Online research in philosophy

In this paper, the traditional view that argumentum ad ignorantiam is a logical fallacy is challenged, and lessons are drawn on how to model inferences drawn from knowledge in combination with ones drawn from lack of knowledge. Five defeasible rules for evaluating knowledge-based arguments that apply to inferences drawn under conditions of lack of knowledge are formulated. They are the veridicality rule, the consistency of knowledge rule, the closure of knowledge rule, the rule of refutation and the rule for argument from ignorance. The basic thesis of the paper is that knowledge-based arguments, including the argument from ignorance, need to be evaluated by criteria for epistemic closure and other evidential rules that are pragmatic in nature, that need to be formulated and applied differently at different stages of an investigation or discussion. The paper helps us to understand practical criteria that should be used to evaluate all arguments based on knowledge and/or ignorance.

It has been common wisdom for centuries that scientific inference cannot be deductive; if it is inference at all, it must be a distinctive kind of inductive inference. According to demonstrative theories of induction, however, important scientific inferences are not inductive in the sense of requiring ampliative inference rules at all. Rather, they are deductive inferences with sufficiently strong premises. General considerations about inferences suffice to show that there is no difference in justification between an inference construed demonstratively or ampliatively. The inductive risk may be shouldered by premises or rules, but it cannot be shirked. Demonstrative theories of induction might, nevertheless, better describe scientific practice. And there may be good methodological reasons for constructing our inferences one way rather than the other. By exploring the limits of these possible advantages, I argue that scientific inference is neither of essence deductive nor of essence inductive.

Lewis Carroll’s 1895 paper “Achilles and the Tortoise” showed that we need a distinction between rules of inference and premises. We cannot, on pain of regress, treat all rules simply as further premises in an argument. But Carroll’s paper doesn’t say very much about what rules there must be. Indeed, it is consistent with what Carroll says there to think that the only rule is -elimination. You might think that modern Bayesians, who seem to think that the only rule of inference they need is conditionalisation, have taken just this lesson from Carroll. But obviously nothing in Carroll’s argument rules out there being other rules as well.

Abstract In Peirce's and Hanson's characterization of abductive inference, the abducted hypothesis (but not others) is present in the premises, so that the inference can hardly be taken as ampliative. Abduction has consequently been treated as part of the process whereby already generated hypotheses are judged in terms of their plausibility, simplicity, etc. I propose an interpretation of abduction which supports an ampliative view. It relies on a distinction between two logical stages in the generation of hypotheses, one ?factual? and one ?explanatory?. I also indicate how we may reconstruct Peirce's and Hanson's original inference in an ampliative form.

An inference to a new explanation may be both logically non-ampliative and epistemically ampliative. Included among the premises of the latter form is the explanadum--a unique premise which is capable of embodying what we do not know about the matter in question, as well as legitimate aspects of what we do know. This double status points to a resolution of the Meno paradox. Ampliative inference of this sort, it is argued, has much in common with Nickles' idea of discoverability and, together with the mapping and correction procedures (briefly summarized) required for such inference, may suggest a broadening of the concept of justification which would incorporate much of what has been defended in theories of discovery.

The usual, comparative, conception of inference to the best explanation (IBE) takes it to be ampliative. In this paper I propose a conception of IBE ('Holmesian inference') that takes it to be a species of eliminative induction and hence not ampliative. This avoids several problems for comparative IBE (for example, how could it be reliable enough to generate knowledge?). My account of Holmesian inference raises the suspicion that it could never be applied, on the grounds that scientific hypotheses are inevitably underdetermined by the evidence (i.e. are inevitably ampliative). I argue that this concern may be resisted by acknowledging, as Timothy Williamson has shown, that all knowledge is evidence. The latter suggests an approach to resisting scepticism different from those (e.g. the reliabilist approach) that embrace fallibilism.

