Argument:  My love is not having and has not had an affair.

How can we prove a partner has not at some point carried on an affair with someone else, and never revealed it?

The affirmative case

Logically and traditionally we begin with the affirmative case:  My partner is not having and has not had an affair.  Premises are required to support the conclusion.  My partner loves me, I trust her, her love has been consistent and unwavering.

Some Conclusions, by the way (I’ve left this out up to this point for sake of simplicity) require a set of specific premises to support them.  Another way to put this is to say that some premises do not in themselves do the job of supporting a conclusion: they require Help.  A third way of looking at this is to say that some premises contain assumptions that require explanation before a conclusion can be accepted.

Premise A + Premise B -> Conclusion

Premise A + Supporting Premise for A -> Conclusion

she is a kind person,  and a kind person would not have an affair, so therefore she would not have an affair

This form of argument is a strong form because it contains a definition that ties kindness to a particular kind of action.

Again, though, it can be seen as hinting at what is MISSING in most arguments:  the complete set of premises and supporting premises required to fully support even a simple conclusion is really never made.

Negative case

So we can concoct a list of comforting reasons, premises that support the assertion that ‘my partner has not had an affair.’

But to complete a dialectic argument (for the best chance of finding the truth) we’re forced to look at the opposing case: My partner is having or has had an affair.

With a kind of dread, we can open Pandora’s box and search for premises supporting this unpleasant conclusion.  The problem is that thinking dispassionately some premises will quickly be found.

For example in spatio-temporal terms it must be considered an affair is possible, recently or in the distant past.  Two people do not spend all their time together, and so there have probably been times unaccounted for in terms of a partner’s activity.

At this point it might be tempting to return to the list of premises supporting the affirmative argument that no affair has been had.  But a dispassionate assessment of the situation does not permit the use of a general hypothesis such as ‘She loves me’ to interfere in the search for premises supporting the dreadful case that something has happened, – some current or past romance with someone else..

If there has been an affair, then there have been lies, and my partner does not lie about important things. So there is no affair, and there has been no affair: “she’s faithful and I trust her.”

The temptation is to slip back to the affirmative case – to try to find the reason why there is NO possibility that something has Gone On, some betrayal.

But the premises suggesting that there MAY HAVE been an affair are insidious: they cannot be properly refuted.  There only has to be a glint of possibility that faithfulness is a lie in order that the case remain open.

Rules of Argument 87:

If the central Proposition of an Argument is an Absolute Statement in the Negative, then it need only be shown that a Possible Truth holds in order to refute the proposition.

 

Having Affairs at Possible Worlds

Another way of thinking about this sort of possibility is to think is ‘is a world where an affair took place possible?’  (Or is there a possible world at which an affair HAS happened).

In order to ascertain whether there is a possible world at which the unthinkable (hyperbole) has occured,  there are two methods:

The first is to look at the list of premises that support the argument that no affair has taken place.  Are any of these absolute truths?  An absolute truth is one that must hold at EVERY world.

Rules of Argument 983:

If any premise supporting an argument is Absolutely True then the conclusion can be said to be true as well.

The second method for considering whether or not an affair may have transpired between one’s partner and some third party is to consider whether the possibility of an affair contradicts any of the Absolute Truths about worlds: any of the things that MUST be true at ALL worlds.  This is a more roundabout approach.

To discover what is absolutely true, or true at all worlds, think about what a world MUST have in order to exist. What things are necessary?

Once it is known what must exist at all worlds the absolutely true premises can be examined.  Do any of these contradict the supporting premises for either side of the argument?  Is there any reason why the possibility of this imagined affair contradicts a necessary truth of the universe?  If so it cannot have taken place.  Is any necessary truth of reality brought into contradiction when the dichotomous opposite is considered – ‘my partner has not had an affair’? If so, it is impossible that no affair has taken place.

The likely conclusion from such speculation  is that one cannot prove one’s partner has not had an affair.  It remains inexorably possible.  A world exists at which an affair is taking or has taken place.  After two digressions.

Identity

A sort of cheap trick around acknowledging that the contingency of my partner having had a romantic liaison with another soul, a better lover, a more handsome man, is to say that my love can’t have done that to me, and if she has then she cannot be my love.

This argument has the advantage of being logically consistent, whether it is determined to be true or not.  Whether it is true or not seems to be dependent as much on arguments about naming and defining things as anything actually in the world.

About Truth Being in Language, Not in the World, Exactly

If a digression while mid-digression is permitted,  the problem of identity brings us near to the idea that Truth, in any case, isn’t in the world exactly. It’s in language about the world.  In the world, things exist or do not.  Things hold.  Things are. Truth is in language, and in the relationship between what can be said and what there is: it’s about statements, propositions, conclusions, arguments, premises.

A statement is true if the situation it describes holds.  For example the statement ‘The sky is blue’ is true if and when the sky is blue.  The sky being blue is not true or false, it just IS. It’s always a statement about the sky’s blueness that is true or false.

(Sky and blueness may themselves just be  constructions..)

To return to my digression proper,

familiar problem in possible worlds’ theory of identity.  We might say that infinite other versions of ourselves exist at an infinite number of possible worlds.  Or we might say that infinite other people a bit like us exist at other worlds.  By what virtue do we say that another version of us is us?  Because another person has the same name?  No, because many people might have the same name.  Name and passport number?  Better, but it’s a very arbitrary measure of individuality and identity.  And given infinite worlds there’s a world at which every other possible David Spencer has my passport number.

As it turns out there is really no simple way to resolve this conflict:  it remains to hint at the collision of problems of logic and semantics at a certain point and in a certain way that is near impossible to untangle.  We might decide on a concrete set of criteria that distinguish  particular identities even across vast numbers of worlds:  Possible David Spencers, for example, are those that have the right name, look roughly like me, live in the same house as me, have the same dog.

But for this sort of argument or list of criteria there is always a problematic case, demonstrating that an arbitrary line has been drawn about who is and who isn’t a David Spencer.  Is there a version of me that does not have a dog?  Well, not by the criteria listed above, because not having a dog means by definition it’s not a version of me.  Because it was added arbitrarily to the definition.

This reasoning can be rather absurdly extended to the present case

Premise A:  My partner would never have an affair.

Premise B:  A woman who greatly resembles my partner in all but Premise A has had an affair.

Conclusion:  A woman who is not my partner has had an affair.

The above  reasoning  can be applied even after the fact of an affair has been confirmed and endorsed by all parties involved.  In this case a trick of identity and semantics is employed to lessen the blow.  The partner that had loved, had been in love – had been true to the relationship and to yourself – she has disappeared.  In her stead there is a human being similar in many respects.  But she has a different history, and her love is not of the same quality, so it cannot really be her.

(part II imminent, in which a Platonic justification of the affirmative is considered, after a bit more on evidence)