I’m fairly sure that walking doesn’t have particularly different notions of what it means in different contexts. So thanks for your counter example, just a pity it’s a fail. Oh, I’m aware, but it just confirms that your entire reason for thread is, as was suspected, a straw man, based on the assumption that mathematicians, in their criticisms (criticisms that you have yet to actually provide examples of, btw), are using the same notion of validity as you are. Different notions, different results, different claims etc. Not a difficult matter to get one’s head around, is it? So you’ve set up a test to help you prove something that it can’t prove due to the different notions of validity being used by either side. And you put yourself up as not being stupid? And understanding logic, perchance?