Academic journal article Journal of Evolutionary Psychology

The Form of Ordinary Statement Logic

Academic journal article Journal of Evolutionary Psychology

The Form of Ordinary Statement Logic

Article excerpt

I. The Glass Bead Game (1)

Once upon a time in Athens, a rather bored woman named Andreia sat thinking of ways to amuse herself. Whereas she had read Sextus Empiricus lost interest in argumentation after the first reading, her friend Bous remained fond of philosophical debate and often frequented the company of philosophers. On this particular day, Bous had gone off to the Academy to hear a lecture, leaving Andreia with nothing but a few pieces of string and ajar of orange and indigo beads. Through sheer boredom, she was inspired to begin threading the beads onto the pieces of string. To her displeasure, she promptly found that the pieces of string were so short that she could not string more than two at a time. Sighing, she saw that her only escape from boredom lay in whatever variety was to be derived from the materials at hand, and so she began investigating how many different ways she could string the orange and indigo beads onto the (boringly short) pieces of string. She laid the beads and string on the sand before her, where they looked something like this:

O-O
O-I
I-O
I-I

She saw that no further strings were possible without repeating one of the four patterns she had already made. Clearly, if the beads were of two colours, and if she could place two beads on each piece of string, then there were 2x2=[2.sup.2]=4 ways of arranging the beads, given that their order on the string was significant (i.e. given that she considered O-I to be different from I-O).

At this point, she also realized to her annoyance that she had run out of string, making some other form of diversion necessary.

Since the only remaining prospect for amusement seemed to be offered by the beads, and recalling the maxim that variety is the spice of fife, she began considering other ways of evolving interesting patterns from the materials at hand. Finally, she decided to begin laying down beads next to the pieces of string; like so:

O-O    O
O-I    I
I-O    I
I-I    O

She decided to think of this as a way of "associating a column of heads with the strings", because thinking of it in this way posed an interesting problem: given that she had enough beads of each colour, how many different ways could she find of associating columns of four heads with the four strings? A bit of experimentation resulted in something like the following arrangement of beads and strings in the sand:

O-O    O I O I    O I O I    O I O I    O I O I
O-I    O O I I    O O I I    O O I I    O O I I
I-O    O O O O    I I I I    O O O O    I I I I
I-I    O O O O    O O O O    I I I I    I I I I
       E G B J    K L M N    P Q R S    U V W X

She also wrote Greek letters beneath each column of beads, which I have here transliterated into Roman letters, omitting the letters I and O, which I use to designate indigo and orange beads. Reflecting on the matter, she saw that if she had beads of two colours, which she was to arrange into columns of four beads, then the total number of possible combinations was 2x2x2x2=[2.sup.4]=16. "Strange," she mused to herself, "given beads of two colours, the entire game was already played out the moment I chose to put two beads on each string." Out of curiosity, she decided to play out a game in which she had only put one head on each string. Of course, she had no string left, so she settled for simply placing lone beads in the sand:

O    O I O I
I    O O I I
     A B C D

Contemplating this arrangement of heads, she saw that given "string" long enough for only one bead, and given beads of two colours, there were only two possible arrangements of beads on the "string". This meant that the columns of beads she associated with the strings would be only two beads long (because in the game she had thought out the columns could only be as long as the number of possible ways of arranging the beads on the string). Accordingly, there would be 2x2=[2. …

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