For example, take "[presidential candidate of your choice] is a nincompoop and bully".

Could this be transcribed as follows?

  • P1: [presidential candidate of your choice] is a nincompoop
  • P2: [presidential candidate of your choice] is a bully


Or could one consider that nincompoop and bully as interdependant?

In other words, that being a nincompoop leads someone to being a bully or being a bully leads to being a nincompoop or they just happen to correlate.

How can I ascertain all of this to understand the reasoning?

Edit: Question details modified as requested in comment below. Edit: Question details further modified.


No. Logical AND is logical constant; English "and" is not. Consider "she opened the door and entered the room", which implies an ordering that AND does not. And you can use "and" with a single argument, as this sentence demonstrates.

  • Good point about underlining how "and" can be used for a sequence of events. – James P. Sep 15 '16 at 12:26
  • This seems wrong to me. If I were to deconstruct the example into truth statements, the order would be irrelevant: "EVENT X OCCURRED" & "EVENT Y OCCURRED", where X = "she opened the door", and Y = "she entered the room". No matter which order I put these statements in, each one would still = TRUE, because she did in fact, do both things. What I see is an imprecise use of "and" as a sloppy substitute for "then": "She opened the door, then she entered the room": as a formulation, perhaps: "IT IS TRUE THAT EVENT X OCCURRED BEFORE EVENT Y OCCURRED", which itself could be true or false as a whole. – Greg Gauthier Sep 15 '16 at 13:04
  • @Greg Gauthier : the point is that translating from natural language into formal logical language does not go both ways. there is nothing sloppy about using "and" the way people normally use it. people are not logic devices. – user20153 Sep 29 '16 at 23:12

To expand on mobileink's correct answer, any given term from formal logic is never exactly "the same" as its natural language analog, because formal logic is an artificial construct created for the purpose of allowing for perfectly consistent definitions with mathematical precision, whereas natural language is messy and organic.

Translating from natural language to formal language and back is a good exercise, but it can be dangerously misleading. Logical AND is (arguably) inspired by the concept of "and" in natural language, and has some obvious similarities, but it is not the same thing. There are subtleties in natural language that defy the exact interpretation necessary for formalization, and levels of precision available in formal language that could only be achieved in natural language with great difficulty.

  • More likely, "arguably inspired" by Latin "et" or Greek "kai". – Luís Henrique Sep 13 '16 at 11:15
  • 1
    @LuísHenrique Edited to address – Chris Sunami Sep 14 '16 at 2:14

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