Formal Logical Analysis

Philosophers often advocate particular positions on philosophical and other questions. When they do so they sometimes appear to be engaged in deductive reasoning, and sometimes make use of what I here call rhetoric, meaning arguments which are intended to support the truth of a claim but which are not deductive.

Sometimes, philosophers appear to be engaged (in part) in deductive reasoning, without having taken care to comply with the necessary preconditions for reliable deductive reasoning. In these cases their arguments are at risk of having the merits neither of rhetoric on its own terms, nor of deductive argument when properly conducted.

The purpose of introducing here the term formal logical analysis is to make the case that a clearer distinction should be drawn between rhetoric (as defined above) and deductive argument, and to try to clarify that distinction. I also hope to present the view that formal logical analysis is a worthwhile method, both for philosophers and for any other discipline in which arguments are used which are believed to be partially or wholly deductive. I also intend to suggest some areas where formal logical analysis may beneficially be applied, and to provide some first experiments in the application this method.

I regret to say that it is entirely possible that what I am attempting to do here has already been done in a wholly satisfactory manner by some other of whose work I am ignorant. I am able to say that the core idea on which this is based goes back at least as far as Bertrand Russell, who has the distinction of having argued that Philosophy is Logic without making concessions to rhetoric.

It certainly is the case that this kind of method has been employed in computing, under the name of Formal Methods.

Where logic is applicable its results will in general be much more reliable than other methods, and such results should be, like the main body of mathematics, uncontroversial in a way in which few philosophical questions today are. While taking a more cautious view on scope of applicability (which is really just a more liberal view on what philosophers may do), I am wholly sympathetic with Russell's view that the methods of modern logic are such as to render disputes about the truths of logic marginal for most philosophical purposes, and hence to make certain parts of philosophy rather more like a scientific discipline than has hitherto been the case.

Russell's own work, for reasons with which I am not familiar, makes no attempt to adopt formal methods in philosophical arguments. He does of course make extensive use of formal reasoning in Principia Mathematica, but these are mathematical rather than philosophical arguments. Elsewhere, so far as I am aware, it is the ontological reductionism in the formalisation of mathematics which has a greater influence on his approach. There does not appear to be any general programme of presenting philosophical arguments to the standards adopted in Principia Mathematica.

Later, the logical positivists seemed to have conceived logical languages as ideal languages for science, rather than as practical languages for philosophy.

The position I intend to advocate here is that Formal Logical Analysis should be undertaken in a manner consistent with full formalisation and machine checking of the deductive arguments presented, and that any non-deductive arguments should clearly be declared as such. The recommended standards of formality fall between those adopted in Principia Mathematica (overlooking some defects in the rigour with which the formal notations are described) and those prevalent in modern mathematics. This intermediate position consists in advocating formalisation of the description of the domain of discourse, while allowing informal arguments once the subject matter has been settled. The intention would then be to expect standards of proof similar to those in mathematics, and a consequent elimination of disagreement on most points in areas where these methods are applicable.

The acid test of applicability I suggest is this. Do you believe that your arguments are deductive? If so then you should be able to establish them more solidly by the use of formality, and I would expect the effort required to achieve this to be well repaid in a sharper understanding of the subject matter.

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