Changes

Now there are many ways to dance around this idea, and I feel like I have tried them all, before one gets down to acting on it, and there many issues of interpretation and justification that we will have to clear up after the fact, that is, before we can be sure that it all really makes any sense, but I think this time I'll just jump in, and show you the form in which this idea first came to me.

Now there are many ways to dance around this idea, and I feel like I have tried them all, before one gets down to acting on it, and there many issues of interpretation and justification that we will have to clear up after the fact, that is, before we can be sure that it all really makes any sense, but I think this time I'll just jump in, and show you the form in which this idea first came to me.

Start with a proposition of the form ''x'' & ''y'', which I graph as two labels attached to a root node, so:

Start with a proposition of the form "<math>x\ \operatorname{and}\ y</math>".  This is graphed as two labels attached to a root node:

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Written as a string, this is just the concatenation ''x y''.

Written as a string, this is just the concatenation "<math>x\ y\!</math>".

The proposition ''xy'' may be taken as a boolean function ''f''(''x'',&nbsp;''y'') having the abstract type ''f''&nbsp;:&nbsp;'''B'''&nbsp;&times;&nbsp;'''B'''&nbsp;&rarr;&nbsp;'''B''', where '''B''' = {0,&nbsp;1} is read in such a way that 0 means ''false'' and 1 means ''true''.

The proposition ''xy'' may be taken as a boolean function ''f''(''x'',&nbsp;''y'') having the abstract type ''f''&nbsp;:&nbsp;'''B'''&nbsp;&times;&nbsp;'''B'''&nbsp;&rarr;&nbsp;'''B''', where '''B''' = {0,&nbsp;1} is read in such a way that 0 means ''false'' and 1 means ''true''.