A syllogism is the most basic form of argument. It consists precisely of two premises and a conclusion. An example I often come across with in philosophy and logic books is this:
1) All men are mortal.
2) Socrates is a man.
3) Therefore, Socrates is mortal.
The first two statements are the premises and the last statement is the conclusion that follows naturally from the premises. Categorically, for an argument to be valid, the premises must be correct and the conclusion must follow naturally from the premises.
If any one of the premises is incorrect, then we likely to end up with the wrong conclusion, even though the conclusion follows naturally from the premises. For example:
1) All birds can fly.
2) The ostrich is a bird.
3) Therefore, the ostrich can fly.
Here, statement 1 is false, since there are some birds that cannot fly.
I used the word ‘likely’ because given a wrong premise, we may still end up with the right conclusion. However, the argument is still invalid. For example:
1) All birds can fly.
2) The eagle is a bird.
3) Therefore, the eagle can fly.
Here, statement 1 is, again, false. However, the conclusion is true. But this does not mean that the argument is valid, because the premise is wrong.
Specifically, the above examples are in the form called ‘universal instantiation’. In the examples, we begin with a universal statement, and end by deducing a property of a particular element (”instance”) from the group that the statement applies to.
A universal statement is one that states a property for a well-defined group of elements. Such a group could be ‘men’, ‘birds’, ‘cars’ etc. The universal statement would then say that a certain property applies to all the elements within that group. Examples are ‘all Singaporeans are kiasu’ and ‘old people are forgetful’.
If we take a careful examination of what goes on around us, syllogisms apply in many of our deductions in and about life. We start with a certain set of premises, and then we work our way, consciously or subconsciously, to arrive at a conclusion.
In particular, I realised that sometimes, we make the wrong conclusions because our premises are incorrect. And our premises are incorrect not necessarily because we fail to verify it carefully; sometimes, we are faced with a lack of information at a particular time, which leads us to think that our premises, and therefore, our conclusions are correct.
Bring back the example about birds. Suppose the world restarted, and we are at a point in time where our knowledge about birds is still incomplete. For years, we observe that this class of animals called ‘birds’ can all fly, and we have not encountered such a bird that cannot fly. At this point in time, to say that “all birds can fly” would be correct, and any argument that makes use of this premise would be valid, with its conclusion correct, too (provided, of course, that the other premise is also true).
Of course, this would go on until someone discovers the ostrich.
The ostrich, is a bird, but it cannot fly. We are thrown into a quagmire. Those who have rightfully believed for years that “all birds can fly” are thrown into disarray. Some might even say, “the ostrich can’t be a bird, it can’t fly!”
As you see, the effect of a lack of information is that great. It would take time for people to adjust to accept precisely the opposite of our initial knowledge, i.e. now, “not all birds can fly”, or equivalently, “some birds cannot fly”.
But perhaps an imaginary situation is not so easy to swallow for some of us.
My point is, we often make reasonable assumptions based on what we already know, without any attention to what we don’t know yet.
For example, we would believe that a street pedlar is selling good otak-otak (based on how it smells), but only until we get diarrhoea the next day (assuming we didn’t eat anything else). We would believe a salesman when he says that we’re getting the best bargain for a digital camera (based on the ‘offer price’), but only until we find another store that sells it for much cheaper. We would believe that there are WMDs in Iraq (based on Colin Powell’s ’satellite evidence’), but only until the US has scoured and destroyed the whole place and yet found no trace of WMDs.
The problem is, we often don’t know of our lack of information until a later time. As a result, we may have drawn our own conclusions and acted upon our conclusions, leading to unexpected results. And we did so not necessarily in careless haste, but because at the point of time when we derived our conclusion, the premises are true (and hence, any conclusion that naturally follows is true, giving a valid argument for the time being).
The process of drawing conclusions from readily available observations is called scientific induction. Put simply, we induce a conclusion from a set of observations so countless that the conclusion must be true, given a small margin of error. We recognise that in plotting a graph depicting a linear relationship between two real-life variables, the points on the graph will almost never form a perfect line. Hence, we draw a “line of best fit”, which is an attempt to arrive at the conclusion whilst acknowledging that small margin of error.
Logical deduction is diametrically opposed to scientific induction, for it enforces that there be absolutely no room for error. In logic, any example that runs counter to the claim of a universal statement i.e. a counterexample, would render the universal statement categorically false, unlike scientific induction, where slight deviations are permissible. I feel that, in this respect, logic is indeed the merciless, unfeeling and cold way to form conclusions and arrive at new knowledge.
In life, it seems that we have a mixture of logical deduction and scientific induction. Sometimes, the only way that we can arrive at our premises is the latter, and we proceed to apply the former to arrive at our conclusions. Logically speaking, this is unsatisfactory, because there is room for error in our premises. But this is how the world works, for as long as perfect knowledge belongs only to Allah.
As a natural consequence, and I even say, necessarily, unsatisfactory logic will lead to unsatisfactory outcomes. This is because this world is designed by Allah such that our actions are tied to their outcomes. If we act upon unsatisfactory logic, that is, if our actions are unsatisfactory, it does not follow that the outcome of our actions can be satisfactory. (This is an example of proving by contradiction, another form of argument, just like universal instantiation.)
Therefore, we can improve our situation by striving to seek more and better information wherever possible. If we have more and better knowledge, insyaAllah, we will be able to draw conclusions that are more accurate, and hopefully, also minimise the impact of acting upon less-than-accurate conclusions.
All this I learn from very difficult lessons in life, and from listening to Dr Leong Yu Kiang’s lectures in his module, GEK1505 Living With Mathematics. I strongly recommend this module to everyone, because I have gained much it, and I really like Dr Leong’s entertaining yet composed style in teaching mathematics.
But if you can’t bid for this module, there’s always the school of hard knocks.
