Can A be defined only by what it implies, and D only by what implies it?

[tgt]

Is there such a definition for A such that A is defined A=>B. Hence nowhere in the definition does it say anything will imply A.

Is there such a definition for D such that D is defined C=>D. Hence nowhere in the definition does it specify what D implies.

If there exist definitions of A and D then please give examples. If not, why not?

 

[JonF]

you aren't being very clear what exactly you are asking... Typically we define things like objects or operations, but in order to use an implication between to defined objects typically you need to say something about those objects. Such as “A exist”, “A is maximal”, “or A is finite”.

Fore example: “if A exist it implies B exist” Makes sense, where A and B are some objects. For example let A be “a countable set” let B be a “countable subset”. Then our statement would read: “If a countable subset exist it implies a countable subset exist”

Now try the same statement without making a statement about the objects (which is what you originally wanted): “A countable set implies a countable subset” doesn’t make much sense.

So what is about A, B, C, and D you are talking about?