In [6] proof tableau formulations were given of the implication/negation fragments of the important zero-order relevant logics E and R and the semirelevant logic RM . The main purpose of this paper then, is to extend results by giving proof tableau formulations of the distribution-free fragments of E, R and RM and of their first order extensions EQ, RQ and RMQ. Where X is one of these logics, we shall follow [13] in calling its distribution-free fragment OX – the ‘O’ (...) standing for ‘ortho’ which is meant to signify the kinship of these logics to quantum logics or ortho-logics as they now tend to be known. Hence in what follows we shall refer to the logics OX simply as relevant ortho-logics. (shrink)

A bivalent valuation is snt iff sound (standard PC inference rules take truths only into truths) and non-trivial (not all wffs are assigned the same truth value). Such a valuation is normal iff classically correct for each connective. Carnap knew that there were non-normal snt valuations of PC, and that the gap they revealed between syntax and semantics could be "jumped" as follows. Let $VAL_{snt}$ be the set of snt valuations, and $VAL_{nrm}$ be the set of normal ones. The bottom (...) row in the table for the wedge 'v' is not semantically determined by $VAL_{snt}$ , but if one deletes from $VAL_{snt}$ all those valuations that are not classically correct at the aforementioned row, one jumps straights to $VAL_{nrm}$ and thus to classical semantics. The conjecture we call semantic holism claims that the same thing happens for any semantic indeterminacy in any row in the table of any connective of PC, i.e., to remove it is to jump straight to classical semantics. We show (i) why semantic holism is plausible and (ii) why it is nevertheless false. And (iii) we pose a series of questions concerning the number of possible steps or jumps between the indeterminate semantics given by $VAL_{snt}$ and classical semantics given by $VAL_{nrm}$. (shrink)

Stit theory (a logic of seeing-to-it-that) is applied to cases involving many agents. First treated are complex nestings of stits involving distinct agents. The discussion is driven by the logical impossibility of "a sees to it that b sees to it that Q" in the technical sense, even though that seems to make sense in everyday language, Of special utility are the concepts of "forced choice", of the creation of deontic states, and of probabilities, Second, joint agency, both plain and (...) strict (every participant is essential) is given a rigorous treatment. A central theorem is that strict joint agency is itself agentive. (shrink)

Following von Wright, ``transitions'' are needed for understanding agency. I indicate how von Wright's account of transitions should be adapted to take account of objective indeterminism, using the idea of branching space-time. The essential point is the need to locate transitions not merely in space-time, but concretely amid the indeterministic, causally structured possibilities of our (only) world. (This is a ``postprint'' of Belnap 1999, as cited in the paper. The page numbers do not, of course, match those of the (...) original.). (shrink)

In this rigorous investigation into the logic of truth Anil Gupta and Nuel Belnap explain how the concept of truth works in both ordinary and pathological..

Here is an important new theory of human action, a theory that assumes actions are founded on choices made by agents who face an open future.

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The theory of branching space-times is designed as a rigorous framework for modelling indeterminism in a relativistically sound way. In that framework there is room for "funny business", i.e., modal correlations such as occur through quantummechanical entanglement. This paper extends previous work by Belnap on notions of "funny business". We provide two generalized definitions of "funny business". Combinatorial funny business can be characterized as "absence of prima facie consistent scenarios", while explanatory funny business characterizes situations in which no localized (...) explanation of inconsistency can be given. These two definitions of funny business are proved to be equivalent, and we provide an example that shows them to be strictly more general than the previously available definitions of "funny business". (shrink)

Using Aristotle's well-known sea battle as our example, we offer a precise, intelligible analysis of future contingent assertions in the presence of indeterminism. After explaining our view of the problem, we present a picture of indeterminism in the context of a tree ofbranching histories. There follows a brief description ofthe semantic bases for our double-time-reference theory of future contingents. We then set out our account. Before concluding, we discuss some ramifications of, and alternatives to, a double-time-reference approach to the problem (...) of future contingents. There are some technical ideas at the foundation of our analysis, ideas of which most philosophers are largely ignorant; on our view, in the absence of mastery ofthese ideas it is quite impossible to speak responsibly about either indeterminism or free will. (shrink)

Branching space-time is a simple blend of relativity and indeterminism. Postulates and definitions rigorously describe the causal order relation between possible point events. The key postulate is a version of everything has a causal origin; key defined terms include history and choice point. Some elementary but helpful facts are proved. Application is made to the status of causal contemporaries of indeterministic events, to how splitting of histories happens, to indeterminism without choice, and to Einstein-Podolsky-Rosen distant correlations.

“Flat pre-semantics” lets each parameter of truth be considered separately and equally, and without worrying about grammatical complications. This allows one to become a little clearer on a variety of philosophical-logical points, such as the usefulness of Carnapian tolerance and the deep relativity of truth. A more definite result of thinking in terms of flat pre-semantics lies in the articulation of some instructive ways of categorizing operations on meanings in purely logical terms in relation to various parameters of truth ; (...) namely, closing vs. leaving open, local vs. translocal, and anchored vs. unanchored. Basic relations among these categories are established. (shrink)

1. Rescher 1964 — henceforth HR — proposes a way of reasoning from a set of hypotheses which may include both some of our beliefs and also hypotheses contradicting those beliefs. The aim of this paper is to point out what I take to be a fault in Rescher’s proposal, and to suggest a modification of it, using a nonclassical logic, which avoids that fault. The paper neither attacks nor defends the broader aspects of Rescher’s proposal, but merely assumes that (...) it is at least prima facie worthwhile and therefore worthy of amendment; consequently, I shall try to tinker as little as possible. In particular, the use of a nonclassical logic which I propose does not replace any use by HR of classical logic — in those places where Rescher is classical, I shall be classical, too. (Instead, the amendment introduces a nonclassical logic at a point where HR uses no logic at all.). (shrink)

permits a sound and rigorously definable notion of ‘originating cause’ or causa causans—a type of transition event—of an outcome event. Mackie has famously suggested that causes form a family of ‘inus’ conditions, where an inus condition is ‘an insufficient but non-redundant part of an unnecessary but sufficient condition’. In this essay the needed concepts of BST theory are developed in detail, and it is then proved that the causae causantes of a given outcome event have exactly the structure of a (...) set of Mackie inus conditions. The proof requires the assumption that there is no EPR-like ‘funny business’. This seems enough to constitute a theory of ‘causation’ in at least one of its many senses. Introduction The cement of the universe Preliminaries 3.1 First definitions and postulates 3.2 Ontology: propositions 3.3 Ontology: initial events 3.4 Ontology: outcome events 3.5 Ontology: transition events 3.6 Propositional language applied to events Causae causantes 4.1 Causae causantes are basic primary transition events 4.2 Causae causantes of an outcome chain 4.3 No funny business Causae causantes and inns and inus conditions 5.1 Inns conditions of outcome chains: not quite 5.2 Inns conditions of outcome chains 5.3 Inns conditions of scattered outcome events 5.4 Inus conditions for disjunctive outcome events 5.5 Inns and inus conditions of transition events Counterfactual conditionals Appendix: Tense and modal connectives in BST. (shrink)