But are we, humans, really as rational as we assume? In this post I will discuss some major types of reasoning including syllogistic, deductive, inductive and conditional reasoning, and will outline numerous biases and logical fallacies that people tend to commit while performing reasoning tasks.
Major premise: All men are mortal
Minor premise: Socrates is a man
Conclusion: Socrates is mortal
Syllogisms can be described in terms of their validity and soundness; it is important not to confuse the two. Validity only refers to the structure of the argument, no matter what the content is. So, for the argument to be valid, if we assume that both premises are true then the conclusion can not be false. For example, the following syllogism:
Major premise: All animals can breath under water
Minor premise: Monkey is an animal
Conclusion: Monkey can breath under water.
It is obvious that the argument is not true, however it is valid, because the logic does follow through. On the contrary, soundness refers to the contents of an argument. For argument to be sound, both of its premises must be true and it must be valid. Thus, the first example bout Socrates is sound.
All Dutchmen (B) are bicycle riders (A)
Some bicycle riders (A) are students (C)
Therefore, some Dutchmen (B) are students (C)
The conclusion seems logical - but actually, it is invalid. In fact, the second premise does not provide enough evidence for neither falsifying nor supporting 'Some Dutchmen are students'. The following diagram (Euler's circles) will show why 'Some A are C' does not mean that 'some B are C'.
Deductive vs. Inductive reasoning
In contrast, inductive reasoning means deriving general principles from specific examples; it is based on bottom-up logic. This kind of reasoning is probabilistic, and does not provide the same level of certainty to a conclusion that deductive reasoning does even when the premise is true; consider the following example: My friend feels pain in her fingers after playing guitar for an hour; therefore all the guitarists feel pain in their fingers after an hour of playing.
Inductive reasoning is widely used in science and everyday life in order to test a hypothesis. For example, lets say you only ever used one microwave. You could then formulate a hypothesis, such as all microwaves have a 'defrost' function. Then you can test it by examining all the microwaves available to you and find evidence which either supports or falsifies your hypothesis.
It might have occurred to you though, that it would be tricky to check whether all the microwaves in the world have this function - however, just one microwave without the function would be enough to falsify the hypothesis. Therefore, in order to arrive to a true conclusion we always should be looking for an evidence which falsifies our hypothesis rather than supports it.
I won't describe the task itself, as you will hopefully see how it works following the link. The amazing thing is that about 70-85% fail at this task, even though the only principle they need to follow is fairly simple and was outlined above: you should be looking for falsifying rather than confirming evidence for any hypothesis.
Conditional Reasoning and Logical Fallacies
Conditional clause consists of two parts; the 'if' part is known as an antecedent, and the 'then' part - consequent; antecedent states a possible clause, while consequent - effect of this possible clause.
The evidence then follows, which states truth or falsity of either antecedent or consequent; so, four different variations. The task is then to take this evidence and make a conclusion as to whether the evidence supports or falsifies the second part of the clause or whether it is irrelevant.
For our conditional clause 'If I go for a run then I will feel good', the four possible evidences are:
(1) P is true ('I go for a run')
(2) P is false ('I don't go for a run')
(3) Q is true ('I feel good')
(4) Q is false ('I don't feel good')
However, only two of these evidences - namely, (1) and (4) - enable us to make a valid inference.
In the first one, when we get an evidence that P is true ('I go for a run'), then Q must be true ('therefore, I feel good'). This is called 'affirming the antecedent' - or, in classical terms, 'modus ponens'. The general form is expressed as If P, then Q. Q; therefore P.
The fourth evidence states that Q is false ('I don't feel good'), which means that P must be false ('therefore, I did not go for a run'). The form can be expressed as If P, then Q. not Q; therefore not P. This is referred to as 'denying the consequent' - or 'modus tollens'.
This is all very well and fairly straightforward. However, consider the other two possibilities. They do not provide enough evidence to make any kind of valid consequence; however people often commit logical fallacies by either denying the antecedent (2) or affirming the consequent (3).
Logical Fallacy I has the form of 'If P, then Q. not P; therefore not P', and is referred to as denying the antecedent. Such inference is invalid; logically, 'I don't go for a run' does not necessarily imply 'I will not feel good' (evidence (2)).
Logical Fallacy II is 'If P, then Q. Q, therefore P', and is called affirming the consequent. Such evidence (3) also does not allow us to make valid inference about the antecedent. Thus, 'I feel good' is not enough evidence to say whether 'I went for a run' is true or false.