Ampliative Inference Research Articles

Depicting Deity: A Metatheological Approach

<i>Depicting Deity: A Metatheological Approach</i>

On the heuristic power of mathematical representations

I argue that mathematical representations can have heuristic power since their construction can be ampliative. To this end, I examine how a representation (a) introduces elements and properties into the represented object that it does not contain at the beginning of its construction, and (b) how it guides the manipulations of the represented object in ways that restructure its components by gradually adding new pieces of information to produce a hypothesis in order to solve a problem.In addition, I defend an ‘inferential’ approach to the heuristic power of representations by arguing that these representations draw on ampliative inferences such as analogies and inductions. In effect, in order to construct a representation, we have to ‘assimilate’ diverse things, and this requires identifying similarities between them. These similarities form the basis for ampliative inferences that gradually build hypotheses to solve a problem.To support my thesis, I analyse two examples. The first one is intra-field (intra-mathematical), that is, the construction of an algebraic representation of 3-manifolds; the second is inter-fields, that is, the construction of a topological representation of DNA supercoiling.

Dogmatism and Ampliative Inference

The evidential role of experience in justifying beliefs has been at the center of debate in philosophy in recent years. One view is that experience, or seeming, can confer immediate (defeasible) justification on belief in virtue of its representational phenomenology. Call this view “representational dogmatism.” Another view is that experience confers immediate justification on belief in virtue of its relational phenomenology. Call this view “relational dogmatism.” The goal of this paper is to pit these two versions of dogmatism against each other in terms of their ability to account for ampliative, or non-deductive, inferential justification. I will argue that only the representational view can provide a plausible account of this type of justification.

Inferentialism, degrees of commitment, and ampliative reasoning

Our purpose in this paper is to contribute to a practice-based characterization of scientific inference. We want to explore whether Brandom’s pragmatist–inferentialist framework can suitably accommodate several types of ampliative inference common in scientific reasoning and explanation (probabilistic reasoning, abduction and idealisation). First, we argue that Brandom’s view of induction in terms of merely permissive inferences is inadequate; in order to overcome the shortcoming of Brandom’s proposal, we put forward an alternative conception of inductive, probabilistic reasoning by appeal to the notion of degrees of commitment. Moreover, we examine the sorts of inferential commitments operative in other types of ampliative inferences, such as abduction or reasoning involving idealizations and assumptions. We suggest that agents engaging in these forms of reasoning often undertake restricted inferential commitments, whose scope and reach are more limited that in the case of the commitments associated with full beliefs.

Reactionary responses to the Bad Lot Objection

As it is standardly conceived, Inference to the Best Explanation (IBE) is a form of ampliative inference in which one infers a hypothesis because it provides a better potential explanation of one's evidence than any other available, competing explanatory hypothesis. Bas van Fraassen famously objected to IBE thus formulated that we may have no reason to think that any of the available, competing explanatory hypotheses are true. While revisionary responses to the Bad Lot Objection concede that IBE needs to be reformulated in light of this problem, reactionary responses argue that the Bad Lot Objection is fallacious, incoherent, or misguided. This paper shows that the most influential reactionary responses to the Bad Lot Objection do nothing to undermine the original objection. This strongly suggests that proponents of IBE should focus their efforts on revisionary responses, i.e. on finding a more sophisticated characterization of IBE for which the Bad Lot Objection loses its bite.

Abductively robust inference

Inference to the Best Explanation (IBE) is widely criticized for being an unreliable form of ampliative inference – partly because the explanatory hypotheses we have considered at a given time may all be false, and partly because there is an asymmetry between the comparative judgment on which an IBE is based and the absolute verdict that IBE is meant to license. In this paper, I present a further reason to doubt the epistemic merits of IBE and argue that it motivates moving to an inferential pattern in which IBE emerges as a degenerate limiting case. Since this inferential pattern is structurally similar to an argumentative strategy known as Inferential Robustness Analysis (IRA), it effectively combines the most attractive features of IBE and IRA into a unified approach to non-deductive inference.

