Class Of Propositions Research Articles

Conventional Realism and Political Inquiry: Channeling Wittgenstein by John G. Gunnell

Reviewed by: Conventional Realism and Political Inquiry: Channeling Wittgenstein by John G. Gunnell Tracy B. Strong GUNNELL, John G. Conventional Realism and Political Inquiry: Channeling Wittgenstein. Chicago: The University of Chicago Press, 2020. 194 pp. Cloth, $40.00 John G. Gunnell has written extensively, dealing mostly with questions in the philosophy of science and its relevance to the practice of thought. In this book, he addresses inter alia Davidson, Sellars, Diamond, Dummett, Fodor, Freeden, Grice, Kripke, McDowell, Putnam, Ryle, Searle, Williams, Winch—and that is but a selection. He approaches them from a conceptual understanding grounded in a reading of Wittgenstein, Austin, and Kuhn. His target is "representational philosophy," which is for him the dominant mode of analytic philosophizing and is based on the claim that the "mind is the source and repository of meaning, while language is [End Page 816] primarily a vehicle of thought and a means of communication." Reality would thus lie "behind" our discursive practices. To this, he opposes "conventional realism" for which all "phenomena are conventional in that they are specified in language," thus "constituted by human agreement." These are "first-order practices," whereas philosophy and social science are "second-order practices." This is a serious and important book. For those not up to speed with contemporary analytic philosophy, it provides generally excellent if necessarily abbreviated accounts (not summaries) and cogent critiques of major analytical thinkers. Gunnell forcefully advances an account of how philosophers and social scientists should think about their business. For spatial concerns, I take two to whom he might be thought sympathetic. Hilary Putnam's final position rejected the assumptions of both realism and antirealism, claiming that "there is a way to do justice to our sense that knowledge claims are responsible to reality without recoiling into metaphysical fantasy." To counter the threat of relativism, Putnam argues for "direct realism" and "conceptual pluralism." Gunnell finds that Putnam wavers, however, between suggesting an identity of language and the world and at other times holding that "language attaches itself to a separate 'world'." Or John Searle: For Gunnell, Searle "assumed something that Austin had not. This was that speech acts are expressions of ontologically prior mental states and processes signified by such terms as 'purpose' and 'intention' and that conventional acts are ultimately based on what Searle referred to as non-conventional 'brute facts'." He suggests that this is in part due to Searle's fear of French-lace relativism. True statements must rather correspond to "a reality totally independent of us." Gunnell devotes a chapter to the "fear of relativism." Such is his general approach: Most considered are either expressly representationalists, privileging some conception of the mind as separate from "reality," or they are covertly (and sometimes unknowingly) so. I find his criticisms generally convincing. What then is "conventional realism"? Our conventional life, manifest in and as our language, is not to be understood as a "proper distinction … between nature and convention but rather between various conventions of linguistic usage and the character of the propositions involved." His argument relies heavily on a reading of Wittgenstein's On Certainty. Too briefly: All language-games rest on a class of propositions that are claims about what elements constitute the world but are not representational. (There is no such thing, therefore, as "the political.") They can thus change over time. "What Wittgenstein continually stressed was that this confluence of foundational and hypothetical propositions constituted a system within which judgments are made and into which people are initiated when they first acquire language as well as when they appropriate new forms of language and belief that at least temporarily become authoritative and excluded from doubt." Gunnell accepts that when two different systems of belief "clash there comes a point at which [End Page 817] there is an end to advancing reasons that might be plausible to both parties." What to make of this sympathetic and important no-holds-barred reading of Wittgenstein? Wittgenstein's word Abmachung is often translated as "convention." Abmachung does mean convention, but also arrangement, agreement, stipulation. Translation matters: A convention is something to which we are attached. An agreement is something that each of us does. "Agreement" places the emphasis more on...

Why Explanatory Considerations Matter

This paper aims at elucidating the connection between explanatory considerations and epistemic justification stipulated by explanationism which take epistemic justification to be definable in terms of best explanations. By relying on the notion of truthlikeness, this paper argues that it is rational for a subject to expect the best explanation she has for her evidence to be more truthlike than any of the other potential explanations available to her by virtue of containing a class of propositions that, given her evidence, she is justified in believing. Based on this elucidation of the connection between explanatory considerations and epistemic justification, an explanationist account of the evidential support relation is then offered.

