Belief bias in syllogistic reasoning

See also my project

Every man prefers belief to the exercise of judgment.
~ Seneca

We speak not strictly and philosophically when we talk of the combat of passion and of reason. Reason is, and ought only to be the slave of the passions, and can never pretend to any other office than to serve and obey them.~ Hume

A well studied phenomenon in the psychology of reasoning is termed belief bias (Evans et al., 1983; Markovits & Nantel, 1989). Belief bias labels the long standing effect that reasoners are more likely to accept a believable conclusion to a syllogism than an unbelievable one, independent of the actual logical validity of the conclusion (i.e. Wilkins, 1928; Henle & Michael, 1956; Kaufman & Goldstein, 1967). For instance, examination of the following syllogism (see appendix for some basic definitions) shows that this argument is logically invalid and that its conclusion does not concord with belief. Consequently, endorsement rates are very low for this type of problem.

Major premise: No police dogs are vicious.
Minor premise: Some highly trained dogs are vicious.
Conclusion: ∴ Some police dogs are not highly trained.

Interestingly, one can construct syllogisms in which validity and believability are discordant, as in the following argument:

Major premise: No addictive things are inexpensive.
Minor premise: Some cigarettes are inexpensive.
Conclusion: ∴ Some addictive things are not cigarettes.

In this example the syllogism is logically invalid (i.e., a non sequitur) but the conclusion is believable. Upon inspection, it can be determined that the two exemplary syllogisms have the same logical form. Despite this fact, a major proportion of participants judge the fallacious but believable conclusion as valid, i.e., participants exhibit the tendency to judge the validity of a syllogism based on its a priori believability. In their classic research on belief bias Evans et al. (1983) reported two main effects, first, participants affirm more believable than unbelievable conclusions and, second, more logically valid than invalid conclusions. Moreover, there was a significant interaction between believability and validity. The effects of belief are stronger on logically invalid than on valid syllogisms. This phenomenon is one of the most prevalent content effects studied in deductive reasoning (for a comprehensive review see Klauer et al., 2000) and it has been demonstrated that response bias to a given syllogism can be influenced by several factors, for example, perceived difficulty of the syllogism (Evans, 2009a), caution (Pollard & Evans, 1980), atmosphere bias (Begg & Denny, 1969), figural bias (Dickstein, 1978; Morley et al., 2004; Jia et al., 2009), presentation order (Lambell et al., 1999), and perceived base rate of valid syllogisms (Klauer et al., 2000), to name just the most prominent factors.

A widely acknowledged descriptive explanation for the belief bias effect is termed the default interventionist (DI) account (see Evans, 2007). Following this account Type 1 and Type 2 processes succeed one another in a sequential order. Primacy is attributed to Type 1 (heuristic) processes which generate a default response whereas recency is ascribed to Type 2 (analytic) processes which approve or override the response generated by Type 1 processes (Stanovich & West, 2000; De Neys, 2006; Evans, 2007; Stanovich, 2008). The process of computing the correct solution and overriding the response cued by Type 1 processes is assumed to be costly in cognitive terms, drawing on limited executive resources. The DI process model is visualized in Figure 1.

Figure 1. Flowchart depicting the default-interventionist model.



The goal of Aristotle’s main works (and of all logic) is to formalize validity. Validity does not guarantee truth but truth preservation. If the premise is true then the conclusion has to be true. What makes an argument valid is structure and not content. Syntax vs. semantics. In other words, the core idea of logic is that validity is a matter of form. Therefore, one can make a completely valid argument consisting of nonsense terms.

Standard form syllogism

Hypothetical modus ponens
A modus ponens (from the Latin ponere, meaning “to affirm”) rule of inference has the following form:
If P, then Q. (1st premise)
P. (2nd premise)
Ergo, Q. (conclusion)

It can be formally written in sequent notation (Sanford, 2003):

That means whenever you accept P you are forced to accept Q. For example, If apples cost £20 a kilo then your name is Peter. Suppose apples cost £20 a kilo. Your name would be Peter then, wouldn’t it? (example adapted from Bornat, 2005, p. 30) The validity of arguments in the modus ponens form can be illustrated in a truth table.

Truth table

A categorical syllogism consists of three categorical propositions. Two of these propositions constitute the premises, or the basis of the inference that can be drawn. The other proposition is offered as the conclusion (the result). These propositions are traditionally labeled A, E I, and O. The A and the I are both affirmative and A and I are the first two vowels in the Latin term affirmo (I affirm). The E and O propositions, on the other hand, are both negative and they are the vowels in the Latin term nego (I deny) (Copi & Cohen, 1994).
A valid argument is put together in such a way that the truth of its premises forces the truth of its conclusion. In other words, if the premises are true the conclusion has to be true (validity occurs with closure). For instance, when the premises in the syllogism depicted in Table 6b are true there is no way to avoid that the conclusion is true as well. Note that the word “Greeks” (the middle term) bridges the gap between the minor term (Athenians) and the major term (mortals). In other words, the minor term and major term are linked by a connector which is labeled the middle term and it occurs in both premises. The middle term is like an intermediate link in a chain through which the connection between minor term and major term is made.

