What do we learn when we find out that an argument is logically incorrect? If logically incorrect means the same as not logically correct, which in turn means not having a valid logical form, it seems that we do not learn anything too useful—an argument which is logically incorrect can still be conclusive. Thus, it seems that it makes sense to fix a stronger interpretation of the term under which a logically incorrect argument is guaranteed to be wrong (and is such for purely logical reasons). In this paper, we show that pinpointing this stronger sense is much trickier than one would expect; but eventually we reach an explication of the notion of (strong) logical incorrectness which we find non-trivial and viable.
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Logic can be, of course, conceived more broadly—for example so that it includes all normative approaches to the study of reasoning. Unlike formal logic these more inclusive accounts of logic normally do not aspire at providing rigorous methods for deciding which arguments are correct (valid) and which are not.
The terminology within logic as well as within argumentation studies is somewhat unsettled. Sometimes the term logically incorrect argument is used as synonymous with fallacious argument. Walton (1986), however, points out that this is improper as there are arguments which are weak but reasonable (to some extent) and hence such arguments are “not really fallacies at all in the sense of being arguments that are incorrect”. On the other hand sometimes the term “fallacious” is used to denominate arguments that are not just incorrect but also misleading in the sense of making a delusive impression of correctness and thus being tokens of common errors in reasoning (c.f. Finocchiario 1981). An argument which is clearly incorrect thus would not be classified as fallacious.
Another, related problem emerges when we do not want to accept that every argument is either correct or incorrect. (This may happen when we accept logic other than the classical one—an intuitionist, for example, may hesitate to classify the argument “It is not true that it does not rain, hence it rains” as logically incorrect. Moreover, when we concentrate on natural language, we can hardly avoid acknowledging a grey zone of arguments that are not determinately classifiable in either of these groups). In general, lumping together all arguments that do not instantiate the favoured form may be problematic.
Or, on the pragmatic level, from meaningful utterances to a meaningful utterance. We will, however, ignore the pragmatic level of argumentation in this article.
It was Lewis Carroll (1895) who taught us that trying to articulate all such ‘covert premises’ explicitly leads us into the blind alley of an infinite regress.
We, however, believe that the delineation of the concept of logical incorrectness we propose could be easily adjusted even to deontic arguments.
Also, arguments with no premises count as containing only premises that are true (under any circumstances)—for it holds for any sentence that if it is a premise of the argument then it is true.
Alternatively this can be formulated so that an argument is correct iff its conclusion follows from its premises.
Here it is worth pointing out that the terms valid argument and correct argument are often used interchangeably in the literature. This terminological promiscuity is usually harmless (we could also speak about valid instead of correct arguments in this paper). We, however, think that some terminological conventions may be useful, so in this paper we will speak about correctness and incorrectness in case of arguments (series of full-fledged statements) and about validity and invalidity in case of argument forms.
We use term “parameter” here, rather than the term “variable”. The reason is that we find it confusing to use the same term both for symbols that are intended to produce sentential schemes (as in the present case) and for those that are intended to be bound by quantifiers and thus produce sentences.
Thus, there cannot be a fully-fledged sentence without a logical form just as there cannot be a sentence without a grammatical form. Which particular form (or forms) a particular sentence ‘has’ is often a controversial issue.
While Frege (1879) gives the impression that reaching a logical form is a matter of merely “forgoing expressing anything that is without significance for the inferential sequence”, already his later writings present finding logical forms as a much more complex and much less transparent process. Russell then turned the uncovering of logical forms (or logical analysis) into a true ‘art’.
See footnote 9.
Though the sentence is bizarre, it is not made up by us—it is the opening sentence of Lewis Carroll’s Jabberwocky.
Though we do not expect that there is any definite, ‘tangible’ reality that is to be described, we are sure that there is a lot more to reveal and understand in this area.
Indeed, we are convinced that if it were not determinate enough the project of building logic could not have been properly launched at all.
What we mean by this are not systems of logic that purport to be ‘natural’ in the sense that they reflect some intuitions of their creator with respect to natural language, but rather true empirical research of representative samples of inferential practices of speakers of natural languages that would gather statistical data allowing the comparison of different systems–e.g., classical and intuitionist logic—as concerns their faithfulness to common speaker’s standards.
Let us note in passing that this is far from an unproblematic presupposition, but it is not a topic that we can go into in the present paper.
This kind of interpretation may even develop into a form of relativism with respect to correctness.
Note that accepting this category of correct arguments is not essential for the explication of logical incorrectness that we pursue in this paper; we include them because it makes, we think, the depiction of the landscape of arguments we present more realistic. Note also that saying that we treat All dogs live on Mars as necessarily false (within the given state of affairs) implies that adding this sentence as an additional premise to (A5) does not change the argument into an incorrect one. (As it is not possible that All dogs live on Mars is true, the resulting argument has premises that cannot be true.) An alternative possibility, which we do not consider in this paper, would be to consider arguments like (A4) or (A5) as correct only ceteris paribus and to assume that the addition of a premise may turn a correct argument into an incorrect one.
But, of course, the classes of incorrect arguments are depicted even in Picture 1—as (overlapping) complements of the respective classes of correct ones.
The arguments classified as “incorrect” simpliciter by this picture are not incorrect in any strong sense. For example arguments like Fido sleeps hence Fido is at home would belong to this area.
We can, of course, imagine that for example the words sister or woman might change their meanings in such a way that the above analytically correct argument becomes incorrect; but then we would say that it is not the same argument anymore.
Notice the contrast between arguments of this kind and the arguments we called status quo correct. In the case of the latter, it is excluded that they would lead us astray (unless very dramatic changes of our world take place); in the case of the former, it is only very improbable.
It is obvious that any conclusion is inconsistent with inconsistent premises.
In footnote 18 we noted that the argument with the premises Fido is a dog and All dogs live on Mars and the conclusion Fido does not live on Mars turns out status quo correct. Now we see that it will not be incorrect—insofar as we treat its premise All dogs live on Mars as impossible and hence inconsistent.
It seems that the concept delineated by DefSAnInCor is coextensive with the concept of an argument having a “counter-valid” argument form, i.e. the form that has only incorrect instantiations (see Woods and Irvine 2004, p. 68).
This is not to suggest that the concepts of strong analytical incorrectness and strong status quo incorrectness (which we put aside because of the lack of space) are uninteresting and not worth elaborating.
We might think of various alternatives—for example, in view of the fact that (AF10) is equivalent to the premiseless argument form with the conclusion A1 → (…(An → B)…), we might think of its opposite counterpart as the premiseless argument with the conclusion ¬(A1 → (…(An → B)…)). But it is readily seen that this would not work at all.
Those who are ready to give up DefCor and classify arguments with inconsistent premises not as trivially correct but as trivially incorrect could even claim that incorrectness of (A15) can be demonstrated by a purely formal method—just by means of logic. We should, however, note that the move is quite radical. The point is that making it deprives one of a formal method of demonstration of correctness of arguments.
Super-invalid argument forms have premises that are formal tautologies and a conclusion that is a formal contradiction, see Cheyne (2012, p. 51).
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Work on this paper was supported by the research Grant No. 13-21076S of the Czech Science Foundation. We are grateful to Georg Brun, Hans Rott, Vít Punčochář, Marta Vlasáková and anonymous reviewers of Argumentation for valuable critical comments.
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Svoboda, V., Peregrin, J. Logically Incorrect Arguments. Argumentation 30, 263–287 (2016). https://doi.org/10.1007/s10503-015-9375-1
- Logical form
- Incorrect argument
- Correct arguments