No Trouble with Poetic Licence: a reply to Xhignesse

Recently, Xhignesse has argued that the principle of poetic licence (PPL), which roughly states that any class of propositions is true in some possible fiction, ought to be rejected. Here, we defend PPL from Xhignesse’s objection by demonstrating that, properly understood, his purported counter-example case is either irrelevant or unproblematic. The upshot is that Xhignesse has given us no reason to reject PPL.

A linear/producer/consumer model of classical linear logic

This paper defines a new proof- and category-theoretic framework forclassical linear logicthat separates reasoning into one linear regime and two persistent regimes corresponding to ! and ?. The resulting linear/producer/consumer (LPC) logic puts the three classes of propositions on the same semantic footing, following Benton's linear/non-linear formulation of intuitionistic linear logic. Semantically, LPC corresponds to a system of three categories connected by adjunctions reflecting the LPC structure. The paper's meta-theoretic results include admissibility theorems for the cut and duality rules, and a translation of the LPC logic into category theory. The work also presents several concrete instances of the LPC model.

A Linear/Producer/Consumer Model of Classical Linear Logic

This paper defines a new proof- and category-theoretic framework for classical linear logic that separates reasoning into one linear regime and two persistent regimes corresponding to ! and ?. The resulting linear/producer/consumer (LPC) logic puts the three classes of propositions on the same semantic footing, following Benton's linear/non-linear formulation of intuitionistic linear logic. Semantically, LPC corresponds to a system of three categories connected by adjunctions reflecting the linear/producer/consumer structure. The paper's metatheoretic results include admissibility theorems for the cut and duality rules, and a translation of the LPC logic into category theory. The work also presents several concrete instances of the LPC model.

The Topoi from the Greater, the Lesser and the Same Degree: An Essay on the σύγκρισις in Aristotle’s Topics

The presence of premises expressing comparison is a problem for the Aristotelian theory of the dialectical method, first because there is no general theory of comparison in the Organon and secondly because along with propositions on the opposition and inflexion of the terms, comparative statements seem to fall outside the explicit description which Aristotle gives of possible premises. The purpose of this paper is to offer a synthetic theory of comparisons according to Aristotle’s Topics, in an attempt both to supply the aforementioned absence and to highlight the importance of the second problem. There are three main types of premises on the more, theless and the similar: some comparing the degree of possession of a predicate, others comparing the plausibility of a predication and finally, others expressing an analogy. Once expounded the very marked differences that occur between these three classes of propositions, the paper analyses the various kinds of argumentation based on comparative premises and offers a formalization of its logical laws. The complexity of this theory and the volume of topoi involved in the comparisons show the magnitude of a problem that has not been sufficiently studied.

Non-Classical Stems from Classical: N. A. Vasiliev’s Approach to Logic and his Reassessment of the Square of Opposition

In the XIXth century there was a persistent opposition to Aristotelian logic. Nicolai A. Vasiliev (1880–1940) noted this opposition and stressed that the way for the novel – non-Aristotelian – logic was already paved. He made an attempt to construct non-Aristotelian logic (1910) within, so to speak, the form (but not in the spirit) of the Aristotelian paradigm (mode of reasoning). What reasons forced him to reassess the status of particular propositions and to replace the square of opposition by the triangle of opposition? What arguments did Vasiliev use for the introduction of new classes of propositions and statement of existence of various levels in logic? What was the meaning and role of the “method of Lobachevsky” which was implemented in construction of imaginary logic? Why did psychologism in the case of Vasiliev happen to be an important factor in the composition of the new ‘imaginary’ logic, as he called it?

