General intelligence (measured by IQ tests) is closely related to reasoning skills. The more intelligent someone is, the better their reasoning skills. The problems you have just done are based on evaluating logical arguments involving deductive reasoning. In this tutorial you will be given the following:
- An explanation of how IQ, reasoning, making inferences and deductive logic are related
- An explanation of what an argument is
- A ‘mindware’ tutorial on strategies to solve deductive reasoning problems, with examples
- Links to additional deductive reasoning resources
Reasoning & Making Inferences
All reasoning involves making inferences. An inference involves drawing a conclusion from some some information when the conclusion is not made explicit in this information. Here is an example of an inference where you may have to think a little:
“If Bill is taller than Peter, and if Bill is shorter than Tom, then Tom is taller than Peter‘
Linking information in the two premises (Bill is taller than Peter, Bill is shorter than Tom), enables you to infer (if your reasoning is good!) that Tom is taller than Peter. In the matrix problems, the ‘conclusion’ of your inference was the figure that completed the matrix. You inferred this based on figuring out rules that were not made explicit in the information that was given to you.
Arguments
An argument in critical thinking circles is not is a conclusion that is supported by a premise or premises, expressed in sentences. For a metaphor, it may be helpful to imagine a roof supported by columns. Without the columns (the supporting premises) the roof (the conclusion) cannot stand. Arguments, like buildings, can be constructed properly and improperly. Like buildings that are constructed poorly, arguments that are built improperly will fall apart easily. We recognize the conclusions within an argument by words such as: ‘therefore’, ‘hence’, ‘thus’, ‘proving that’, ‘implying’. We recognize the premises within an argument with words such as: ‘for’, ‘because’, ‘in so far as’, ‘as supported by’. Critical thinking – an important higher order cognitive skill (HOCS) – is largely based on the ability to form and evaluate good arguments.
Deductive Arguments
Deductive arguments are logically valid inferences. This means that if you assume the premises are true, the conclusion is guaranteed to be true. In other words, if the premises are true, then it follows necessarily that the conclusion is also true. Valid arguments are sometimes called ‘truth preserving’ for this reason.
Deductive arguments are built according to valid rules of inference which we will look at below.
Invalid Arguments & Fallacies
A ‘fallacy’ is a mistake in inference or reasoning in constructing an argument.
An invalid argument is where the the conclusion can be false even when the premisses are true. The truth of the premisses does not guarantee the truth of the conclusion.
How To Use Mindware Strategies to Improve Your Deductive Reasoning Skills
Valid Rule of Inference 1: Modus Ponens
The first problem you did illustrates a valid deductive inference.
If the button is pressed, then the light goes on.
The button is pressed.
—————————
Therefore, the light goes on.
This is a valid deductive argument based on a valid rule of inference (technically called Modus Ponens)
If P then Q
P
————-
Therefore Q
There are no circumstances – no ‘states of affairs’ – in which the first two premisses are true, and the conclusion is false. If it’s true that ‘If the button is pressed, then the light goes on” and it’s true that ‘The button is pressed’, then it’s necessarily true, without any exceptions, that ‘The light goes on’.
Logical Fallacy 1: Affirming the Consequent
In the second problem the argument is invalid:
If the button is pressed, then the light goes on.
The light goes on.
—————————–
Therefore, the button is pressed.
This is a logical fallacy (see above) called ‘affirming the consequent’. This kind of badly constructed argument looks like this:
If P then Q
Q
————-
Therefore P
You can see this is the same fallacy that we found in the 4-card selection problem!
Why is this a fallacy? Because it’s possible for the premisses to be true while the conclusion is false. You can imagine another reason for the light going on – for instance because of a power surge in a lightening storm!
In this particular argument is certainly reasonable to believe that the button was pressed if the light went on – because that’s usually how lights work. We know that from experience. But because something is reasonable doesn’t mean it is logically necessary.
You can see how the form of this argument is not deductively valid in this argument which has exactly the same form:
If Liza lives in London then Liza lives in England.
Liza lives in England.
———————
Therefore Liza lives in London.
Clearly the truth of the conclusion is not guaranteed by the premisses. The premisses may be true while Liza in fact lives in Manchester. And even if Liza does live in London, it’s not something logically guaranteed by the premisses.
Here’s another invalid argument with the same form:
If I am in love, then I am obsessive in my thoughts.
I am obsessive in my thoughts.
———————
Therefore, I am in love.
Obviously being in love is not the only cause of obsessive thoughts. There are many causes for obsessive thoughts – for example, I may be an obsessive-compulsive, or I may be under intense pressure to complete a task.
Valid Rule of Inference 2: Modus Tollens
Is this argument valid?
If the light goes on, then the dog barks.
The dog doesn’t bark.
————————-
Therefore, the light doesn’t go on.
The answer is yes. If the dog always barks when the light goes on, and the dog doesn’t bark, the light didn’t go on! This is necessarily true. The conclusion is guaranteed by the premises – by a rule of inference called ‘Modus Tollens’
If P then Q
Not Q
————-
Therefore Not P
Here’s another example of this form of valid deductive argument: ‘If being a criminal is genetically determined, then there are genetic markers common to all criminals. There are not genetic markers common to all criminals. Therefore, it’s not true that being a criminal is genetically determined.’
Logical Fallacy 2: Denying the Antecedent
Here is another example of a fallacy in deductive reasoning – which is technically called ‘denying the antecedent’ (the complement of the ‘affirming the consequent’ fallacy):
If Elsie is competent, she will get an important job.
But Elsie is not competent.
————————
So she will not get an important job.
You can see that there are many routes to an important job. Elsie may be married to the boss! The truth of the premisses does not guarantee (by necessity) the truth of the conclusion. This badly constructed argument has the form:
If P then Q
Not P
————-
Therefore Not Q
Here’s another example. ‘If scientists discover carbon based lifeforms on other planets, there is likely to be extra-terrestrial intelligence. Scientists haven’t discovered carbon based lifeforms on other planets – so there is not likely to be extra-terrestrial intelligence.’
This may be plausible, but it is not logically valid. Try to generate your own example of this fallacy – one that is plausible but is not logically valid.
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