Aristotle’s assertoric syllogistic and modern relevance logic

This paper sets out to evaluate the claim that Aristotle’s Assertoric Syllogistic is a relevance logic or shows significant similarities with it. I prepare the grounds for a meaningful comparison by extracting the notion of relevance employed in the most influential work on modern relevance logic, Anderson and Belnap’s Entailment. This notion is characterized by two conditions imposed on the concept of validity: first, that some meaning content is shared between the premises and the conclusion, and second, that the premises of a proof are actually used to derive the conclusion. Turning to Aristotle’s Prior Analytics, I argue that there is evidence that Aristotle’s Assertoric Syllogistic satisfies both conditions. Moreover, Aristotle at one point explicitly addresses the potential harmfulness of syllogisms with unused premises. Here, I argue that Aristotle’s analysis allows for a rejection of such syllogisms on formal grounds established in the foregoing parts of the Prior Analytics. In a final section I consider the view that Aristotle distinguished between validity on the one hand and syllogistic validity on the other. Following this line of reasoning, Aristotle’s logic might not be a relevance logic, since relevance is part of syllogistic validity and not, as modern relevance logic demands, of general validity. I argue that the reasons to reject this view are more compelling than the reasons to accept it and that we can, cautiously, uphold the result that Aristotle’s logic is a relevance logic

Some False Laws of Logic

This paper argues that some widely used laws of implication are false, and arguments based upon them invalid. These laws are Exportation, Commutation, (as well as various restricted forms of these), Exported Syllogism and Disjunctive Syllogism. All these laws are false for the same reason – that they license the suppression or replacement in some position of some class of propositions which cannot legitimately be suppressed or replaced. These laws fail to preserve the property of sufficiency of premiss set for conclusion. They are false, and can be seen to be false, independently of their respon- sibility for the paradoxes. Hence the main ‘independent’ argument for the paradoxes – that they follow from an allegedly immaculate set of laws – is undermined. Counterexamples to all these laws are produced

Farewell to Suppression-Freedom

Val Plumwood and Richard Sylvan argued from their joint paper The Semantics of First Degree Entailment (Routley and Routley in Noûs 6(4):335–359, 1972, https://doi.org/10.2307/2214309) and onward that the variable sharing property is but a mere consequence of a good entailment relation, indeed they viewed it as a mere negative test of adequacy of such a relation, the property itself being a rather philosophically barren concept. Such a relation is rather to be analyzed as a sufficiency relation free of any form of premise suppression. Suppression of premises, therefore, gained center stage. Despite this, however, no serious attempt was ever made at analyzing the concept. This paper shows that their suggestions for how to understand it, either as the Anti-Suppression Principle or as the Joint Force Principle, turn out to yield properties strictly weaker than that of variable sharing. A suggestion for how to understand some of their use of the notion of suppression which clearly is not in line with these two mentioned principles is given, and their arguments to the effect that the Anderson and Belnap logics T, E and R are suppressive are shown to be both technically and philosophically wanting. Suppression-freedom, it is argued, cannot do the job Plumwood and Sylvan intended it to do.publishedVersio

Boundary Algebra: A Simpler Approach to Boolean Algebra and the Sentential Connectives

Boundary algebra [BA] is a algebra of type , and a simplified notation for Spencer-Brown’s (1969) primary algebra. The syntax of the primary arithmetic [PA] consists of two atoms, () and the blank page, concatenation, and enclosure between ‘(‘ and ‘)’, denoting the primitive notion of distinction. Inserting letters denoting, indifferently, the presence or absence of () into a PA formula yields a BA formula. The BA axioms are A1: ()()= (), and A2: “(()) [abbreviated ‘⊥’] may be written or erased at will,” implying (⊥)=(). The repeated application of A1 and A2 simplifies any PA formula to either () or ⊥. The basis for BA is B1: abc=bca (concatenation commutes & associates); B2, ⊥a=a (BA has a lower bound, ⊥); B3, (a)a=() (BA is a complemented lattice); and B4, (ba)a=(b)a (implies that BA is a distributive lattice). BA has two intended models: (1) the Boolean algebra 2 with base set B={(),⊥}, such that () ⇔ 1 [dually 0], (a) ⇔ a′, and ab ⇔ a∪b [a∩b]; and (2) sentential logic, such that () ⇔ true [false], (a) ⇔ ~a, and ab ⇔ a∨b [a∧b]. BA is a self-dual notation, facilitates a calculational style of proof, and simplifies clausal reasoning and Quine’s truth value analysis. BA resembles C.S. Peirce’s graphical logic, the symbolic logics of Leibniz and W.E. Johnson, the 2 notation of Byrne (1946), and the Boolean term schemata of Quine (1982).Boundary algebra; boundary logic; primary algebra; primary arithmetic; Boolean algebra; calculation proof; G. Spencer-Brown; C.S. Peirce; existential graphs