A Reflection on Russell's Ramified Types and Kripke's Hierarchy of Truths

Both in Kripke's Theory of Truth KTT [8] and Russell's Ramified Type Theory RTT [16, 9] we are confronted with some hierarchy. In RTT, we have a double hierarchy of orders and types. That is, the class of propositions is divided into different orders where a propositional function can only depend on objects of lower orders and types. Kripke on the other hand, has a ladder of languages where the truth of a proposition in language Ln can only be made in Lm where m)n. Kripke finds a fixed point for his hierarchy (something Russell does not attempt to do). We investigate in this paper the similarities of both hierarchies: At level n of KTT the truth or falsehood of all order-n-propositions of RTT can be established. Moreover, there are order-n-propositions that get a truth value at an earlier stage in KTT. Furthermore, we show that wrr is more restrictive than KTT, as some type restrictions are not needed in KTT and more formula., can be expressed in the latter. Looking back at the double hierarchy of Russell, Ramsey [11] and Hilbert and Ackermann [7] considered the orders to cause the restrictiveness, and therefore removed them. This removal resulted in Church's Simple Type Theory STT [1] We show however that orders in RTT correspond to levels of truth in KTT. Hence, KTT can be regarded as the dual of STT where types have been removed and orders are maintained. As RTT is more restrictive than KTT, we can conclude that it is the combination of types and orders that was the restrictive factor in RTT.

Mystical Experience and Non–Basically Justified Belief

Two theses are central to foundationalism. First, the foundationalist claims that there is a class of propositions, a class of empirical contingent beliefs, that are ‘immediately justified’. Alternatively, one can describe these beliefs as ‘self–evident’, ‘non–inferentially justified’, or ‘self–warranted’, though these are not always regarded as entailing one another. The justification or epistemic warrant for these beliefs is not derived from other justified beliefs through inductive evidential support or deductive methods of inference. These ‘basic beliefs’ constitute the foundations of empirical knowledge. One can give a reason for the justification of a basic belief even though the justification for that belief is not based on other beliefs. Thus, according to Chisholm, if asked what one's justification was for thinking that one knew, presently, that one is thinking about a city one takes to be Albuquerque, one could simply say ‘what justifies me…is simply the fact that I am thinking about a city I take to be Albuquerque’.

A GENERALIZED VIEW OF NONMONOTONIC KNOWLEDGE: A SET OF THEORETIC PERSPECTIVE

Abstract We provide a set theoretic framework for looking at the classical logical inference problem. We then introduce within this framework a new class of propositions, called second order propositions, which provide a prototypical characterization of nonmonotonic type default knowledge. We study the properties of this new class of propositions.

Leibniz on Truth and Contingency

Leibniz’ principal doctrine of truth is an attempt to set out the truth-conditions for a certain syntactically-defined class of propositions. As such, it constitutes an attempt to provide at least one portion of a semantical theory. The doctrine itself is found for example in Elementa Calculi:Every true categorical proposition, affirmative and universal, signifies nothing but a certain connection between the predicate and the subject… This connection is such that the predicate is said to be in the subject, or to be contained in it, and this either absolutely and viewed in itself, or in some particular case. Or in the same way, the subject is said to contain the predicate; that is, the notion of the subject, either in itself or with some addition, involves the notion of the predicate.It is clear, from this work as well as from “First Truths” and “On Freedom”, that the doctrine is not restricted to universal affirmatives, but applies as well to particular affirmatives.

Epistemology and Communication Theory

Logical positivists describe certain classes of propositions as analytic or synthetic. Their position would be unassailable if they left the matter at that. Unfortunately they add a rider to the effect that all propositions are one or the other. Pseudo–propositions, being neither one nor the other, are described as nonsense. The above rider itself appears to fall into neither class and an immediate objection may be made to the positivist's standpoint on the ground that it commits him to nonsense by his own definition.

A basic logic

This paper is concerned with finding a fairly simple system of logic which is “basic” in the sense that every system of logic is definable in it. If a “system”is regarded as being a class of propositions, rather than a class of sentences, then every class of propositions which is a system should be definable in the basic logic. The system of logic proposed in this paper will not be proved to be a basic logic, but strong evidence that it is basic will be given at the end of the paper. Evidence will also be given that the class of propositions which are not provable in the system is not definable in any system of logic. It will be established that the decision problem is unsolvable for the system. Notable characteristics of the system are its lack of negation and universal quantification, and its similarity to systems proposed by Church, Curry, and Rosser.By a “system” will be meant a class of propositions the membership of which can be specified by ordinary recursive methods, so that if the membership of a given proposition in the class can be established at all, such membership can be established in a finite number of steps. (This is not the same as demanding that a criterion must exist for determining, in a finite number of steps, whether or not some given proposition is a member of the class. Such a demand would require a solution of the decision problem for every system.)