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Just a layman and slow learner. Thank you for your enlightenment and patience, and for giving me the best memory in my life.


Jul
20
comment theory, theorems and axioms
@ThomasAndrews: My bad. the first question is: is the theory the set of axioms or the set of theorems?
Jul
20
revised theory, theorems and axioms
added 22 characters in body
Jul
20
asked theory, theorems and axioms
Jul
20
asked Meaning of abstractness and concreteness
Jul
19
comment Axiom Systems and Formal Systems
Thanks. +1. (1) Do "rules of formation" generate strings from nothing? (2) Are "rules of formation" the formal grammar? (3) Are "rules of transformation" used in defining a language inductively or recursively from some basic strings? (4) how do you transform between "rules of formation" or a formal grammar and "rules of transformation"? See also cs.stackexchange.com/q/28534/336
Jul
19
asked Are axioms assumed to be true in a formal system?
Jul
19
comment Is a definition either intensional or extensional?
@QiaochuYuan: do you happen to have some idea?
Jul
19
comment Is a definition either intensional or extensional?
@hardmath: I simplified the example, see the edit. I hope you can understand what I meant earlier with the original example. Both examples are similar in that there is only one object that satisfies their definitions.
Jul
19
comment Is a definition either intensional or extensional?
@GitGud: I simplified the example, see the edit. I hope you can understand what I meant earlier with the original example. Both examples are similar in that there is only one object that satisfies their definitions.
Jul
19
revised Is a definition either intensional or extensional?
added 774 characters in body
Jul
19
revised Is a definition either intensional or extensional?
added 774 characters in body
Jul
19
comment Is a definition either intensional or extensional?
@GitGud Here I am defining A, not if an object is its element. So I think either of your and my definitions is both intensional and extensional..
Jul
19
comment Is a definition either intensional or extensional?
@hardmath: I am defining $A$, not if an object is its element. So I think the definition of $A$ is both intensional and extensional.
Jul
19
comment Is a definition either intensional or extensional?
@GitGud: I think both your and my ways of defining $A$ are both intensional and extensional. See my edit
Jul
19
revised Is a definition either intensional or extensional?
added 774 characters in body
Jul
19
comment Is a definition either intensional or extensional?
Is it intensional? @Git
Jul
19
asked Is a definition either intensional or extensional?
Jul
16
comment What do “completely described” and “complete formalisation” mean?
Thanks. I am also wondering what the axioms, inference rules, and semantics of a lambda calculus are. I don't find it in Boolos' book. Do I miss it or is there some other references for that?
Jul
15
revised Are there formal systems that are not logical systems?
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Jul
15
comment Are there formal systems that are not logical systems?
@Squirtle I don't know the definition of an illogical formal system. From the link "A logic system is sound if all sentences that can be derived are true in the interpretation, and complete if, conversely, all true sentences can be derived."