# KEHOME/doc/axprop.txt
# Jul/14/2002

#========================#
# axiomatic propositions #
#                        #
# Richard H. McCullough  #
#========================#

# Reference:
# Ayn Rand, "Introduction to Objectivist Epistemology",
# Expanded Second Edition, Meridian, 1990.


# Rand describes three axiomatic concepts:
# existence, identity, consciousness.
# Her discussion can be neatly summarized
# using KR:

	existent is existent
	entity, characteristic isa existent
	entity has characteristic

	man isa entity
	man has consciousness
	man do sense od existent done

# Adding in the implied propositions (with some
# refinement of characteristic)

	attribute, action, relation isa characteristic
	consciousness isa attribute
	sense isa action
	"is", "isa" isa relation
	"has", "do od done" isa relation

# we get the total set of axiomatic propositions.
# This total context, or "view", can be conveniently
# displayed as an entity-characteristic-proposition
# hierarchy:

    existent
        entity
            man
        characteristic
            attribute
                consciousness
            action
                sense
            relation
		"is"
                "has"
		"do od done"
		"isa"
        proposition
            { entity has characteristic }
            { man has consciousness }
            { man do sense od existent done }


# Note that the hierarchy

	existent
	    entity
	    characteristic

# is equivalent to the three propositions

	{ existent is existent }
	{ entity isa existent }
	{ characteristic isa existent }

#============================================================#

# Seeing where Rand's axiomatic concepts of existence, identity
# and consciousness fit into the picture is more difficult.
# For simplicity, I will consider only existence and identity.
# From my current perspective, I consider these two concepts
# to be collective concepts (see section 18 of KEtutorial.txt)
# which subsume the same units (lowest level existents) using
# different views (hierarchies) of those units.

# So far, we have discussed only floating abstractions;
# now it's time to get down to units.  Here is my example
# hierarchy.

	existent
	    entity
		cat
		    BooBoo
		    Samantha
		dog
		    Dutchess
		    Reno
	    characteristic
		attribute
		    color
			gray
			brown
			black
			white
		action
		    bark
			bark_1
			bark_2
		    meow
			meow_1
			meow_2
		relation
	    proposition
		BooBoo has color=gray
		Samantha has color=brown
		Dutchess has color=black
		Reno has color=white
		BooBoo do meow=meow_1 done
		Samantha do meow=meow_2 done
		Dutchess do bark=bark_1 done
		Reno do bark=bark_2 done

# In this example the units are:

	BooBoo
	Samantha
	Dutchess
	Reno
	gray
	brown
	black
	white
	meow_1
	meow_2
	bark_1
	bark_2
	BooBoo has gray
	Samantha has brown
	Dutchess has black
	Reno has white
	BooBoo do meow_1 done
	Samantha do meow_2 done
	Dutchess do bark_1 done
	Reno do bark_2 done

# My intuition tells me that the focus of Rand's
# existence and identity is

	existence isall entity, characteristic
	identity isall proposition

# or, in terms of units,

	existence isall
		BooBoo, Samantha, Dutchess, Reno,
		gray, brown, black, white,
		meow_1, meow_2, bark_1, bark_2
	identity isall 
		BooBoo has gray
		Samantha has brown
		Dutchess has black
		Reno has white
		BooBoo do meow_1 done
		Samantha do meow_2 done
		Dutchess do bark_1 done
		Reno do bark_2 done
		
# But Rand says that

	existence is identity

# meaning that they subsume the same units.
# My best interpretation of Rand's point of view
# is that "existence" and "identity", as described
# in the hierarchy above, cannot be separated.
# But they can be merged together, with a focus
# more on the entity view, or
# more on the proposition view.

# Here is my best attempt at doing that.

	existence isall existent
	    BooBoo
		BooBoo has gray
		BooBoo do meow_1 done
	    Samantha
		Samantha has brown
		Samantha do meow_2 done
	    Dutchess
		Dutchess has black
		Dutchess do bark_1 done
	    Reno
		Reno has white
		Reno do bark_2 done


	identity isall proposition
	    "isa"
		BooBoo isa existent
		Samantha isa existent
		Dutchess isa existent
		Reno isa existent
	    "has"
		BooBoo has gray
		Samantha has brown
		Dutchess has black
		Reno has white
	    "do done"
		BooBoo do meow_1 done
		Samantha do meow_2 done
		Dutchess do bark_1 done
		Reno do bark_2 done
