Richard Routley

The semantics of entailment — III

Publisher Summary This chapter discusses the semantics of entailment. Earlier, modal logics had no semantics. Bearing a real world G, a set of worlds K, and a relation R of relative possibility between worlds, Saul Kripke beheld this situation and saw that it was formally explicable and made model structures. It came to pass that soon everyone was making model structures, and some were deontic, some were temporal, and some were epistemic, according to the conditions on the binary relation R. The models made by Kripke, Hintikka, and Thomason were, however, not relevant. Central to the semantics being developed is a ternary relation R that takes the place for the relevant logics of the Kripke binary relation for standard modal and intuitionistic logics.

The American plan completed: Alternative classical-style semantics, without stars, for relevant and paraconsistent logics

American-plan semantics with 4 values 1, 0, { {1, 0}} {{}}, interpretable as True, False, Both and Neither, are furnished for a range of logics, including relevant affixing systems. The evaluation rules for extensional connectives take a classical form: in particular, those for negation assume the form 1 ∈ τ(∼A, a) iff 0 ε τ (A, a) and 0 ∈ τ (∼A, a) iff 1 ∈ τ (A, a), so eliminating the star function *, on which much criticism of relevant logic semantics has focussed. The cost of these classical features is a further relation (or operation), required in evaluating falsity assignments of implication formulae.Two styles of 4 valued relational semantics are developed; firstly a semantics using notions of double truth and double validity for basic relevant systemB and some extensions of it; and secondly, since the first semantics makes heavy weather of validating negation principles such as Contraposition, a reduced semantics using more complex implicational rules for relevant systemC and various of its extensions. To deal satisfactorily with elite systemsR,E andT, however, further complication is inevitable; and a relation of mateship (suggested by the Australian plan) is introduced to permit cross-over from 1 to 0 values and vice versa.

Alleged problems in attributing beliefs, and intentionality, to animals

The ordinary attribution of intentionality to (nonhuman) animals raises serious problems for fashionable linguistic accounts of belief and of intentionality generally; and many of the alleged problems arise from such linguistic theories of mind. Another deeper source of alleged problems is the apartness thesis, that there is a significant difference in kind, with substantial moral import, between humans and other animals; for the last lines of defence of this erroneous thesis consist in making out that there are significant intentional differences. A wide range of recent arguments against assigning intentionality (in the full sense) to animals are criticized in detail: those of Stich and Williams, in terms of animals lacking effective or specifiable concepts (concepts now replacing souls); those of Stich and Davidson based on the requirement for beliefs of an isomorphic belief network; those based on the usual opacity of intentionality; those of Descartes and Davidson and others based on the requirement o...

Problems and Solutions in the Semantics of Quantified Relevant Logics. I.

The main problem investigated is the adequacy of constant domain relational world semantics for quantified relevant logics. The problem is solved, though in a disagreeably circuitous way, for many weaker relevant logics, and an outline of how the solution may be extended to stronger logics such as RQ is given. Alternative necessity and intensional-conjunction style rules for the evaluation of quantifiers are studied and shown to simply force the main problems above with the usual (extensional conjunction style) quantifier - rule to reappear, unmitigated, at alternative outlets. Finally some philosophical problems allegedly engendered by constant domain world semantics are examined briefly: it is argued that the “problems” are no problems.

Necessary limits to knowledge: unknowable truths

The paper seeks a perfectly general argument regarding the non-contingent limits to any (human or non-human) knowledge. After expressing disappointment with the history of philosophy on this score, an argument is grounded in Fitch’s proof, which demonstrates the unknowability of some truths. The necessity of this unknowability is then defended by arguing for the necessity of Fitch’s premise—viz., there this is in fact some ignorance.

I. The durability of impossible objects

Meinongs theory of impossible objects is defended against a number of objections, in particular against Karel Lamberts argument (see Impossible Objects’, Inquiry, Vol. 17 [1974], pp. 303–14) that no objects are impossible.

I. On the alleged inconsistency, moral insensitivity and fanaticism of pacifism

All the standard and some esoteric objections to pacifism are refuted, either directly or (as with the charge of impracticality) in outline. Familiar arguments to the inconsistency and irresponsibility of pacifism are shown to turn upon illegitimately construing pacifist activities such as resisting, preventing, and defending as involving violence. Several arguments against pacifism from violence as a lesser evil turn out to be fallacious; some involve the erroneous assumption that violence is the only evil, but some lead into what pacifism can simply concede, moral dilemmas. It is argued that pacifism is not a form of fanaticism, is not morally insensitive, does not imply anarchism, or vegetarianism, is not completely impractical, and can be positively underpinned. In the course of the arguments various types of pacifism are classified, pacifism is distinguished from nonviolent action, and pacifism and, differently, pacificity are disassociated from passivity: The question of a more general characterizat...

Alternative semantics for quantified first degree relevant logic

A system FDQ of first degree entailment with quantification, extending classical quantification logic Q by an entailment connective, is axiomatised, and the choice of axioms defended and also, from another viewpoint, criticised. The system proves to be the equivalent to the first degree part of the quantified entailmental system EQ studied by Anderson and Belnap; accordingly the semantics furnished are alternative to those provided for the first degree of EQ by Belnap. A worlds semantics for FDQ is presented, and the soundness and completeness of FDQ proved, the main work of the paper going into the proof of completeness. The adequacy result is applied to yield, as well as the usual corollaries, weak relevance of FDQ and the fact that FDQ is the common first degree of a wide variety of (constant domain) quantified relevant logics. Finally much unfinished business at the first degree is discussed.