Page 400 - Encyclopedia of Philosophy of Language

Formal Semantics
may temporally precede, and spatially or temporally overlap or include one another.
&now, Jon; 0 » needs to be a member of s, and this possibility captures the credited partiality of real situ- ations. But it is also possible that both an infon and its negation are an element of a situation. This possibility does not seem to be grounded in reality. (However, in the context of attitude reports (cf. below) this possi- bility might be useful again.) An important notion, therefore, is that of a coherent situation: a situation s is coherent if, for no /P*,/,^,...,^, both «*",/,«,,...,an; 1» and «/T,/,a,,...,a,,;0>> arein
From these 'primitives' and (0,1}, an additional
set of 'polarity markers' ({no, yes} in S&A), other
situation theoretic objects can be built up. First,
sequences of basic information units, 'infons,' are con-
structed: «/?",/, fli,..., an;/» consisting of an w-ary
relation P", a location /, a sequence of n individuals
a,,...,an, and a polarity marker /. Such sequences
reflect the fact that the individuals a,,...,an, do (in
case1=7)ordonot(incase/=0)standinrelationR" s.Itwillbeassumedthatallactualsituationsare
at location / in some situation. (In S&A the location argumentofaninfonisfronted: </,</f,a,,...,an;/». In more recent work, it has become optional.) For instance, the infon «LOVES, here&now, Jon, John; 1» reflects the fact Jon loves John here and now, and « LOVES, here&now, Jon, John; 0 » reflects the fact that Jon does not love John here and now. Notice that facts are talked about here without making reference tosituations.Theconnectionbetweenfactsandthe reality of situations comes about by what is called the 'supports'-relation. If an infon i is a fact in a real situation s, then s is said to support /, which is written as: s¥i. So if sN^LOVES, here&now, Jon, John; 0 » , then in s Jon does not love John at the location here and now. Furthermore, sNCLOVES, here&now, Jon, John; 0 » itself is called a proposition which is either true or
false.
Infons are the basic information units of situation
coherent.
It was said above that meaning in situation sem-
antics is, basically, a relation between situations, a relation which itself is considered 'real.' However, in order to account for this relation, more complex uni- formities need to be introduced—so-called 'situation types.' For that purpose 'basic indeterminates' (also called 'parameters') are introduced. These are abstract stand-insforrealprimitives:a,b,...forindividuals; r,r',...for relations; and /,/',...for locations. An indeterminate (or 'parametrized') infon is a sequence «/f,/,a,,...,an;/» where /?",/,a,,...,a, are inde- terminates or real primitives, and i is a polarity marker. A 'situation-type' (or 'parametrized situ- ation') is a set of indeterminate infons, i.e., an abstract situation in which zero or more indeterminates are substituted for real primitives. An example: situation- type 5= (CLOVES,/,a,b;!»} contains one inde- terminate infon «LOVES,/,a,A;l», with three inde- terminates: /, a, and b. Note that, since every infon is also an indeterminate infon (one with zero inde- terminates), every situation is a situation type.
theory. More complex information is gathered in sets
of infons, called 'abstract situations.' So real situ-
ations, parts of the world which are recognized as
such by agentive organisms, are distinguished from
abstract situations (or just 'situations'), mathematical
compounds of primitives abstracted from real situ-
ations. Notice that real situations are even more primi-
tive than the theoretical primitives from which 'Anchors' are partial functions from individual,
abstract situations are built up. (In S&A, abstract situations are called 'courses of events.' Certain courses of events are called 'states of affairs,' situ- ations whose infons all have the same location argu- ment.) Abstract situations 5 may also be said to support an infon /, where,of course, sti if and onlyif ies. Furthermore, real and abstract situations can be related in the following way. An abstract situation 5 corresponds to a real situation 5 iff for all infons i:ieso$¥i. If an abstract situation corresponds to some real situation then it is said to be 'actual.' A weaker notion is in use as well. An abstract situation s classifies a real situation s iff for all infons i: if ies then *Ni. In case an abstract situation classifies some real situation, then it is called 'factual.' In a sense, then, an actual situation is some kind of complete factual situation: if some situation 5 is factual, then there is some actual situation 5' such that s^s'.
A situation can leave the issue whether certain indi- viduals stand in a particular relation undecided. Neither ^WALK, here&now, Jon; 1» nor « WALK, here
relation, and location indeterminates to individuals, relations, and locations, respectively. An anchor/is a total anchor for situation-type 5 if / i s defined on all indeterminates in 5. Write S[f] for the situation-type 5 ' which results from simultaneously substituting/^*) for x in S for all indeterminates x in the domain of/. Then can be defined: s is of type S (also written as s: S) if there is a total anchor/for S such that S[f]^s. For instance, / = {</, here&now), <a, Jon), <ft, John)} is a total anchor for situation-type S= {«LOVES, /, a, b; 1»}, and S[f] ={CLOVES, here&now, Jon, John; !>>}=$. Since S\f]—s,s is of type S. However, observe that also S' = {«LOVES, here&now, Jon, John; 1», ASMOKE, there&then; 0»} is of type S.
The notion 'constraint' models the idea that mean- ings reside in the world, as regularities which allow attuned agents to derive information about situations from situations. It is a fact that situations of a certain kind entail the presence of situations of another kind. In situation theory this fact is captured by infons of theform«/NVOLVES,S,S';1».SandS'aresituation-
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Situation types are conceived of as uniformities in theirownright.Theymaybeusedtoclassify situations and can be linked up with situations using anchors.