On the So-called Logic of Practical Inference

There is no special logic of practical inferences. Intentions, like beliefs, have contents that are subject to standard logic. Yet being a special kind of belief, they have a role in causing, and not just expecting, action. Practical inference, like action itself, is in the service of an end of action, and is intelligible within that teleological perspective. ‘I will φ’ may entail ‘I will ψ’, and both be possible objects of intention, without their being intelligibly related by a practical inference; for inferring ‘I will ψ’ may get the agent who intends to φ no closer to φ-ing (as is evident when ‘ψ’ means ‘φ or χ’, with an arbitrary χ). Other inferences may look practical, but fail to serve any goal within their contingent context. The assessment of a piece of practical inference must be sensitive to the teleology of intentions.

My aim in this paper is to discuss some of the things Sellars has said over the years about the logic of practical inference. His views on this subject are becoming progressively more complicated, and I think this development is unfortunate. I shall argue that if Sellars’ early views are simplified in the right way, he could reasonably draw the conclusion, which I now accept, that there is actually no need for a special logic of practical inference.

Epistemic Logic and Practical Inference

The traditional approach in philosophy of using logic to reconstruct scientific theories and methods operates by presenting or representing a scientific theory or method in a specialized formal language. The logic of such languages is deductive, which makes this approach effective for those aspects of science that use deductive methods or for which deductive inference provides a good idealization. Many theories and methods in science, however, use non-deductive forms of approximation. Approximate inferences, which produce approximately correct conclusions and do so only under restricted conditions before becoming unreliable, behave in a fundamentally different way. In the interest of developing accurate models of the structure of inference methods in scientific practice, the focus of this paper, we need conceptual tools that can faithfully represent the structure and behaviour of inference in scientific practice. To this end I propose a generalization of the traditional notion of logical validity, called effective validity, that captures the form of approximate inferences typically used in applied mathematics and computational science. I provide simple examples of approximate inference in mathematical modeling to show how a logic based on effectively valid inference can directly, faithfully represent a wide variety of the forms of inference used in scientific practice. I conclude by discussing how such a generalized logic of scientific inference can provide a richer understanding of problem-solving and mathematical modeling processes.

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Different questions generate different forms of practical reasoning. A contextually unrestricted ‘What shall I do?’ is too open to focus reflection. More determinately, an agent may ask, ‘Shall I do X, or Y?’ To answer that, he may need to weigh things up—as fits the derivation of ‘deliberation’ fromlibra(Latin for ‘scales’). Ubiquitous and indispensable though this is, I mention it only to salute it in passing. Or he may ask how to achieve a proposed end: if his end is to do X, he may ask ‘How shall I do X?’ Or he may ask how to apply a universal rule or particular maxim. Aristotle supplies examples inDe Motu Animalium(7.701a7 ff.), whose wording I freely adapt to my own purposes:A1 reasons to a necessary means to achieving an end:I will make a cloak.To make a cloak I must do A.So, I will do A.

The aim of this chapter is to clarify the formal logic appropriate for practical reasoning. Several theories of practical reasoning have been proposed in recent years, of which Kenny’s theory, discussed in the last chapter, is a representative example. Although in criticizing Kenny’s theory I raised no doubts about the need for a special logic, involving special operators like Kenny’s ‘Fiat(…)’, I shall argue that practical reasoning can be interpreted as requiring no more than ordinary ’assertoric’ first-order logical principles. My view here is not based on general considerations or on philosophical ideology. I think there is a good prima facie case for a special logic of practical inference, and any dissenting view, such as mine, requires careful, detailed defense. I shall therefore proceed by considering important alternative views and develop my own position in the process of criticizing them.

On an internalist account of logical inference, we are warranted in drawing conclusions from accepted premises on the basis of our knowledge of logical laws. Lewis Carroll’s regress challenges internalism by purporting to show that this kind of warrant cannot ground the move from premises to conclusion. Carroll’s regress vindicates a repudiation of internalism and leads to the espousal of a standpoint that regards our inferential practice as not being grounded on our knowledge of logical laws. Such a standpoint can take two forms. One can adopt either a broadly externalist model of inference or a sceptical stance. I will attempt, in what follows, to defend a version of internalism which is not affected by the regress. The main strategy will be to show that externalism and scepticism are not satisfying standpoints to adopt with regard to our inferential practice, and then to suggest an internalist alternative.

InOn Certainty,Wittgenstein addressed the issue of beliefs that are not to be argued for, either because any grounds we could produce are less certain than the belief they are supposed to ground, or because our interlocutors would not accept our reasons. However, he did not address the closely related issue of justifying a conclusion to interlocutors who do not see that it follows from premises they accept. In fact,Wittgenstein had discussed the issue in theRemarks on the Foundations of Mathematics; his view had been that certain inferential practices are constitutive of our notions of thinking and inferring. I argue that his treatment of unfounded beliefs inOn Certaintyessentially replicates,mutatis mutandis, his treatment of basic logical inference.

This paper attempts to take a new look at the famous Lewis Carroll paradox about Achilles and the Tortoise. It examines in particular the connections between Lewis Carroll's regress argument for logical inferences and a similar regress for practical inferences. The Tortoise's point of view is espoused: no norm of reasoning or of conduct can in itself “make the mind move,” only the brute force of belief can. This conclusion is a Humean one. But it does not imply that we renounce altogether the normative force of such principles of reasoning as modus ponens. Connexions with the Wittgensteinian rule-following problem are indicated.

This article presents alternative analyzing method of extracted dissolved gases related to insulating oil of power transformers. Analysis of soluble and free gas is one of the most commonly used troubleshooting methods for detecting and evaluating equipment damage. Although the analysis of oil-soluble gases is often complex, it should be expertly processed during maintenance operation. The destruction of the transformer oil will produce some hydrocarbon type gases. The development of this index is based on two examples of traditional evaluation algorithms along with fuzzy logic inference engine. Through simulation process, the results of the initial fractures in the transformer are obtained in two ways by the "Duval Triangle method” and "Rogers’s ratios". In continue, three digit codes containing the fault information are created based on the fuzzy logic inference engine to achieve better results and eliminate ambiguous zones in commonly used methods, especially in the “Duval Triangle method”. The proposed method is applied to 80 real transformers to diagnose the fault by analyzing the dissolved oil based on fuzzy logic. The results illustrate the proficiency of this alternative proposed algorithm. Finally, with utilization of a neural network the alternative practical inference function is derived to make the algorithm more usable in the online condition monitoring of power transformers.