Mathematical- such statements are much like analytical statements because they have the means to prove their truth, e.g. two plus two does indeed equal four.
Synthetic- theses statements are different from both analytical and mathematical as they can be proved true or false by testing. For example ‘there is a giant obelisk in your bedroom!’ one can prove this to be true by simply getting up and looking in ones room.
The verification principle demands that only empirical statement have meaning as observations verify them. Therefore if there is a statement that does not fall under synthetic, mathematical or analytical, is nonsense.
However the VP does run into problems, on of which the talk of god. Statements about god are no, mathematically or analytically true, and they cannot be proven by observation, and claimed experiences of god are merely subjective and biased, therefore all talk of god is nonsense in the verification principle.
Also all statements that express unverifiable opinions or emotions are invalid, according to logical positivist, therefore all ethical statements ore nonsense. As they aim to persuade people by evoking certain emotions from them, they are therefore subjective and opinion, therefore meaningless. Bertrand Russell, a Cambridge mathematician and philosopher shares this. He claims that moral judgments merely express wishes and are therefore not factual.
However it is not just ethical statements that the verification principle disagrees with. There is also a disagreement with science, general laws of science, that are accepted as true cannot actually verified as there is no way they can be verified. For example to say that all water boils at 100°c cannot be tested so therefore it is meaningless. Historical statements also suffered this consequence.
To say that the battle of Hastings took place in 1066 cannot be verified as there is no one alive to prove it, therefore it is also meaningless.
A.J Ayer proposed a weak form of the verification principle. He said that if it is possible to know what would in principle verify a statement, that it is meaningful. However religious language still did not fit in this category, things that refer to a transcendental being, which is in principle, unverifiable.
The verification principle was therefore fatally flawed, so flawed that statements about the verification principle itself could not be verified (therefore making it meaningless). It failed to consist with modern science it actually sought to promote as scientific language uses metaphor and analogy to describe concepts beyond the naked eye.
From the ashes of the Verification Principle rose the Falsification Principle. This principle demands that the speaker must be able to say what would count in the falsification of the statement. It was developed by Anthony Flew, who took influence form Karl Hopper, a philosopher of science. Hopper
