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 Maarten Maartensz:    Philosophical Dictionary | Filosofisch Woordenboek                      

 R - Reasoning - defeasible


 
Defeasible reasoning: Reasoning that leads to plausible conclusions from given assumptions or premisses, without being necessary.

Much of everyday reasoning is defeasible in this sense - and indeed: "Life is the art of drawing sufficient conclusions from insufficient premises." (Samuel Butler II) 

A broad class of examples defeasible arguments is indicated by arguments that have tacit premisses, especially of a statistical kind. Thus, 'Heinz is German, so he speaks German' and 'Tweety is a bird, so Tweety can fly' are plausible for readers who presume the factual truths that most living Germans speak German and that most birds can fly, yet it is well-known there are exceptions to both statements (such as very young Germans or penguins, respectively).

It is interesting that Aristotle in his Topics paid considerable attention to defeasible reasoning as defined, but that since he did, little attention was paid to it, until recently.

1. An ambiguity about defeasible arguments: It should be noted that there is an ambiguity here, that can be brought out by considering three schemes of inference which all can be seen as varieties of the socalled Statistical Syllogism:

Most A's are B's.               prob(B/A) is high              freq[B/A] is high
This is an A.                     Ac                                 Ac 
---------------------        --------------------        ------------------
Therefore, this is a B.        Therefore, Bc.                 Therefore, Bc.

Here "prob(B/A)" = "the probability that someting is a B given that it is an A", and
"freq[B/A]" = "the frequency of B's among A's", and both can be seen as precisifications of the first schema in terms of "Most A's are B's", which is the most common everyday form of the Statistical Syllogism, and also the most common type of defeasible reasoning.

The problem is that, as stated, the conclusions do not deductively follow from the premisses and that, consequently, some - like Pollock - claim, explicitly or implicitly, that the above schemes are schemes of defeasible reasoning.

The objection here is that if one restates the conclusion not apodictically as "Therefore, Bc" but instead probabilistically, namely as "Therefore, probably Bc" a good case may be made for the thesis that thus restated the schemes can be made deductively valid, although this does require some work, and intuitively also a premiss to the effect that the second premiss - "This is an A" etc. - is in fact a random selection from the things that are A.

In more general terms: If one has an argument with premisses P1 .. Pn and conclusion C that is not deductively valid in the sense that if it all the premisses are true, then the conclusion cannot fail to be true also, but that nevertheless seems plausible in the sense that if all the premisses are true, then the conclusion is probably or plausibly true, it seems as if one has a valid argument if the conclusion is properly qualified.

It is for this reason that I do not believe in some fairly widely accepted accounts of defeasible reasoning: It suggests the inference of conclusions with certainty from premisses that are stated with probability, and calls that sort of inference 'defeasible', whereas I want to qualify such conclusions from merely probable premisses also in probabilistic terms, and thus make the inference deductively valid in form, but from explicitly uncertain premisses, and therefore itself provably uncertain, rather like one argues intuitively that 'If most A's are B's, and this is a randomly chosen A, then it is more probable than not that it also is a B, given those premisses'.

2. Qualified premisses: Thus it would seem as if defeasible reasoning involves qualified premisses, in the sense that one argues that if P1 ... Pn are true, then C is true, and this is a good explanation for C's being the case, provided P1 .. Pn are properly qualified in some way.

A classical example of such a qualification is the ceteris paribus (= other things being equal) qualification, that also may take the form of ceteris absentibus (= other things being absent). Indeed, one may argue that many arguments about empirical facts have a tacit premiss to the effect 'exceptions excepted, but exceptions are rare'. (An instance is the case of reasoning with the Statistical Syllogism as presented in the previous section.)

Similarly, there are the '
for all I know' and 'so far as known' qualifications, that also may take the form 'to the best of our knowledge' or 'so far as the known evidence goes' qualifications. This sort of qualification is common both in judicial courts and in many applications of theoretical models in empirical science: 'To the best of our knowledge, this situation is a kind of case like so-and-so'.

Another convenient term that covers many of the stated arguments and qualification is 'prima facie reason' (as first introduced by Ross, in discussion of ethical problems): P is a 'prima facie reason' for C if 'normally' or 'usually' or 'often' or if with one of the earlier qualifications in this section, if P then C.

Indeed, if one considers not ethics but supposed or proposed laws of nature, one has contingent formulas of the form if P then C, that are supposed to be always true, but may be qualified in several of the above ways, especially in terms of 'ceteris paribus' and varieties of 'to the best of our knowledge'.

Furthermore, in cases of supposed laws of nature there may be a chance factor involved, implicitly or explicitly as with quantum mechanics or thermodynamics, and the arguments of the form if P then C often have tacit or explicit qualifications of the form 'probably' or 'apart from uncommon chance variations' and the like.

Still considering supposed laws of nature, there often seems to be a kind of persistence or inertia qualification: 'these kinds of things persist, unless and until we have evidence they do not'. (See Newton's Rules of Reasoning and Invariance)

Also, there is a further kind of well-known principle of theorizing that seems to be a kind of qualified premisses principle: Ockham's Razor, which says that one should not make more assumptions than are necessary to explain the case. For this can be stated in the form if P1 ... Pn are true, then C is true, provided all of P1 .. Pn are necessary to infer C.

3. Predictions, tests and induction: An important special case of qualified premisses is the case of predictions and tests of empirical theories, which includes also induction, at least if the latter is construed probabilistically and in Bayesian terms.  For then one always has the situation that one's predictions involve the tacit or explicit assumption that 'there are no unknown factors that might upset one's predictons', or indeed the tacit or explicit assumption that anything that 'the theory does not entail that is relevant in fact is irrelevant'. For more on this see: Problem of Induction.
 


See also: Rationality, Reason, Reasoning - non-monotonic, Science, Theory, Rules of Probabilistic Reasoning


Literature:

Cohen & Nagel, Pollock, Polya, Stegmüller,

 Original: Feb 27, 2005                                                Last edited: 12 December 2011.   Top