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Originally Posted by yaaarrrgg  It's not clear that tautologies are true statements. A common view is that mathematical statements are neither true nor false. IMO a mathematical axiom like '1=0' is perfectly valid, just not very useful. Maybe one could think of it as a degenerate case like '1=0 (mod 1)'. In this case "Water is wet" could be neither true nor false. |
Well, I would say that mathematical statements have a truth value based on the system they exist in. That can be extended everywhere. In the framework that 'wet' means 'having the properties of water', and that water certainly has its own properties, then 'water is wet' resolves to true. In a different system, it may very well be false. So really, mathematically speaking, true really means consistent with the system we are currently working within. So, yeah, '1=0' is valid in some systems, just not in the usual one. That's why it's important to declare the rules.
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Also, IMO the object/property way of talking is also reducible to the more basic concepts of 'similiarity' and 'difference'. For example, if something is brown and solid, we don't call it water. IOW we classify things into object catagories, to begin with, based on similarity and differences. Then we call something a property if there's a similarity between all the objects.
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I agree that 'similar'/'different' is more primitive, so to speak. But I think that carefully defined properties are more useful, and more basic in a certain sense. I think of it analogously to chemistry/physics. As science has advanced, we (humanity) have discovered ever more basic building blocks of matter. In one sense, electrons are more basic than gold; in another sense, they are far more advanced.