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By higher level, I mean big picture. Not necessarily introductory, but ones that don't employ logical concepts such as "proof", "formal" etc, because you cannot
by boris_m 5y ago
By higher level, I mean big picture. Not necessarily introductory, but ones that don't employ logical concepts such as "proof", "formal" etc, because you cannot define a field of study using concepts from that field. This example is good, but not sure what are you trying to say by posting it (I didn't say that noone ever wrote anything on what logic is.)
- drdeca 5y ago> because you cannot define a field of study using concepts from that field. Why not?
- boris_m 5y agoBecause the definition would be circular.
- drdeca 5y agoDoes a field of study have to be defined in order for the concepts in it to be defined? I don’t see why. Can’t you define concepts x,y,z, and then define the field of study as being “about x,y,z and the things related to them”? I’m guessing you mean something different by “defining a field of study” (different from my default/initial interpretation of the phrase I mean), but I’m not sure what else you mean by it.
- deleted 5y ago[deleted]
- boris_m 5y agoYou can do that, but that's surely not the best way to do it, unless the concepts don't have anything to do with each other aside from being part of that field of study.
- drdeca 5y agoIf it lets me avoid a circular definition, I’m willing to tolerate a bit of ugliness in my definitions (at least, provided that it can be shown to be equivalent (under assumptions of some results that can also be proven under the awkward form) to a nicer framing).
- deleted 5y ago[deleted]
- leoc 5y agoGraham Priest's Introduction to Non-Classical Logic https://www.cambridge.org/core/books/an-introduction-to-nonclassical-logic/61AD69C1D1B88006588B26C37F3A788E https://www.cambridge.org/core/books/an-introduction-to-nonc... is so good and deserves to have a SICP-like fandom. But it's certainly going to talk to you in terms of proof, formality and so on.
- slibhb 5y agoAn excerpt: > 6.2.1 Let us start with a look at the original rationale for intuitionism. Consider the sentence ‘Granny had led a sedate life until she decided to start pushing crack on a small tropical island just south of the Equator.’ You can understand this, and indefinitely many other sentences that you have never (I presume) heard before. How is this possible?