amounts to: in each of its deductions the conclusion is a consequence of the premises. The same definitions apply to deduction rules considered as systems of deductions. Every consequence-preserving system is truth-preserving. It is not as well-known that the converse fails: not every truth-preserving system is consequence-preserving. Likewise for rules: not every truth-preserving rule is consequence-preserving. There are many famous examples. In ordinary first-order Peano-Arithmetic, the induction rule yields the conclusion ‘every number x is such that: x is zero or x is a successor’—which is not a consequence of the null set—from two tautological premises, which are consequences of the null set, of course. The arithmetic induction rule is truth-preserving but not consequence-preserving. Truth-preserving rules that are not consequence-preserving are non-logical or extra-logical rules. Such rules are unacceptable to persons espousing traditional truth-and-consequence conceptions of demonstration: a demonstration shows its conclusion is true by showing that its conclusion is a consequence of premises already known to be true. The 1965 Preface in Benson Mates (1972, vii) contains the first occurrence of truth-preservation fallacies in the book. (shrink)