1. Some important distinctions
2  Verificationism


Here we discuss: (1) the analytic/synthetic distinction, the a priori/a posteriori distinction, and (2) in principle verifiability versus verifiability in practice, and weak versus strong verifiability.
The following are definitions that we, for now, will take any philosophical account to need to accomodate.  Thus, in a slightly anachronistic way, we will present Kant, Mill, and Ayer as agreeing on these definitions but characterizing the notions defined differently.

One way to test for a sentences being analytically true is to consider if it is possible for the sentence to be false without changing the meaning of any of the words in the sentence.  If it is not possible to do this, then we have good evidence that the sentence is analytically true.

Prima facie examples-
Mathematical truths such as ``2 + 2 = 4.''
Linguistic truths such as ``All bachelors are unmarried.''
Logical truths such as ``Either Jon smokes, or Jon doesn't smoke.''

(Note- This test isn't always sure fire, as Kant thought mathematical and geometrical truths were synthetic.  Wthout getting into heavy duty Kant exegesis we?ll see why one might take mathematical and geometrical truths to be synthetic.)

A good test to see whether a sentence is synthetic is to see if it can be made false both by the world being different than the way it is when the meaning of the words is held fixed.  Consider the sentence, ``Bill Clinton is President.''  This could be false even when the words meant the same as they do now, but the world was such that Dole had gotten elected.

Ayer thought that there were no synthetic/a-priori truths, and no analytic/a-posteriori truths.  That is all truths are either synthetic/a-posteriori or analytic/a-priori.  He also thought that synthetic truths were all verifiable, but we will need to consider some other distinctions to get clear on this claim.  This will be discussed below.

Importantly, the analytic/synthetic distinction is a semantic distinction; it only concerns what makes sentences true or false.  The a-posteriori/a-priori distinction is an epistemological distinction; it concerns what justifies our knowledge of the truth of certain sentences.

2  VERIFICATIONISM Now we can turn to the different senses of verifiability that Ayer works with.  We start with verifiability in practice.

For example, I can currently falsify the sentence ``There is a cat on my desk'' right now.  I look on my desk and there is no cat.  Thus, the sentence ``There is a cat on my desk''  is verifiable in practice.  The sentence, ``There is a cat in front of my apartment'' is also verifiable in practice, as I currently possess the means to go determine whether or not the sentence is true.

In-principle verifiability is defined in this manner.

For example, the sentence ``The 10 raised to the billionth power raised to the billionth power raised to the billionth powerth  prime numer is the sum of two primes'' is not in practice verifiable, but it is in-principle verifiable.  Or consider sentences about planets in galaxies far away, they are not verifiable in practice but are verifiable in principle.  Every sentence that is verifiable in practice is verifiable in principle, and many sentences that were only verifiable in principle become verifiable in practice as techonology and mathematical techniques get better and better.

Strong verifiability is defined in this manner:

Ayer holds that very few propositions are strongly verifiable in this manner.  Good examples come from mathematics.

Weak verifiability is defined in this manner

Most factual claims are weakly verifiable.  Notice that if a proposition  is strongly verifiable then it is also weakly verifiable.

As we study Ayer's text more we need to see what his account of evidence is such that he can coherently say that metaphysical and ethical claims are not even weakly verifiable.

Now Ayer's critierion of meaningfulness can be stated clearly.

{In the above I have been using ``proposition'' and ``sentence'' interchangeably, though we may need to make a distinction between the two in the course of our studies.  In contexts where the distinction is important the principle of meaningfulness will be stated thus:

Let's unpack the principle of meaningfulness so that we don't let Ayer slide with anything later on.  I think what Ayer has in mind is this:

{Again, this could be rephrased in terms of propositions.}

It is this criterion that Ayer will attempt to use to argue that many sentences are not meaningful.