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Jun 2 '20 at 11:40 comment added Mr. White I would agree that the sheer use of "=" does not guarantee identity. "=" could be used contextually and in a certain context not mean identity.
Jun 2 '20 at 10:44 comment added pglpm The question comes actually from a discussion I've had about "random variables" in probability theory, which typically has statements of the form "X = x". Someone said that this is an equality, as shown by the "=" sign. I tend to disagree, but I'd like to read more literature about this.
Jun 2 '20 at 10:40 comment added pglpm The problem is that some mathematical or physical statements do not make sense depending on the intepretation. From the statements "v1 = 300 km/s" and "v2 = 300 km/s", where v1 and v2 refer to velocities in completely different physical contexts (say, an instantaneous velocity vs a mean velocity), I could deduce "v1 = v2", which from some interpretation does not make sense: an instantaneous velocity is not a mean velocity – they have different definitions.
Jun 2 '20 at 10:33 comment added pglpm I understand that it's up to us how to model such a statement. That is, I could consider it within propositional logic and avoid speaking of predicates and functions; or within some first-order logic considering it as a predicate among many or as a relation or as a function; or within some second-order logic so that I can take "300 km/s" an an argument and quantify over it...
Jun 2 '20 at 9:35 history edited Mr. White CC BY-SA 4.0
added 69 characters in body
Jun 2 '20 at 9:34 comment added Mr. White To say that "is" is used predicatively, as I did above, does not ontologically imply that there exist qualities -- I have added that to my answer. This is a decision an ontologist has to make. However, I am very surprised that a physicist does go into such philosophical depth. Yet, I don't know much how physicists work.
Jun 2 '20 at 8:27 comment added pglpm Thank you for these thoughts. The question is also how "300 km/h", per se, can refer to an object, and what does this mean. We could of course introduce a set of "individuals" and a set of "qualities" and introduce the relation "... has the quality ..." between the two sets. But this seems a roundabout way to introduce predicates.
Jun 2 '20 at 8:15 history answered Mr. White CC BY-SA 4.0