If we are to have a discussion about something there are a few things we first need to agree upon in order to communicate efficiently and intelligibly. A good way to test for what we need is to transcribe a discussion between two individuals and afterwards hand this over to a third non-participating individual, who should be able to unambiguously interpret the transcription.
Let’s say one of the individuals in the discussion frequently talks about ‘Jennifer’, while the other uses ‘Jen’. In order to avoid possible confusion, it should be agreed upon that ‘Jen’ and ‘Jennifer’ is the same person. This can be done by the introduction of a unique identifier, say ‘J42’, such that the transcript may read “I talked to Jen (J42) today.” and “Oh, how is Jennifer (J42) doing?”. We need to agree upon the identities of the things we talk about.
Assuming the respose is “Jen (J42) is doing good.” followed by “I figured as much, new boyfriend and all, so Jennifer (J42) must be good.”. In this case ‘good’ is a value that should mean the same thing to both individuals. However, ‘good’ is not scientifically precise, but there is a consensus and familiarity with the value that let’s us assume that both parties have sufficiently equal definitions to understand each other. Imprecisions that would lead to confusion could of course be sorted out in the discussion itself. If “Jen (J42) is doing so so.”, then “What do you mean ‘so so’, is something the matter?” is a natural response. We need to agree upon values, and that any imprecisions lie within the margin of error with respect to the mutual understanding of their definitions.
Now, if the transcription needs to be done efficiently, leaving out the nuances of natural language, that challenge can be used to test whether or not the two constructs above can capture the essence of any discussion. Using identities and values we can construct pairs, like (J42, Jen), (J42, Jennifer), (J42, good). Forget that you’ve heard anything and put yourself in the shoes of the third party. Apparently, something is missing. There is no way to tell what ‘Jen’, ‘Jennifer’, and ‘good’ are with respect to the thing having the identitiy J42. This can be sorted out by adding the notion of a role that an identity takes on with respect to a value. Using roles, the pairs become triples (J42, nickname, Jen), (J42, first name, Jennifer), and (J42, mood, good). We need to agree upon the roles that identities take on with respect to values.
Surely this is enough? Well, not quite, unless Jen is permanently in a good mood. The triple (J42, mood, good) is not temporally determined, so how could we tell when it applies? The third party may be reading the transcript years later, or Jen may even have broken up with her boyfriend before the discussion took place, unbeknownst to the two individuals talking about her. Using a temporal determinator, interpretable as ‘since when’, the triples can be extended to quadruples (J42, nickname, Jen, 1988), (J42, first name, Jennifer, 1980-02-13), and (J42, mood, good, 9.45 on Thursday morning the 20th of August 2019). The way the point in time is expressed seems to differ in precision in these quadruples. Actually, there is no way to be perfectly precise when it comes to expressing time, due to the nature of time and our way to measure it. It’s not known exactly when Jennifer got her nickname Jen, but it was sometime in 1988. We need to agree upon the points in time when identities took or will take on certain roles with respect to certain values, to some degree of precision.
This is almost all we need, except that the quadruple can only express properties of an individual. What about relationships? Let B43 be the identitiy of Jen’s boyfriend. We may be led to use a quadruple (J42, boyfriend, B43, 2019), but this has some issues. First, B43 is in the third position, where a value is supposed to be, not an identity. If we can overlook this, the second issue is more severe. Can we really tell if B43 is the boyfriend of J42 or if J42 is the boyfriend of B43? The way we introduced the role, as something an identity takes on with respect to a value, the latter alternative is the natural interpretation. Finally, the nail in the coffin, relationsships may involve more than two identities. Where in the quadruple would you put the third party?
The solution is to return to a triple, but where the first position contains a set of ordered pairs ({(J42, girlfriend), (B43, boyfriend)}, official, 2019). This resolves the issue of who is the boyfriend and who is the girlfriend. The second position is again a value and the third is the temporal determinator. Looking back, we can actually consolidate the quadruple used to express properties to a triple as well ({(J42, nickname)}, Jen, 1988). The only difference being that the cardinality of the set is one for properties and more than one for relationships. Triples like these are called posits in #transitional modeling.
We could leave it here and be able to represent a whole lot of information this way. But, let us return to the three individuals we have been talking about. Now that the transcript is in place, consisting of a number of posits, what if they cannot agree upon it being the single version of the truth? What if some of what was written down is not 100% certain? What if someone is of an opposite opinion? This sounds like important information, and it can actually easily be transcribed as well, but it requires another construct, the assertion. This will be the topic of the next article; “What can be disagreed upon”.