Logic of syllogisms

Looking for the rational foundations of knowledge Aristotle observed that the validity of a syllogism depends on a limited number of rules. If any of these rules is violated a syllogism is invalid. However, if each of these rules is met then the syllogism flies (is valid). Aristotle mapped out in detail these rules which differentiate between standard form syllogisms which are valid and those that are not. One of these rules applies to distribution. Distribution refers to whether or not a categorical statement claims something about each and every member of a class that it refers to. If a categorical statement does that it is said to be distributive if it does not it is said to be undistributive. For instance, an A proposition distributes its subject term but not its predicate term. The distribution patterns capture the relationship of contradictoriness. In other word, the distribution patterns in two contradictory statements are exactly reversed.

Schopenhauer - The art of controversy

The Art of Controversy


Preliminary: Logic and Dialectic.

By the ancients, Logic and Dialectic were used as synonymous terms; although [Greek: logizesthai], “to think over, to consider, to calculate,” and [Greek: dialegesthai], “to converse,” are two very different things.

The name Dialectic was, as we are informed by Diogenes Laertius, first used by Plato; and in the Phaedrus, Sophist, Republic, bk. vii., and elsewhere, we find that by Dialectic he means the regular employment of the reason, and skill in the practice of it. Aristotle also uses the word in this sense; but, according to Laurentius Valla, he was the first to use Logic too in a similar way.* Dialectic, therefore, seems to be an older word than Logic. Cicero and Quintilian use the words in the same general signification.

* He speaks of [Greek: dyscherelai logicai], that is, “difficult points,” [Greek: protasis logicae aporia logicae]

Cic. in Lucullo: Dialecticam inventam esse, veri et falsi quasi disceptatricem. Topica, c. 2: Stoici enim judicandi vias diligenter persecuti sunt, ea scientia, quam Dialecticen appellant. Quint., lib. ii., 12: Itaque haec pars dialecticae, sive illam disputatricem dicere malimus; and with him this latter word appears to be the Latin equivalent for Dialectic. (So far according to “Petri Rami dialectica, Audomari Talaei praelectionibus illustrata.” 1569.)

This use of the words and synonymous terms lasted through the Middle Ages into modern times; in fact, until the present day. But more recently, and in particular by Kant, Dialectic has often been employed in a bad sense, as meaning “the art of sophistical controversy”; and hence Logic has been preferred, as of the two the more innocent designation. Nevertheless, both originally meant the same thing; and in the last few years they have again been recognised as synonymous.

It is a pity that the words have thus been used from of old, and that I am not quite at liberty to distinguish their meanings. Otherwise, I should have preferred to define Logic (from [Greek: logos], “word” and “reason,” which are inseparable) as “the science of the laws of thought, that is, of the method of reason”; and Dialectic (from [Greek: dialegesthai], “to converse”— and every conversation communicates either facts or opinions, that is to say, it is historical or deliberative) as “the art of disputation,” in the modern sense of the word. It it clear, then, that Logic deals with a subject of a purely à priori character, separable in definition from experience, namely, the laws of thought, the process of reason or the [Greek: logos], the laws, that is, which reason follows when it is left to itself and not hindered, as in the case of solitary thought on the part of a rational being who is in no way misled. Dialectic, on the other hand, would treat of the intercourse between two rational beings who, because they are rational, ought to think in common, but who, as soon as they cease to agree like two clocks keeping exactly the same time, create a disputation, or intellectual contest. Regarded as purely rational beings, the individuals would, I say, necessarily be in agreement, and their variation springs from the difference essential to individuality; in other words, it is drawn from experience.

Logic, therefore, as the science of thought, or the science of the process of pure reason, should be capable of being constructed à priori. Dialectic, for the most part, can be constructed only à posteriori; that is to say, we may learn its rules by an experiential knowledge of the disturbance which pure thought suffers through the difference of individuality manifested in the intercourse between two rational beings, and also by acquaintance with the means which disputants adopt in order to make good against one another their own individual thought, and to show that it is pure and objective. For human nature is such that if A. and B. are engaged in thinking in common, and are communicating their opinions to one another on any subject, so long as it is not a mere fact of history, and A. perceives that B.‘s thoughts on one and the same subject are not the same as his own, he does not begin by revising his own process of thinking, so as to discover any mistake which he may have made, but he assumes that the mistake has occurred in B.‘s. In other words, man is naturally obstinate; and this quality in him is attended with certain results, treated of in the branch of knowledge which I should like to call Dialectic, but which, in order to avoid misunderstanding, I shall call Controversial or Eristical Dialectic. Accordingly, it is the branch of knowledge which treats of the obstinacy natural to man. Eristic is only a harsher name for the same thing.