The usual, comparative, conception of Inference to the Best Explanation (IBE) takes it to be ampliative. In this paper I propose a conception of IBE (‘Holmesian inference’) that takes it to be a species of eliminative induction and hence not ampliative. This avoids several problems for comparative IBE (e.g. how could it be reliable enough to generate knowledge?). My account of Holmesian inference raises the suspicion that it could never be applied, on the grounds that scientific hypotheses are inevitably underdetermined by the evidence (i.e. are inevitably ampliative). I argue that this concern may be resisted by acknowledging, as Timothy Williamson has shown, that all knowledge is evidence. This suggests an approach to resisting scepticism different from those (e.g. the reliabilist approach) that embrace fallibilism.

In this article I take a loose, functional approach to defining induction: Inductive forms of reasoning include those prima facie reasonable inference patterns that one finds in science and elsewhere that are not clearly deductive. Inductive inference is often taken to be reasoning from the observed to the unobserved. But that is incorrect, since the premises of inductive inferences may themselves be the results of prior inductions. A broader conception of inductive inference regards any ampliative inference as inductive, where an ampliative inference is one where the conclusion ‘goes beyond’ the premises. ‘Goes beyond’ may mean (i) ‘not deducible from’ or (ii) ‘not entailed by’. Both of these are problematic. Regarding (i), some forms of reasoning might have a claim to be called ‘inductive’ because of their role in science, yet turn out to be deductive after all—for example eliminative induction (see below) or Aristotle’s ‘perfect induction’ which is an inference to a generalization from knowledge of every one of its instances. Interpretation (ii) requires that the conclusions of scientific reasoning are always contingent propositions, since necessary propositions are entailed by any premises. But there are good reasons from metaphysics for thinking that many general propositions of scientific interest and known by inductive inference (e.g. “all water is H2O”) are necessarily true. Finally, both (i) and (ii) fail to take account of the fact that there are many ampliative forms of inference one would not want to call inductive, such as counter-induction (exemplified by the ‘gambler’s fallacy’ that the longer a roulette wheel has come up red the more likely it is to come up black on the next roll). Brian Skyrms (1999) provides a useful survey of the issues involved in defining what is meant by ‘inductive argument’. Inductive knowledge will be the outcome of a successful inductive inference. But much discussion of induction concerns the theory of confirmation, which seeks to answer the question, “when and to what degree does evidence support an hypothesis?” Usually, this is understood in an incremental sense and in a way that relates to the rational credibility of a hypothesis: “when and by how much does e add to the credibility of h?”, although ‘confirms’ is sometimes used in an absolute sense to indicate total support that exceeds some suitably high threshold..

This paper considers how explanatory factors can play a role in our ampliative inferential practices. Van Fraassen has argued that there is no possible rational rule that governs ampliative inferences and includes weightings for explanatory beauty. In opposition to van Fraassen, Douven has argued that ampliative inferential rules that include weightings for explanatory factors can be rationally followed. There is, however, a crucial difficulty with Douven's approach: applying the ampliative rule that he suggests leads into irrational belief states. A way to remove the difficulties with Douven's account is suggested. The implications of rationally including explanatory factors in ampliative inferences are then considered. Introduction The proposed interpretations Van Fraassen's justification of the Bayesian approach A rational non-Bayesian interpretation? Further restrictions on D(A,B) Conclusion.

This book by one of the world's foremost philosophers in the fields of epistemology and logic offers an account of suppositional reasoning relevant to practical deliberation, explanation, prediction and hypothesis testing. Suppositions made 'for the sake of argument' sometimes conflict with our beliefs, and when they do, some beliefs are rejected and others retained. Thanks to such belief contravention, adding content to a supposition can undermine conclusions reached without it. Subversion can also arise because suppositional reasoning is ampliative. These two types of nonmonotonic logic are the focus of this book. A detailed comparison of nonmonotonicity appropriate to both belief contravening and ampliative suppositional reasoning reveals important differences that have been overlooked.