Rodger Scruton says that maths is not analytic. An analytic statement means one that is true by definition. It seems obvious that 1 and 1 is 2. If you define 1, define adding, define 2 then you seem to have an a priori truth. A is A is a real analytic truth. Maths is not for you have to test it.

What is the alternative to analytic? Synthetic statements are evidence based. They are the alternative. We call looking at the evidence a posteriori. An example of a synthetic statement is this, “John needs a blood supplement of iron.” That is not something that is clearly true. It comes from evidence and it is down to what the evidence says. It needs checking.

Kant looked at Hume’s thought that the truths of mathematics are analytic. Hume would take the notion that the shortest distance between point a and point b is a straight line as an example. That seems plainly and obviously true just if you look at the statement. In fact it needs checking. You draw the two points and the line. You try different lines all twisted and so on and measure. Find the shortest. So it is not an obvious truth. It is something that you have to test and apply evidence to. This being the case, you need evidence to support your mathematical findings and as science uses maths it follows that science is fundamentally about synthetic statements.

But he says objective morality as in do the right thing or make yourself immoral is analytic. Does that add up? No. We see that we mistake the simple for the obvious which means we mistake statements that need evidence for analytic ones. If objective morality is in fact real it does not follow we are able to apply ourselves to it and it to us. A blind person needs evidence that the rock is there. She cannot make it obvious to herself that the rock is there. Morality could be the rock.

If God grounds morality why is he not giving us the power to see it clearly? Why is a moral statement not an analytic statement? The answer is that God if real is not that concerned about giving us morals at all.

Hume noticed that religious “truths” cannot be backed up by evidence and are not true by definition. For example, you cannot look at the statement “God exists” and just know it is true. It's not therefore an analytic statement. And there is no proper evidence so it is not a synthetic statement either. So he argued that statements like that are meaningless. Untrue or true is not the word for them. It is meaningless.

As Hume’s argument here is not based on evidence we are told and is not a priori it defeats itself. So where does that leave us? If it is a half truth we still see there is something there. There is still enough there to suggest not taking seriously certain things that we don't need like God and miracles and Jesuses. We need bread and we need maths. If Hume is wrong, we still have no warrant to glorify and make a big deal out of believing in religion. Religion being treated as opinion and custom might be okay but religion wants more than that!

It has been noticed that if Hume is right to say that human beings are too prone to lying perhaps without realising it and to prone to error for us to believe in their miracle claims it also goes the other way. Humankind cannot eliminate lying and error in deciding what the unchanging laws of science are thus there is room left for miracles. This is not the same thing. Science keeps rechecking for it is aware that lies and errors will be present. Miracle believers stop checking and don't check correctly.

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