Controversial Dialectic is the art of disputing, and of disputing in such a way as to hold one’s own, whether one is in the right or the wrong — per fas et nefas.* A man may be objectively in the right, and nevertheless in the eyes of bystanders, and sometimes in his own, he may come off worst. For example, I may advance a proof of some assertion, and my adversary may refute the proof, and thus appear to have refuted the assertion, for which there may, nevertheless, be other proofs. In this case, of course, my adversary and I change places: he comes off best, although, as a matter of fact, he is in the wrong.

* According to Diogenes Laertius, v., 28, Aristotle put Rhetoric and Dialectic together, as aiming at persuasion, [Greek: to pithanon]; and Analytic and Philosophy as aiming at truth. Aristotle does, indeed, distinguish between (1) Logic, or Analytic, as the theory or method of arriving at true or apodeictic conclusions; and (2) Dialectic as the method of arriving at conclusions that are accepted or pass current as true, [Greek: endoxa] probabilia; conclusions in regard to which it is not taken for granted that they are false, and also not taken for granted that they are true in themselves, since that is not the point. What is this but the art of being in the right, whether one has any reason for being so or not, in other words, the art of attaining the appearance of truth, regardless of its substance? That is, then, as I put it above.

Aristotle divides all conclusions into logical and dialectical, in the manner described, and then into eristical. (3) Eristic is the method by which the form of the conclusion is correct, but the premisses, the materials from which it is drawn, are not true, but only appear to be true. Finally (4) Sophistic is the method in which the form of the conclusion is false, although it seems correct. These three last properly belong to the art of Controversial Dialectic, as they have no objective truth in view, but only the appearance of it, and pay no regard to truth itself; that is to say, they aim at victory. Aristotle’s book on Sophistic Conclusions was edited apart from the others, and at a later date. It was the last book of his Dialectic.

If the reader asks how this is, I reply that it is simply the natural baseness of human nature. If human nature were not base, but thoroughly honourable, we should in every debate have no other aim than the discovery of truth; we should not in the least care whether the truth proved to be in favour of the opinion which we had begun by expressing, or of the opinion of our adversary. That we should regard as a matter of no moment, or, at any rate, of very secondary consequence; but, as things are, it is the main concern. Our innate vanity, which is particularly sensitive in reference to our intellectual powers, will not suffer us to allow that our first position was wrong and our adversary’s right. The way out of this difficulty would be simply to take the trouble always to form a correct judgment. For this a man would have to think before he spoke. But, with most men, innate vanity is accompanied by loquacity and innate dishonesty. They speak before they think; and even though they may afterwards perceive that they are wrong, and that what they assert is false, they want it to seem the contrary. The interest in truth, which may be presumed to have been their only motive when they stated the proposition alleged to be true, now gives way to the interests of vanity: and so, for the sake of vanity, what is true must seem false, and what is false must seem true.

However, this very dishonesty, this persistence in a proposition which seems false even to ourselves, has something to be said for it. It often happens that we begin with the firm conviction of the truth of our statement; but our opponent’s argument appears to refute it. Should we abandon our position at once, we may discover later on that we were right after all; the proof we offered was false, but nevertheless there was a proof for our statement which was true. The argument which would have been our salvation did not occur to us at the moment. Hence we make it a rule to attack a counter-argument, even though to all appearances it is true and forcible, in the belief that its truth is only superficial, and that in the course of the dispute another argument will occur to us by which we may upset it, or succeed in confirming the truth of our statement. In this way we are almost compelled to become dishonest; or, at any rate, the temptation to do so is very great. Thus it is that the weakness of our intellect and the perversity of our will lend each other mutual support; and that, generally, a disputant fights not for truth, but for his proposition, as though it were a battle pro aris et focis. He sets to work per fas et nefas; nay, as we have seen, he cannot easily do otherwise. As a rule, then, every man will insist on maintaining whatever he has said, even though for the moment he may consider it false or doubtful.*

* Machiavelli recommends his Prince to make use of every moment that his neighbour is weak, in order to attack him; as otherwise his neighbour may do the same. If honour and fidelity prevailed in the world, it would be a different matter; but as these are qualities not to be expected, a man must not practise them himself, because he will meet with a bad return. It is just the same in a dispute: if I allow that my opponent is right as soon as he seems to be so, it is scarcely probable that he will do the same when the position is reversed; and as he acts wrongly, I am compelled to act wrongly too. It is easy to say that we must yield to truth, without any prepossession in favour of our own statements; but we cannot assume that our opponent will do it, and therefore we cannot do it either. Nay, if I were to abandon the position on which I had previously bestowed much thought, as soon as it appeared that he was right, it might easily happen that I might be misled by a momentary impression, and give up the truth in order to accept an error.

