Last Update: 25 March 2010
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The last wff in the sequence is often called a "theorem".
If all of the theorems are true, then the formal system is said to be "sound".
"This sentence cannot be proved."
As an analogy to a formal system, consider a "Transformer" toy made of Lego blocks.
For those of you who don't have (or who weren't themselves) children
(probably boys) of a
certain elementary-school age,
Transformers are toys that, in one
configuration, look like monsters, but can be manipulated so that
they turn into something else, often (believe it or not) a truck or
other vehicle.
Lego blocks are small building blocks that can be attached to each other to form larger structures.
To continue the analogy, suppose that
the only wffs are Transformers, either monsters or trucks.
(This is
a bit imaginary: You can't make Transformers out of Lego blocks;
even if you could, the manipulations to turn them from monsters into
trucks would probably cause them to fall apart.)
The above analogy falls apart if you look at it too closely, so please don't!
It can be more generally understood as the study of the relations among the entities of some domain, preferably a domain that can be understood more or less in the terms of a formal system.
The most accurate meaning is probably that pragmatics is the study of everything else that is interesting about formal systems and their interpretations that isn't covered by either syntax or semantics.
Most people would agree that pragmatics includes the study of the relations among symbol systems, their interpretations, and the cognitive agents who use them.
It is also often characterized as the study of "contexts" in which symbols are used.
It can mean "social" context, or
"situational" context, or "indexical" context
(e.g., the fact that
the sentence "I am hungry" (which contains an "indexical" or "deictic" term:
"I")
means the same thing (in one sense of "means") no matter who says it
(i.e., it means that the speaker is hungry),
yet means different things (in another sense of "means") depending on who says it
(if you say it, it means that
you are hungry, whereas if I say it, it means that I am hungry, which
might have different truth values).