Logic is concerned with the form of an argument. One of the simplest argument forms is as follows:
Paul is taller than Peter.
John is taller than Paul.
Therefore John is taller than Peter.
We do this kind of deduction all of the time in our daily lives. It follows a standard logical form with which we are all familiar (even if we didn’t know that it is a standard logical form).
The next deduction follows the same logical form:
Paul is better than Peter.
John is better than Paul.
Therefore John is better than Peter.
Here, we have simply replaced the relational operator ‘taller’ for a new one – ‘better’ – in every occurrence of the derivation.
We can also replace the nouns in the derivation without changing the form, as long as we replace them consistently throughout; So, replacing Paul, Peter, and John, we get:
Adam is better than Betty.
Charles is better than Adam.
Therefore Charles is better than Betty.
Going with one more substitution, we get:
Nothing is better than eternal happiness.
A dollar is better than nothing.
Therefore a dollar is better than eternal happiness.
Something has gone wrong here, although exactly what may not be clear.
Logicians also have a somewhat unusual view of what is true. For example, the statement:
If I am eight feet tall then the moon is made of green cheese.
is true in standard logic, even though I am clearly (if you could see me) not eight feet tall, and even though my height doesn’t have anything at all to do with the base ingredient of the moon.
The reason it is a true statement is that, since I am not eight feet tall, the conclusions reached from this false premise are inconsequential.
In standard logic, anything at all can follow from a false premise; the ultimate false premise being a contradiction – something which can be shown to be false simply by it’s form. For example, the expression:
I exist and I do not exist.
is a contradiction, although people say this sort of thing all of the time – usually without realizing it. According to standard logic, anything at all follows from a contradiction. So, if I can find a contradiction in a theory, then there is nothing that I can’t prove with it. For example, if the statement “I exist and I do not exist” is found in my metaphysical theory, I could also derive from it that “You are a dark green ‘57 Chevy.”
Those schooled in logic will realize that I am playing games with things at this point – these are examples, not of how logic is used, but instead how logic can be misused. Like bad statistics, bad logic can seem to produce any result one wishes. But there are some less obvious and potentially more damaging fallacies and paradoxes which are not as easy to explain away.
Imagine a village in which there is a male barber who shaves all and only those men in the village who don’t shave themselves. Who shaves the barber?
This paradox (called Russell’s paradox after the philosopher Bertrand Russell who first proposed it), has been the source of discussion in logic for almost a century. Part of the problem with logic is that it is very black and white – there are no shades of gray. For example:
This sentence contains seven words.
is false, so it’s opposite should be true, right?
This sentence does not contain seven words.
Oops. This kind of thing can be very scary if you have grown up, as I did, believing that logic is the preeminent mode of thought. Fictional characters such as Sherlock Holmes and Mr. Spock seemed to be telling us that all we need to do is be patient and think logically and “all else will come.” The mistake that people make is mixing up being logical with making sense.
Logic never adds information – it only reshuffles it. Logic is an internally consistent system with no necessary direct bearing on real life. Logic is not only tricky, it is, in fact, irrelevant in most situations. A logician named Schiller once wrote that “the central doctrine of the most prevalent logic still consists of a flat denial of Relevance.” So, the first thing that the student of logic must give up is the idea that logic will somehow help him in the real world.
A logical argument bears very little resemblance to most “real” arguments. A logical argument is “a connected series of propositions or statements intended to establish a conclusion.” How many real arguments are like that?
The following argument is a classic example showing the difference between rational and real-life arguments (click the image to see the video):
This argument is much more like what we get with our political “debates” — where logic or even sound reasoning doesn’t seem to have anything at all to do with it.