To some extent every man is armed against such a procedure by his own cunning and villainy. He learns by daily experience, and thus comes to have his own natural Dialectic, just as he has his own natural Logic. But his Dialectic is by no means as safe a guide as his Logic. It is not so easy for any one to think or draw an inference contrary to the laws of Logic; false judgments are frequent, false conclusions very rare. A man cannot easily be deficient in natural Logic, but he may very easily be deficient in natural Dialectic, which is a gift apportioned in unequal measure. In so far natural Dialectic resembles the faculty of judgment, which differs in degree with every man; while reason, strictly speaking, is the same. For it often happens that in a matter in which a man is really in the right, he is confounded or refuted by merely superficial arguments; and if he emerges victorious from a contest, he owes it very often not so much to the correctness of his judgment in stating his proposition, as to the cunning and address with which he defended it.

Here, as in all other cases, the best gifts are born with a man; nevertheless, much may be done to make him a master of this art by practice, and also by a consideration of the tactics which may be used to defeat an opponent, or which he uses himself for a similar purpose. Therefore, even though Logic may be of no very real, practical use, Dialectic may certainly be so; and Aristotle, too, seems to me to have drawn up his Logic proper, or Analytic, as a foundation and preparation for his Dialectic, and to have made this his chief business. Logic is concerned with the mere form of propositions; Dialectic, with their contents or matter — in a word, with their substance. It was proper, therefore, to consider the general form of all propositions before proceeding to particulars.

Aristotle does not define the object of Dialectic as exactly as I have done it here; for while he allows that its principal object is disputation, he declares at the same time that it is also the discovery of truth.* Again, he says, later on, that if, from the philosophical point of view, propositions are dealt with according to their truth, Dialectic regards them according to their plausibility, or the measure in which they will win the approval and assent of others. He is aware that the objective truth of a proposition must be distinguished and separated from the way in which it is pressed home, and approbation won for it; but he fails to draw a sufficiently sharp distinction between these two aspects of the matter, so as to reserve Dialectic for the latter alone. The rules which he often gives for Dialectic contain some of those which properly belong to Logic; and hence it appears to me that he has not provided a clear solution of the problem.

Poster plain text

In the psychological literature logical reasoning is
associated with System 2 processes
(characterized as slow, controlled, limited in
capacity, and effortful) whereas belief based
judgments are frequently linked to System 1
processes (described as fast, automatic, high in
capacity, and effortless). This dichotomization of
cognitive processes forms the basis for a variety
of dual process models in cognitive science (i.e.,
Kahneman, 2002). Here we focus on the default-
interventionist account (DI account; Evans, 2007)
which postulate that these processes operate in
a sequential fashion.

We investigated the effects of ego depletion on
hypothetical syllogistic reasoning by
manipulating self regulatory resources between
groups. Participants were subsequently
instructed to evaluate conclusions of syllogisms
either on the basis of their semantic believability
or logical validity.
We hypothesized that belief based judgments
would be faster and more accurate relative to
logic judgments and that
ego–depletion would interfere with the latter but
not with the former. This hypothesis was
motivated by the strength model of self-control
(Baumeister et al., 2007) and
the default-interventionist account of reasoning
(Evans, 2007).
The statistical results provide a replication of the
observations made by Handley et al. (2011) and
implicate that logical reasoning precedes belief
based reasoning, which stands in direct contrast
with the predictions
derived from the DI model (Evans, 2007).
In our view the dichotomous DI account draws
an oversimplified picture which leaves no room
for any gray shadings between Type 1 and Type 2
processes. It seem more plausible that the
transitions between Type 1 and Type 2 processes
are gradual and that these processes constantly
interact and never reside in absolute stasis.
Baumeister, R. F., Vohs, K. D., & Tice, D. M. (2007). The strength model of self–
control. Current Directions in Psychological Science, 16(6), 351–355.
• Evans, J. S. B. T. (2007). On the resolution of conflict in dual process theories of
reasoning. Thinking & Reasoning, 13(4), 321–339.
• Kahneman, D. (2002). Nobel Prize lecture by Daniel Kahneman. [Video file].
Available from:
• Handley, S. J., Newstead, S. E., & Trippas, D. (2011). Logic, beliefs, and
instruction: a test of the default interventionist account of belief bias. Journal of
Experimental Psychology: Learning, Memory, and Cognition, 37(1), 28–43.


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