A model for scientific discovery in psychological logics

The critical methods for the scientific discovery should include abduction and induction that Peirce named as ampliative (synthetic) inferences, as well as analogy and metaphor that did not mentioned by Peirce but were very favor by contemporary cognitive scientists. In the authors view, abduction, induction, analogy and metaphor are the methods to be used in search of and set up hypothesis, and deduction, explicative (analytic or deductive) inferences named by Peirce, can be used in validating that hypothesis. The study advocates that all logical processing is accompanied with psychological processes in humans cognition, therefore, all logics are psychological. The author indicates that every process of proof is abductive by tracing the inferences in philosophy, logic and mathematics in the western world since Socrates. The authors also illuminate the effects of abduction, induction and analogy in scientific discovery with some examples in modern sciences such as continental drift and plate tectonics, Big Bang Cosmology, and theorem-proving with Balcon machine. Especially, this paper analyzes carefully the characters of psychological logics such as deduction and abduction with a famous Wason selection task as example. Then, a discipline frame of cognitive logic will be created, while abduction would be placed into this new frame becomingly, belonged to a sub-discipline of cognitive logic, i.e., psychological logics. Finally, a model in psychologcical logics with three parallel channels and a serial channel will be set up. With this model, abduction, analogy and induction should be used in describing or even to finding hypotheses in scientific discovery, while deduction should be used in validating the hypotheses. This model is an integrative model based on the cognitive scientific comprehensions, which is more advanced than any other similar models and has stronger explanations for scientific discovery. With this model, the author will discuss some problems related with scientific discovery and get some meaningful conclusions in this paper.

On the distinction between Peirce’s abduction and Lipton’s Inference to the best explanation

I argue against the tendency in the philosophy of science literature to link abduction to the inference to the best explanation (IBE), and in particular, to claim that Peircean abduction is a conceptual predecessor to IBE. This is not to discount either abduction or IBE. Rather the purpose of this paper is to clarify the relation between Peircean abduction and IBE in accounting for ampliative inference in science. This paper aims at a proper classification—not justification—of types of scientific reasoning. In particular, I claim that Peircean abduction is an in-depth account of the process of generating explanatory hypotheses, while IBE, at least in Peter Lipton’s thorough treatment, is a more encompassing account of the processes both of generating and of evaluating scientific hypotheses. There is then a two-fold problem with the claim that abduction is IBE. On the one hand, it conflates abduction and induction, which are two distinct forms of logical inference, with two distinct aims, as shown by Charles S. Peirce; on the other hand it lacks a clear sense of the full scope of IBE as an account of scientific inference.

Demonstrative Induction and the Skeleton of Inference

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.

Utilising Explanatory Factors in Induction?

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.

The pragmatics of inferential content

Carnap took the content of a particularsentence or set of sentences to consist in the set ofthe consequences of the sentence or set. This claimequates meaning with inferential role, but itrestricts the inferences to deductive or explicativeones. Here I reject a recent proposal by RobertBrandom, where inductive or ampliative inferences arealso meant to confer contents on expressions. I arguethat if Brandom's inferentialist picture is upheld, andboth explicative and ampliative inferences confermeaning, one consequence of this is that the contentof a sentence is to be read off from our ways ofrationally altering our beliefs. Meaning and contentthen are largely concepts of pragmatics, with no cleartheoretical interest. My critique affects certainaspects of Dummett's meaning-theoretic picture too,and the discussion also links up with the developmentof `dynamic semantics'.

A General Framework for Ampliative Inference Patterns

Non trivial reasoning from contradictory premises is being acknowledged as one of the most important features in intelligent systems. Expert systems, planners and schedulers, and diagnosers, are almost always faced to potentially fallacious information, errors, uncertainty, and difference of opinions. In thesecases, we expect that the reasoning systems will not collapse. Instead, the rational expected behavior is to isolate the source of contradiction. Several systems for reasoning from contradictory premises have been advanced, usually within acontext of strict, monotonic knowledge. In this work we investigate how defeasible knowledge can be also handled in these systems. The key idea is to represent pieces of defeasible knowledge ordered within anepistemic importance relation. A semantic characterization is provided, and a sound and complete procedure to compute conclusions is also given. Then, we show how nonmonotonic reasoning and other patterns of ampliative inference like abduction and induction can be adequately recast within the general pattern of reasoning from contradiction. We discuss some applications, in particular, a brief formalization of scientific research programmes.

