See first Perspective and Perspectivism, for a clarification of terminology, and the Logic of Propositional Attitudes and Basic Logic for a clarification of the terminology to be used in the rest of this lemma, which sketches in some logical foundations for a treatment of personal perspectives.

Psycho-logic of Personal Perspectives.

The title constitutes an interesting but ill-researched subject. This lemma only sketches a few foundational thoughts (that are taken up elsewhere in this dictionary also).

A. Your body and mind and my body and mind

With O for Outside (Body) and I for Inside (Mind) and with S for Senses (proprioception) we may write, using "E" for "experiences" and let "Zab" mean "a and b experience each other and are not the same" (i.e. Zab IFF aEb & bEa & a≠b):

(a)(b)(Zab --> aEOb&Ia&~Oa&~Ib&Sa&~Sb  & bEOa&Ib&~Ia&~Ob&Sb&~Sa) c.q.
(a)(b)(Zab --> aEBb&Ma&~Ba&~Mb&Sa&~Sb & bEBa&Mb&~Ma&~Bb&Sb&~Sa)

Note the interesting facts for a (and b by parity) by rearranging terms:

aE   Bb&~Mb&~Sb & ~Ba&Ma&Sa

We all normally feel our bodies and experience our minds but do not see our bodies, while we do not feel others bodies nor experience their minds but may see their bodies.

This also means that it is likely that the readings of the bodies of other humans, so to speak, is basically instinctual, though much is added and needs to be learned, for a society of human role-players and dressers, who may easily deceive or mislead one, even unintentionally.

Anyway - these facts are important for human consciousness and interaction and cooperation.

And it is true that

• (1) there are exceptions e.g. with mirrors or cameras and screens and

• (2) there are people specially trained to manufacture experiences by pretending (stage-players, conjurors, con-men, clergy, TV-presenters, priests, politicians) and

• (3) all sane persons in complicated societies, with roles, ranks, riches, statuses and powers, know how to pretend lots of things, and learned so mostly through playing roles and by example, mostly of family or friends or what are called "idols" (pop stars, sports stars, film stars, society people - that ilk).

Even so, it would seem that most bodily expression is learned intuitively, for one normally does not see oneself do it, from another's point of view.

Incidentally - this is a good sort of reason for nakedness: To improve communication. And it is interesting that the Athenians decided on nakedness as the norm, at least in sport, and anyway as normal.

Note also there is an interesting point about adding "aK" for "a knows that":

aK aE Bb&~Mb&~Sb & ~Ba&Ma&Sa

One may ask about non-human social animals. Do they know such a thing? If so, do they know that they know? Very probably, if they do - and some of them must do to some extent, in order to cooperate - not with the distinctness and preciseness with which human language enables putting it.

B. Perspectives on perspectives

Now note that for humans the levels are quite complicated, in a way. This can be written as follows, first for convenience abbreviating a long conjunction:

Q = aE Bb&~Mb&~Sb & ~Ba&Ma&Sa & bE Ba&Mb&~Ma&~Bb&Sb&~Sa

This was used above, and it is here taken as example, though it should be obvious that Q may be any proposition whatsoever - and I write it out so as to make it clear rather than concise:

aK aK                    aE Q &
aK aK bK bK           aE Q &
aK aK bK bK aK aK   aE Q 

bK bK                   aE Q &
bK bK aK aK           aE Q &
bK bK aK aK bK bK   aE Q 

The point of the double Ks, so to speak, is to insist that the knowledge involved at the stated level is fully conscious: one knows and knows that one knows. (Actually, for the Q used, it would seem most humans are usually not fully conscious of it, even though they know and use its various logical implications, such as that the one cannot experience the other's mind, nor another one's own.)

Note that all of this is knowledge implies that both a and b are right about the long conjunction (always the same) that attributes experiencing or not the notions of bodies, minds and senses of oneself and others, or of a and b.

Next, there is the much weaker parallel and implication for "believes, written as "B", that is much more common, and comes with many more problems, since much more is uncertain and may be mistaken - and I do not write double B's to simplify matters (and merely mention in passing the case of aBq & ~aBaBq, where a believes q, but is not - now or ever - conscious of it):

aB           Q &
aB bB       Q &
aB bB aB   Q &

bB           Q &
bB aB       Q &
bB aB bB   Q        (*)

Both of these six-fold schemes, for B and for K, are very fundamental schemes, for human interaction, for human cooperation, for human competition, for human (dis)agreement, and for human (mutual) (mis)understanding.

Note that this does not merely apply to the long conjunction Q, but to any proposition q whatsoever that a and b may (dis)believe, and come to have beliefs about what the other believes about the subject.

And it is noteworthy the full K series seem necessary for very many human interactions, if they are to succeed: One must know that the other knows that one knows. It is interesting there seem to be quite a few implications, for the case of full knowledge, as listed by the schema of the six conjuncts.

