This type of logical reasoning is tested on the GAMSAT every year in one form or another. It won’t always be confined to Section 1, and appears often in Section 3 – Biological and Physical Sciences.
The most common topics to feature propositional logic based questions are:
Section I: Argumentative passages and Data Analysis units
Section III: Hormones, Genetics, Electricity and circuit-related physics questions.
For some examples see:
- Acer Practice Paper 1: Section III, unit 20 and, to an extent, unit 28.
- Acer Practice Paper 2: Section 1, Questions 22 – 26
- Practice Paper Alpha: Unit: 8
- Practice Paper Zappa: Unit: 5
(If you are within 1-2 months of sitting the GAMSAT you should be gearing up to attempt these practice papers under test conditions. Practice Papers Alpha and Zappa are both available for download here)
What is Propositional Logic
Propositional logic is about determining the truthfulness of statements or ‘propositions’. Sentences considered through the lens of propositional logic are always concluded to be either true or false.
Statements are most commonly denoted by letters such as p, q or c. A statement for which the truth / falsity has not yet been established may be denoted by the letters X, Y or Z.
A statement may be simple or compound. An example of a simple statement is:
My dog’s name is Glen.
A compound statement is a number of simple statements connected by [the aptly named] ‘connectives’. An example of a compound statement is:
My dog’s name is Glen and he is a border collie.
A compound statement connected by AND is only true if both of its components are true, and false otherwise.
Eg. My dog’s name is Glen and the sky is yellow = false.
In order for a compound statement connected by NOT to be true, then the part of the statement that is modified by the NOT must be false.
Eg. Glen is NOT not my dog’s name.
If a compound statement is connected by the word OR, then we can infer that at least one of the components is true. The statement is also true if both components are true.
Eg. Either this pie is made of apples OR my tongue is broken = True, the pie is made of apples, but your tongue also happens to be broken.
A common logical progression in argument might go:
Either p or q
IF __ THEN __
This connective connects two propositions such that the truth of the latter is dependant on the truth of the former.
Eg. If the sky is clear then we will be able to see the stars.
All the above can be interchanged and linked together to form complex propositions. We do this in casual conversation without realising it.
Eg. If Glen gets hit by a car or drinks hydrochloric acid then I will have to take him to the vet or have him put down.
Objectively breaking statements down into their constituent parts makes it easier to analyse their logic and uncover flaws.
Uncovering Logical Fallacies
This is the most common logical fallacy which arises from the proposition “If X then Y.” The mistake is to assume that since X is a prerequisite for Y, that Y is a prerequisite for X. This is rarely the case.
Eg. If it snows tonight there will be snow in the garden tomorrow. But if there is snow in the garden tomorrow, that doesn’t mean it has snowed – someone may have put the snow there….
This may also be referred to as a deductive fallacy.
(GSQ Unit Highlight: Comparing GAMSAT Songs)
An inductive fallacy occurrs when conclusions are drawn based on very limited information.
On your way to your first med school lecture, you see two Indian girls enter the classroom ahead of you. You then deduce that most of your classmates will be Indian.
Can you think of a way to write the above sentence in the language of propositional logic? If you can’t it’s probably because the deduction is highly illogical and disconnected from the premise.
In experiments based on The Scientific Method, the premise of seeing two Indian girls would be referred to as not being statistically significant.
Hidden Assumptons / Unspoken Premises
Is there more at work in the logic of this argument than is stated? Sometimes arguments are not completely stupid, but are simply based on unspoken premises.
It is bad to be unhappy. Doing homework makes me unhappy. Therefore I should avoid doing my homework.
In this simplistic example, I am making an unspoken assumption. The assumption is that there will be no consequences for not doing my homework. Unfortunately this is unlikely to be true, and if I do not do my homework now, I may find that I am punished later and made more unhappy as a result.
Some questions to ask yourself when dissecting these arguments:
- Does this logic hold true for every similar scenario? (For different values of X & Y)
- If not, are there any circumstances in which this logic may hold true? (For which values of X and Y might this statement be true)
A contingent proposition arises when the validity of a statement depends on factual information from the external world – in this case any information which is not provided in the GAMSAT passage. Be careful with this one, as Section 1 is not a general knowledge test. If the information is not provided in the passage it does not exist.
Although the above list is far from exhaustive, most common logical fallacies are derivatives of the above, and it is crucial to be familiar with at least some of these in order to advance your critical reasoning skills.
I’m currently working on an E-book guide to GAMSAT Section 1 in which I will cover more of these in detail. More info coming soon.