Originally Posted by Samuel Dravis
Anyways, I don't think that 2+2=4 is true because we think that way. It's true that 2+2=4 is confirmed by observation, but the generality of the equation is not justified by those observations (this is part of Bahnsen's argument, actually). However, the proposition 2+2=4 is a part of our language and used in a certain way within it, and that use is intertwined with how we can talk about it. So, if an alien were to come and learn how we use it - see the context in which we apply it - then they'd know what we meant by 2+2=4. It's universal in that anyone who uses our methods of solving mathematical problems will inevitably come up with 4 as the answer to 2+2. Of course, there's no warranty for the results coming from anyone using some other method!
But doesn't that still reflect an objective truth? 2+2=4 is true. It just happens to be our language and the categories we think in that make it a "2+2=4". But the concept itself is, arguably, simply representing the truth, regardless of human constructs (such as language etc). Our numbers and our language as well as our logic are merely the means to talk and think about it.
And if an alien were to come, it would probably have a completely different approach to it, something we might not be able to understand, but 2+2 would still be 4. If that makes any sense.
To be honest, I don't understand your point entirely, but I find it very interesting. Please expand! (I know you already did in this thread, but I still don't get it
Originally Posted by Samuel Dravis
Additionally, there is a tendency to use the scientific method as an end-all way of coming to The Truth(tm), which I commented on with a note on Ayer, Popper and Feyerabend. I think it's important to keep in mind that not all knowledge is scientific, nor does it need to have a litmus test applied to it to make sure we really do know it. An art critic might know what a splash of paint means without having a theory which he uses to identify a particular case. I can even know what a stranger intends to do without needing to see him do it (except in extraordinary circumstances), if he tells me. We can be wrong about knowing something, but that's not a problem. In fact, that's often what distinguishes knowing from believing.
I read about half-way through Against Method some time ago. (And I fully intend to finish
). From what I remember, Feyerabend used Galilei as an example to get his point across. His point is, that quite a lot of scientific accomplishments were not achieved by adhering to strict rules and that imposing such a set of rules can seriously hinder our scientific progress. He argued that Galilei's Copernicanism was in fact irrational at that time. Irrational, because people back then had different "natural interpretations" of facts. Nonetheless, Galilei was persistent and eventually Copernicanism was shown to be correct
I agree with Feyerabend insofar as I believe that it doesn't matter how one comes up with a theory. Any restrictions here would certainly hinder our thinking and our creativity. But the process of determining if a theory actually reflects the real world is always the same.
(The art critic might indeed think he knows what a splash of paint means, but that knowledge would be entirely subjective)
Edit: If anything is unclear or doesn't make sense, it is due to my inferior English, not my flawed thinking! xD