The reason that knowledge (and trust) are involved, and not mere belief, is that many human cooperative enterprises just can't work without the one knowing that the other knows that the one knows something relevant, and the other way around.

The case of full belief (as rendered above, in the six-fold way) is far more complicated, because far more may be mistaken. If probabilities are added this becomes more complicated still, though it helps to simply consider first probalities lower, equal and higher than 1/2, at least for broad outlines. But in this lemma I will not enter into personal probabilities (other than 1 or 0).

So let's first consider simple propositions with belief as in the full belief schema, but this time with differences, as in

aB            q    &
aB bB      ~q   &
aB bB aB   q    &

bB             q   &
bB aB       ~q  &
bB aB bB     q

Here both a and b believe the same about q but are otherwise completely mistaken about each other. (A situation that often arises in marital quarrels, it seems. See Laing et al.)

If they don't trust each other, this can last a long time, it seems, for each will then consider that the other may lie about what he or she believes. Here enter many modes of deception, also, including being deceived about one's deceptions.

And this is yet another interesting complication: beliefs about whether another lies or not, and about whether the other believes one's own lies.

But let that also be for the moment, and consider some other basic general six-fold schemata. Here is a first one:

aB            q     &
aB bB      ~q    &
aB bB aB  ~q    &

bB           ~q  &
bB aB       ~q  &
bB aB bB     q

Here a is quite right and b quite wrong about the other and they also disagree about q (about which, to add a little drama, a may be mistaken).

Next there is:

aB            q     &
aB bB        q     &
aB bB aB  ~q    &

bB            q     &
bB aB        q     &
bB aB bB  ~q

Here both agree and both are right about the other's own belief while both are wrong about the other's belief about them.

This is a case that ought to be easy to straighten out to mutual comprehension and mutual agreement, which is simply this (though neither a nor b may know that any of their beliefs about the other is true):

aB           q  &
aB bB       q  &
aB bB aB   q  &

bB           q  &
bB aB       q  &
bB aB bB   q

Note also that even though the above may hold, each may hold his various beliefs about the other and about q with varying degrees of conviction, also for the various levels - but that is a complication to be left out for the moment.

Incidentally, an interesting case is when both have mutual comprehension and agreement and are mistaken about q. (This may also last a long time if both do not inquire into the evidence for q, e.g. on the ground that both agree about it anyway, and shared prejudice feels nice.)

Apart from that it is also interesting that a case of mutual comprehension and agreement may be based on much or little (argument, consideration) and may be difficult for either party to provide evidence for where the other is concerned. (A modern complication is web-forums with aliases with strong opposed beliefs.)

It's also interesting to consider the cases of evidence more systematically:

• both have seen the same, or not
• both have the same sources or authorities, or not
• both have the same or similar relevant information, or not
• both are of comparable intelligence (age, background, educaton, faith, country etc.), or not

and also

• what each knows about the sources of information of the other

The perspectives

aB            q    &
aB bB      ~q   &
aB bB aB   q    &

bB             q   &
bB aB       ~q  &
bB aB bB     q

show there is something to clarify and define

agreement(a,b,q)       =df aBq & bBq
understanding(a,b,q)  =df agreement(a,b,q) &
                                   aBagreement(a,b,q) & bBagreement(a,b,q)
comprehension(a,b,q) =df understanding(a,b,q) &
                                  aBunderstanding(a,b,q) & aBunderstanding(a,b,q)

These also show what components may make for disagreement, misunderstanding and miscomprehension (in the senses defined).

Next, there is the difference between L = |q: aBbBq and M = |bBq: aBbBq. Clearly, since bBq is a propostion M inc L. And (Es)(s e |q: aBbBq. & ~(s e |bBq: aBbBq)) viz. the s of which a believes that b believes them but not consciously, i.e. on the pattern of aBbBs & ~aBbBbBs. Hence M inc L but ~(L inc M).

And the |q: aBbB....q seems mostly fit and the tool to describe agreement and disagreements about smple non-attitudinal facts at the basis of perspectives. Thus it  may be the case that the q that a and b misunderstand, disagree and miscomprehend are all or most of a certain kind or kinds (e.g. religious, cultural or sexual) - or not.

In any case, there remains a lot to do in this field, both logically and psychologically, and the present lemma merely sketched in a few basics.

Note:

(*) To write this out, for clarity's sake, without linefeeds and white space, and with "q" for "Q": aBq & aBbBq & aBbBaBq & bBq & bBaBq & bBaBbBq.    

Incidentally, about the virtues of logical notation and the presumed fact that every human being engages, consciously or partially so, all day in this manner and these levels of reasoning: "a believes q and a believes that b believes q and a believes that b believes that a believes q and b believes q and b believes that a believes q and b believes that a believes that b believes q" seems rather a bit less tractable than the notation just offered.