In Support of Valerie Plumwood

This paper offers general support for what Valerie Plumwood’s paper is trying to achieve by supporting the rejection of each of her four “false laws of logic”: exportation, illegitimate replacement, commutation (aka. permutation) and disjunctive syllogism. We start by considering her general characterizations of entailment, beginning with her stated definition of entailment as the converse of deducibility. However, this applies to a wide range of relevant logics and so is not able to be used as a criterion for deciding what laws to include in a logic. In this context, we examine the two key differences between deduction from premises to conclusion and entailment from antecedent to consequent. We also consider her use of sufficiency as a general characterizing feature. We then discuss Plumwood’s syntactic criteria used to reject the first three of her false laws of logic and add the Relevance Condition in this context. We next consider semantic characterizing criteria for a logic. After making a case against using truth, we introduce Brady’s logic MC of meaning containment. We then examine the content semantics for MC and use it to reject all of Plumwood’s false laws of logic together with some others. We follow with the related Depth Relevance Condition, which is a syntactic cri- terion satisfied by MC. This clearly rejects the first three of these laws and many others, but not the fourth law. We conclude by giving our overall support for her general enterprise

Reason and Delusion

Delusion represents an exceptional test case for the principal categories of common sense and philosophical thought such as ‘reason’, ‘truth’, ‘reality’. With the engagement of a hidden part of Freud’s legacy and the most discussed results of twentieth-century psychiatry, my aim will be to analyze its paradoxical forms and to shed light on the logics that underlie and orient its specific modalities of temporalization, conceptualization and argumentation. Delusion, then, has been traditionally interpreted as synonymous with irrationality (absurdity, groundlessness, error, chaos), whereas by contrast its mirror image, reason, has been defined in terms of evidence, demonstrability, truth and order. I will analyze and contrast their paradoxical definitions

Jeffersonian Walls and Madisonian Lines: The Supreme Court’s Use of History in Religion Clause Cases

In Everson v. Board of Education (1947), Justice Wiley Rutledge observed that \u27[n]o provision of the Constitution is more closely tied to or given content by its generating history than the religious clause of the First Amendment. It is at once the refined product and the terse summation of that history.\u27 Scholars and activists argue about the relevance or irrelevance of the Supreme Court’s use of history in general, and the extent to which Justices are good historians. These debates have been particularly furious with respect to the Court’s use of history in religion clause cases. Although broad claims are often made about the Court’s use of history in these cases, they are either unsupported generalities or extrapolations from a careful reading of only a handful of the Court’s many Free Exercise and Establishment Clause cases. In my essay I offer a systematic analysis of every religion clause case decided by the Supreme Court. I begin by providing original data drawn from these cases that clearly and succinctly address how Justices have used history in their opinions. I show the extent to which Justices have appealed to history and, when they do so, to whom or what they appeal. I then look at the distribution of religion clause cases over time and consider whether there are patterns with respect to the Court’s use of history. I proceed to study individual Justices, particularly the extent to which they tend to write opinions in religion clause cases and how often they use history. In this discussion I define what it means to be \u27liberal\u27 or \u27conservative\u27 in these cases and place Justices on an ideological continuum based upon every vote cast between 1940 and 2005. I follow this with an examination of the extent to which jurisprudential liberals and conservatives differ in their use of history. In the essay’s penultimate section I offer a narrative account of the Court’s use of history in religion clause cases with an emphasis on opinions where Justices consciously reflect on the relevance or irrelevance of history. I conclude by arguing that if Justices are going to make historical arguments that they should make good ones, and I suggest ways in which their historical arguments in religion clause opinions could be significantly improved

Bayesian confirmation, connexivism and an unkindness of ravens

Bayesian confirmation theories (BCTs) might be the best standing theories of confirmation to date, but they are certainly not paradox-free. Here I recognize that BCTs’ appeal mainly comes from the fact that they capture some of our intuitions about confirmation better than those the- ories that came before them and that the superiority of BCTs is suffi- ciently justified by those advantages. Instead, I will focus on Sylvan and Nola’s claim that it is desirable that our best theory of confirmation be as paradox-free as possible. For this reason, I will show that, as they respond to different interests, the project of the BCTs is not incompatible with Sylvan and Nola’s project of a paradox-free confirmation logic. In fact, it will turn out that, provided we are ready to embrace some degree of non-classicality, both projects complement each other nicely