We show that the implicational fragment of intuitionism is the weakest logic with a non-trivial probabilistic semantics which satisfies the thesis that the probabilities of conditionals are conditional probabilities. We also show that several logics between intuitionism and classical logic also admit non-trivial probability functions which satisfy that thesis. On the other hand, we also prove that very weak assumptions concerning negation added to the core probability conditions with the restriction that probabilities of conditionals are conditional probabilities are sufficient to (...) trivialize the semantics. (shrink)

Conclusions reached using common sense reasoning from a set of premises are often subsequently revised when additional premises are added. Because we do not always accept previous conclusions in light of subsequent information, common sense reasoning is said to be nonmonotonic. But in the standard formal systems usually studied by logicians, if a conclusion follows from a set of premises, that same conclusion still follows no matter how the premise set is augmented; that is, the consequence relations of standard logics (...) are monotonic. Much recent research in AI has been devoted to the attempt to develop nonmonotonic logics. After some motivational material, we give four formal proofs that there can be no nonmonotonic consequence relation that is characterized by universal constraints on rational belief structures. In other words, a nonmonotonic consequence relation that corresponds to universal principles of rational belief is impossible. We show that the nonmonotonicity of common sense reasoning is a function of the way we use logic, not a function of the logic we use. We give several examples of how nonmonotonic reasoning systems may be based on monotonic logics. (shrink)

In [2] Hempel and Oppenheim give a definition of “explanation” for a certain formal language. In [1] Eberle, Kaplan, and Montague prove five theorems demonstrating that the Hempel and Oppenheim definition is not restrictive enough. In [3] Kim proposes two further conditions to supplement the Hempel and Oppenheim definition in order to avoid the objections posed in [1]. In this paper it is shown that the definition of Hempel and Oppenheim supplemented by Kim's conditions is open to a trivialization very (...) analogous to that given in [1]. (shrink)

The usual semantics for the modal systems T, S4, and S5 assumes that the set of possible worlds contains at least one member. Recently versions of these modal systems have been developed in which this assumption is dropped. The systems discussed here are obtained by slightly weakening the liberated versions of T and S4. The semantics does not assume the existence of possible worlds, and the accessibility relation between worlds is only required to be quasi-reflexive instead of reflexive. Completeness and (...) independence results are established. (shrink)

The intuitive notion behind the usual semantics of most systems of modal logic is that of ?possible worlds?. Loosely speaking, an expression is necessary if and only if it holds in all possible worlds; it is possible if and only if it holds in some possible world. Of course, contradictory expressions turn out to hold in no possible worlds, and logically true expressions turn out to hold in every possible world. A method is presented for transforming standard modal systems into (...) systems of modal logic for impossible worlds. To each possible world there corresponds an impossible world such that an expression holds in the impossible world if and only if it does not hold in the possible world. One can then talk about such worlds quite consistently, and there seems to be no logical reason for excluding them from consideration. (shrink)

Almost every formal model of explanation thus far proposed has been demonstrated to be faulty. In this paper, a new model, proposed by Raimo Tuomela, is also demonstrated to be faulty. In particular, one condition of the model is shown to be too restrictive, and another condition of the model is shown to be too permissive.

In this paper we examine the thesis that the probability of the conditional is the conditional probability. Previous work by a number of authors has shown that in standard numerical probability theories, the addition of the thesis leads to triviality. We introduce very weak, comparative conditional probability structures and discuss some extremely simple constraints. We show that even in such a minimal context, if one adds the thesis that the probability of a conditional is the conditional probability, then one trivializes (...) the theory. Another way of stating the result is that the conditional of conditional probability cannot be represented in the object language on pain of trivializing the theory. (shrink)

We prove consistent, assuming there is a supercompact cardinal, that there is a singular strong limit cardinal $\mu$ , of cofinality $\omega$ , such that every $\mu^{+}$ -chromatic graph X on $\mu^{+}$ has an edge colouring c of X into $\mu$ colours for which every vertex colouring g of X into at most $\mu$ many colours has a g-colour class on which c takes every value. The paper also contains some generalisations of the above statement in which $\mu^{+}$ is replaced (...) by other cardinals < $\mu$. (shrink)

The following statement is a report of the Committee on Philosophy in Education of the American Philosophical Association and was approved by the Association's Board of Officers in September, 1959. The Committee was composed of the following: C. W. Hendel, Chairman, H. G. Alexander, R. M. Chisholm, Max Fisch, Lucius Garvin, Douglas Morgan, A. E. Murphy, Charner Perry, and R. G. Turnbull. Primary responsibility for the preparation of this report belonged to a subcommittee composed of Roderick M. Chisholm, Chairman, (...) H. G. Alexander, Lewis Hahn, Paul C. Hayner, and Charles W. Hendel. (shrink)

Most of us came into ecology with memories of special personal places. A cliff top that Claude Monet might have painted. Allen as a youth spent his holidays on the Dorset Coast near Swanage; he can still smell the sea breeze of his childhood. Curtin grow up on a farm in southwestern Wisconsin, the dew of the grass and the bright green on a June morning remains vivid. The catching of reptiles and insects for him awakened a curiosity about the (...) natural world that has remained to this day. But once into the field there came the scholarship. With ever tighter grant monies, the pressure to publish takes so much of the fun out of it. A climate of unbridled careerism prevails and shows itself in the incremental state of the literature: little things to list on this year's activities report. There are now even predatory journals that cynically do not seriously review submissions, and only collect page charges. As journal editors have a desperate time getting reviews done by mature scholars, instead of a hand off to their overworked graduate students. So what is to be done - how can we bring the joy and importance of discovery back into it all? After all ecology is done by human beings. Mostly it is a personal mission, for what great ecologists write is frequently personal and life changing. So an undercurrent of this book is to remind and reveal the original purpose of science. Not professional advancement, but the genuine search for novel ideas and the imperative to share hard won insights and personal passions. (shrink)

Counterfactual imaginings are known to have far reaching implications. In the present experiment, we ask if imagining events from one's past can affect memory for childhood events. We draw on the social psychology literature showing that imagining a future event increases the subjective likelihood that the event will occur. The concepts of cognitive availability and the source monitoring framework provide reasons to expect that imagination may inflate confidence that a childhood event occurred. However, people routinely produce myriad counterfactual imaginings (i.e., (...) daydreams and fantasies) but usually do not confuse them with past experiences. To determine the effects of imagining a childhood event, we pretested subjects on how confident they were that a number of childhood events had happened, asked them to imagine some of those events, and then gathered new confidence measures. For each of the target items, imagination inflated confidence that the event had occurred in childhood. We discuss implications for situations in which imagination is used as an aid in searching for presumably lost memories. (shrink)

Modern cells present no signs of a putative prebiotic RNA world. However, RNA coding is not a sine qua non for the accumulation of catalytic polypeptides. Thus, cellular proteins spontaneously fold into active structures that are resistant to proteolysis. The law of mass action suggests that binding domains are stabilized by specific interactions with their substrates. Random polypeptide synthesis in a prebiotic world has the potential to initially produce only a very small fraction of polypeptides that can fold spontaneously into (...) catalytic domains. However, that fraction can be enriched by proteolytic activities that destroy the unfolded polypeptides and regenerate amino acids that can be recycled into polypeptides. In this open system scenario the stable domains that accumulate and the chemical environment in which they are accumulated are linked through self coding of polypeptide structure. Such open polypeptide systems may have been the precursors to the cellular ribonucleoprotein (RNP) world that evolved subsequently. (shrink)