Life, the Universe, and Everything

A Course Blog for GET1029/GEK1067

Month: September 2018

Necessary and Sufficient Condition

From previous experience, the ideas of a necessary condition, vs. a sufficient condition, and a necessary and sufficient condition are often not easily grasped by students. The handout in IVLE Files (“Everything you always wanted to know about arguments”) covers the relevant topics and your tutors will also be reinforcing the ideas. Below is a refresher.

For our purposes, take note of the following equivalences (everything in the same column are logically equivalent to each other):

P is a necessary condition for Q P is a sufficient condition for Q P is a necessary and sufficient condition for Q
P is necessary for Q P is sufficient for Q P is necessary and sufficient for Q
Q only if P Q if P P if and only if Q
Only if P, then Q If P then Q Q if and only if P
If Q then P P only if Q
If not P then not Q If not Q then not P

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Insufficient Information

Several questions in Quiz 01 (and beyond) hang upon your ability to notice that you have insufficient information. As the hint also puts it, sometimes, the lack of information is itself information. One question students sometimes ask is how they are supposed to take into account the lack of information, since in principle, there could be many things out there that are unstated, and that could affect the answer. But the point is not for you to take into account what is merely hypothetical and or anything that could have been (even though they are often useful in helping us realize the extent of our ignorance). Let me explain using an example.

Supposed I give you the information that Ah Seng did X, which was happiness neutral for him, but which resulted in an increase of happiness for Ah Lian, and a decrease of happiness for Ah Hwe, where the former (the increase of Ah Lian’s happiness) is larger than the latter (the decrease of Ah Hwe’s happiness).

Now supposed I ask you whether Ah Seng is a Utilitarian. Given the information provided, the correct answer would be that we simply don’t know. To say that Ah Seng is a Utilitarian, what we mean is that he believes that the right thing to do is the one that maximizes the world’s happiness. Do we know that he believes such a thing? The information doesn’t allow us to conclude one way or another.

But now suppose I ask you if a Utilitarian (someone like Dave) would have said that Ah Seng did the morally right thing given just the information provided. Then, the answer is that he did the right thing given the information provided. This will still be true even if it turns out that–unbeknownst to all, Ah Seng’s action actually also caused Ah Beng to be really, really unhappy such that if this additional fact had been taken into account, you will need to change your judgment and say that he did the wrong thing from a Utilitarian perspective. That is, given the information (earlier) provided, Ah Beng did the morally right thing according to Utilitarianism.

Notice that in both cases, you can draw a type of definite conclusion–for the first case, you can draw the conclusion that we don’t know if Ah Seng is a Utilitarian, given the information provided; and in the second case, that he did the right thing from a Utilitarian perspective, given the information provided.

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