Cathy Legg

This paper offers an expressivist account of logical form, arguing that in order to fully understand it one must examine what valid arguments make us do (or: what Achilles does and the Tortoise doesn’t, in Carroll’s famed fable). It introduces Charles Peirce’s distinction between symbols, indices and icons as three different kinds of signification whereby the sign picks out its object by learned convention, by unmediated indication, and by resemblance respectively. It is then argued that logical form is represented by the third, iconic, kind of sign. It is noted that icons uniquely enjoy partial identity between sign and object, and argued that this holds the key to Carroll’s puzzle. Finally, from this examination of sign-types metaphysical morals are drawn: that the traditional foes metaphysical realism and conventionalism constitute a false dichotomy, and that reality contains intriguingly inference-binding structures.

This substantial book is a highly original and thorough work of synthetic first philosophy. Although it has some recognizable roots in the Kantian/Sellarsian tradition of the Pittsburgh school, it adds a wealth of precise discussion of examples from science and mathematics, made possible by Macbeth's dual training in arts and sciences. It presents a developmental story of human reason bootstrapping itself towards greater power and clarity through the Western tradition (which is the sole purview of the discussion). This development is divided into three distinct stages, which might be summarized very roughly as knowledge of: i) Objects, ii) Concepts applied to Objects and iii) Concepts alone.

Much discussion of meaning by philosophers over the last 300 years has been predicated on a Cartesian first-person authority (i.e. “infallibilism”) with respect to what one’s terms mean. However this has problems making sense of the way the meanings of scientific terms develop, an increase in scientific knowledge over and above scientists’ ability to quantify over new entities. Although a recent conspicuous embrace of rigid designation has broken up traditional meaning-infallibilism to some extent, this new dimension to the meaning of terms such as “water” is yet to receive a principled epistemological undergirding (beyond the deliverances of “intuition” with respect to certain somewhat unusual possible worlds). Charles Peirce’s distinctive, naturalistic philosophy of language is mined to provide a more thoroughly fallibilist, and thus more realist, approach to meaning, with the requisite epistemology. Both his pragmatism and his triadic account of representation, it is argued, produce an original approach to meaning, analysing it in processual rather than objectual terms, and opening a distinction between “meaning for us”, the meaning a term has at any given time for any given community and “meaning simpliciter”. the way use of a given term develops over time (often due to a posteriori input from the world which is unable to be anticipated in advance). This account provocatively undermines a certain distinction between “semantics” and “ontology” which is often taken for granted in discussions of realism.

Peirce wrote that Hume’s argument against miracles (which is generally liked by twentieth century philosophers for its antireligious conclusion) "completely misunderstood the true nature of" ’abduction’. This paper argues that if Hume’s argumentative strategy were seriously used in all situations (not just those in which we seek to "banish superstition"), it would deliver a choking epistemological conservatism. It suggests that some morals for contemporary naturalistic philosophy may be drawn from Peirce’s argument against Hume.

This paper contrasts the scholastic realisms of David Armstrong and Charles Peirce. It is argued that the so-called 'problem of universals' is not a problem in pure ontology (concerning whether universals exist) as Armstrong construes it. Rather, it pertains to which predicates should be applied where, issues which Armstrong sets aside under the label of 'semantics', and which from a Peircean perspective encompass even fundamentals of scientific methodology. It is argued that Peirce's scholastic realism not only presents a more nuanced ontology (distinguishing existence and reality) but also illuminates why scholastic realism is a position worth fighting for.

As an informational technology, the World Wide Web has enjoyed spectacular success. In just ten years it has transformed the way information is produced, stored, and shared in arenas as diverse as shopping, family photo albums, and high-level academic research. The “Semantic Web” was touted by its developers as equally revolutionary but has not yet achieved anything like the Web’s exponential uptake. This 17 000 word survey article explores why this might be so, from a perspective that bridges both philosophy and IT. (*Also translated into Croatian and republished in Vjesnik bibliotekara Hrvatske 53, 1(2010), 155-206: See external link #2)

Would be fairer to call Peirce’s philosophy of language “extensionalist” or “intensionalist”? The extensionalisms of Carnap and Quine are examined, and Peirce’s view is found to be prima facie similar, except for his commitment to the importance of “hypostatic abstraction”. Rather than dismissing this form of abstraction (famously derided by Molière) as useless scholasticism, Peirce argues that it represents a crucial (though largely unnoticed) step in much working inference. This, it is argued, allows Peirce to transcend the extensionalist-intensionalist dichotomy itself, through his unique triadic analysis of reference and meaning, by transcending the distinction between (as Quine put it) “things” and “attributes”.

Robert Brandom’s expressivism argues that not all semantic content may be made fully explicit. This view connects in interesting ways with recent movements in philosophy of mathematics and logic (e.g. Brown, Shin, Giaquinto) to take diagrams seriously - as more than a mere “heuristic aid” to proof, but either proofs themselves, or irreducible components of such. However what exactly is a diagram in logic? Does this constitute a semiotic natural kind? The paper will argue that such a natural kind does exist in Charles Peirce’s conception of iconic signs, but that fully understood, logical diagrams involve a structured array of normative reasoning practices, as well as just a “picture on a page”.

Charles S. Peirce’s semiotics uniquely divides signs into: i) symbols, which pick out their objects by arbitrary convention or habit, ii) indices, which pick out their objects by unmediated ‘pointing’, and iii) icons, which pick out their objects by resembling them (as Peirce put it: an icon’s parts are related in the same way that the objects represented by those parts are themselves related). Thus representing structure is one of the icon’s greatest strengths. It is argued that the implications of scaffolding education iconically are profound: for providing learners with a navigable road-map of a subject matter, for enabling them to see further connections of their own in what is taught, and for supporting meaningful active learning. Potential objections that iconic teaching is excessively entertaining and overly susceptible to misleading rhetorical manipulation are addressed.

Much mainstream analytic epistemology is built around a sceptical treatment of modality which descends from Hume. The roots of this scepticism are argued to lie in Hume’s (nominalist) theory of perception, which is excavated, studied and compared with the very different (realist) theory of perception developed by Peirce. It is argued that Peirce’s theory not only enables a considerably more nuanced and effective epistemology, it also (unlike Hume’s theory) does justice to what happens when we appreciate a proof in mathematics.