A General Framework for Ampliative Inference Patterns

Non trivial reasoning from contradictory premises is being acknowledged as one of the most important features in intelligent systems. Expert systems, planners and schedulers, and diagnosers, are almost always faced to potentially fallacious information, errors, uncertainty, and difference of opinions. In thesecases, we expect that the reasoning systems will not collapse. Instead, the rational expected behavior is to isolate the source of contradiction. Several systems for reasoning from contradictory premises have been advanced, usually within acontext of strict, monotonic knowledge. In this work we investigate how defeasible knowledge can be also handled in these systems. The key idea is to represent pieces of defeasible knowledge ordered within anepistemic importance relation. A semantic characterization is provided, and a sound and complete procedure to compute conclusions is also given. Then, we show how nonmonotonic reasoning and other patterns of ampliative inference like abduction and induction can be adequately recast within the general pattern of reasoning from contradiction. We discuss some applications, in particular, a brief formalization of scientific research programmes.

A note on measures of fuzziness applied to nonmonotonic fuzzy propositional logic

Abstract We undertake a mathematical investigation of the problem of inferring a truth value(s) for a propositional sentence. given truth values for some other set of sentences. Interpreting such a set of sentences and truth values as an abstraction of a fuzzy knowledge base, this mathematical problem can be seen as an abstraction of the important problem of inference in fuzzy expert systems. We postulate axioms for nonmonotonic fuzzy propositional logic (inspired by Paris and Vencovska's axioms for ampliative probabilistic inference). We prove simple but new results regarding the consistency of the axioms. We consider one method of inference. Maximum Fuzziness — infer the truth value that is most fuzzy and yet consistent with the knowledge base. We demonstrate that under certain plausible assumptions about the measure of fuzziness, several of the axioms are not sound for Maximum Fuzziness. Finally, we show that computing close approximations to truth values inferred by Maximum Fuzziness is at least as difficult as monotonic deductive propositional logic.

Ampliative inference: on choosing a probability distribution

Ampliative inference is the choice of a probability distribution on the basis of incomplete information. We consider some psychological and normative questions that arise about this kind of reasoning. The discussion is largely tutorial although a substantive hypothesis is also advanced.

Criteria and Methods for Performing and Evaluating Solar-Weather Studies

Abstract Research criteria and methods are presented for performing and evaluating the growing discipline of solar-weather studies. A clear distinction among preliminary, exploratory, and confirmatory studies is presented, and it is shown that this distinction affects all dimensions and findings of a study. Particular attention is given to conceptual models, variables and data, sample designs, analyses, and formal ampliative inference issues under exploratory and confirmatory conditions. The utility of the proposed criteria and methods are illustrated by evaluating two recent solar-weather claims of strong association between solar flux and stratospheric temperature at the North Pole when partitioned by the phase of the quasi-biennial oscillation. The results of the evaluation indicate that these claims are only exploratory ones and are still in need of confirming evidence. Last, a reanalysis of the solar flux and temperature relation, using some of the proposed methods, indicates that the association act...

On the Psychology of Ampliative Inference

It is sometimes necessary to guess which probability distribution governs random sampling over a given event space. When the correct guess cannot be deduced from information available about the space, the problem is said to require ampliative inference. The most familiar form of ampliative inference is represented in the principle of maximum entropy. We examine this principle from a descriptive, psychological point of view.

On the nature of explanation: A PDP approach

Neural network models of sensory processing and associative memory provide the resources for a new theory of what explanatory understanding consists in. That theory finds the theoretically important factors to reside not at the level of propositions and the relations between them, but at the level of the activation patterns across large populations of neurons. The theory portrays explanatory understanding, perceptual recognition, and abductive inference as being different instances of the same more general sort of cognitive achievement, viz. prototype activation. It thus effects a unification of the theories of explanation, perception, and ampliative inference. It also finds systematic unity in the wide diversity of types of explanation (causal, functional, mathematical, intentional, reductive, etc.), a chronic problem for theories of explanation in the logico-linguistic tradition. Finally, it is free of the many defects, both logical and psychological, that plague models in that older tradition.

Probabilistic Inference and Probabilistic Reasoning

Abstract : There are two profoundly different (though not exclusive) approaches to uncertain inference. According to one, uncertain inference leads from one distribution of (non-extreme) uncertainties among those propositions. According to the other, uncertain inference is like deductive inference in that the conclusion is detached from the premises (the evidence) and accepted as practically certain; it differs in being non-monotonic: and augmentation of the premises can lead to the withdrawal of conclusions already accepted. We show here, first, that probabilistic inference is what both traditional inductive logic (ampliative inference) and non-monotonic reasoning are designed to capture, third, that acceptance is legitimate and desirable, fourth, that statistical testing provides a model of probabilistic acceptance, and fifth, that a generalization of this model makes sense in AI.

Discovery and Ampliative Inference

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 explanandum—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.