However formalism is syntactic, I am talking about semantics here.
You can construct a formal language that way, but you can also not construct it that way.
In terms of bivalent logic, you can make a choice between constructive and non-constructive.
Because you can make the choice for non-constructive math, what I say is still true, as humans can do non-constructive math, as I just displayed to you. The truth of what I say is not dependent on whether someone else uses symbols like I do. It is related to the reality that we can and do reason in non-constructive ways. That is not a choice, so in that semantic sense non-constructive math is not a choice, as others will do it whether you like or not, and you can do it, whether you like or not.
It is true in constructive math you can construct everything. You can construct 1=2 if you define the symbol 2 to mean the natural number S(0). You can do that without a problem, formally speaking. So in terms of symbols, everything can mean everything just purely syntactically speaking.
I can define each finite set of symbols to mean any other finite set of symbols, purely from the rules of syntax.
Indeed you can literally do that, so all symbols mean the same per definition. I guess a computer does that in certain sense when it reads comments as that is just data that is not computed further (usually), meaning all symbols mean ( ).
Semantically what I say is still true. Of course syntactically you can define the set of symbols I said to mean Habeck would be the best Kanzler ever.
And maybe that would also be a good statement semantically speaking, but that is not what the post is about.
Yes, that is what the link in my post refers to.
However formalism is syntactic, I am talking about semantics here.
You can construct a formal language that way, but you can also not construct it that way.
In terms of bivalent logic, you can make a choice between constructive and non-constructive.
Because you can make the choice for non-constructive math, what I say is still true, as humans can do non-constructive math, as I just displayed to you. The truth of what I say is not dependent on whether someone else uses symbols like I do. It is related to the reality that we can and do reason in non-constructive ways. That is not a choice, so in that semantic sense non-constructive math is not a choice, as others will do it whether you like or not, and you can do it, whether you like or not.
It is true in constructive math you can construct everything. You can construct 1=2 if you define the symbol 2 to mean the natural number S(0). You can do that without a problem, formally speaking. So in terms of symbols, everything can mean everything just purely syntactically speaking.
I can define each finite set of symbols to mean any other finite set of symbols, purely from the rules of syntax.
Indeed you can literally do that, so all symbols mean the same per definition. I guess a computer does that in certain sense when it reads comments as that is just data that is not computed further (usually), meaning all symbols mean ( ).
Semantically what I say is still true. Of course syntactically you can define the set of symbols I said to mean Habeck would be the best Kanzler ever.
And maybe that would also be a good statement semantically speaking, but that is not what the post is about.