We often of a proposition use the term self evident or a similar variant. But we often use it incorrectly. We say for instance, “It is obvious that Mr Obama is a bad president,” when what we really mean is, “Given a certain collection of evidence which I am holding and which I assume you also hold, we infer that Mr Obama is a bad president.”
Error creeps in when the inference doesn’t lead to a certain conclusion, and it is instead only probable, or when the two parties do not agree on the same set of probative evidence. Hence arises politics, with which I assume the reader is familiar with many examples.
Sometimes we use the phrase correctly, as in “We hold these truths to be self evident, that all men are created equal (where men means all human beings)…” Or in the proposition, “For all natural numbers x and y, if x = y, then y = x.” Or in, “Obviously I exist.” Or in a host of other propositions which we say as true.
But notice the difference in these two phrases: “It is true I exist” and “It is self evident that I exist.” It is strictly a mistake to use the first phrase, but fine to use the second. The difference is subtle here and the mistake passes unnoticed, but only because of the example: you will agree that it is true that you exist, so the two phrases might seem equal, but they are not.
The first fails because it is like Alice coming up to you and announcing, “It is true that some chickens are creatures understanding French.” It most certainly is not true—unless we first accept the conditions Alice heard but we did not, but which would have allowed us to deduce this proposition as true.
The reason “It is self evident that I exist” works is because it carries with it the evidence we need to judge the truth of the proposition “I exist.” The evidence, which all arguments need, comes from saying “It is self evident”, which is just a translation of “Given my intuition” or “Given my most fundamental thoughts.”
Thus the second phrase is equivalent to “Given my intuition, it is true that I exist.” This allows us to recast our mathematical axiom “Given my intuition, it is true that for all natural numbers x and y, if x = y, then y = x.”
Now, we often as a harmless shorthand skip the qualifier and just say that “It is true that for all natural numbers x and y, if x = y, then y = x.” We get away without the qualifier in cases like this because the truth is so obvious and non-controversial. And it would be tedious to bring along qualifiers for everything item which we assert is true. For example, “It is true the car is in the garage.” Well, to be perfectly clear, you must say at least, “Given my observation and assuming my senses have not failed me and nothing has left the garage since last I’ve seen it, it is true the car is in the garage.” What a chore! Much easier to state, “The car is in the garage.”
No harm is done in the vast majority of these cases because the evidence which is required to make these propositions true is in fact shared by speaker and listener. But, as in the cases of politics, ethics, and metaphysics, it can be a positive menace to fail to specify the conditioning evidence.
Hold on a minute, did we make a slip? Yes, and a big one. Can you spot it?
Re-examine the “full” garage example. To make the proposition “The car is in the garage” true we had to carry a lot of baggage. Perhaps our slip arises because we did not fully specify the exact conditions which make the proposition true? If so, we can fix it up; after all, we use statements like these all the time without running into difficulties. This isn’t our mistake, so let’s just assume we do have the right evidence.
Our slip is something deeper, more fundamental. Ready? We had to know that, “given the evidence, the proposition is deduced.” We had to have built-in knowledge that lets us take statements of evidence and tie them to propositions. In other words, the operation of going from the evidence to the conclusion is a logical step, the validity of which we must take for granted. We don’t just need the evidence and conclusion, we need the logical glue that binds them.
This “glue” is also in our intuition. Alice needed it, and so do we, for every inference we make.
Next time: a proof of this last claim. It will also be the case that relativism is false.