What is a 'slithy tove'?
By Richard Weyhrauch

This note is called: [SLITHY-TOVE]
The notations used in this note is described in [NOTATION]
Under development

                           JABBERWOCKY

            'Twas brillig, and the slithy toves
              Did gyre and gimble in the wabe;
            All mimsy were the borogoves,
              And the mome raths outgrabe.

            'Beware the Jabberwock, my son!
              The jaws that bite, the claws that catch!
            Beware the Jubjub bird, and shun
              The frumious Bandersnatch!'

            He took his vorpal sword in hand:
              Long time the manxome foe he sought--
            So rested he by the Tumtum tree,
              And stood awhile in thought.

            And as in uffish thought he stood,
              The Jabberwock, with eyes of flame,
            Came whiffling through the tulgey wood,
              And burbled as it came!

            One, two!  One, two!  And through and through
              The vorpal blade went snicker-snack!
            He left it dead, and with its head
              He went galumphing back.

            'And hast thou slain the Jabberwock?
              Come to my arms, my beamish boy!
            O frabjous day!  Callooh!  Callay!'
              He chortled in his joy.

            'Twas brillig, and the slithy toves
              Did gyre and gimble in the wabe;
            All mimsy were the borogoves,
              And the mome raths outgrabe.

This note is about mental images and denoting. It addresses the question of what is the extent of 'imagining' and claims the the Russel 'solution' to thinking about definite descriptions as not refering is a technical solution that is not useful if trying to understand what is in a head when we hear about things that we either have not heard of before or that 'do not exist'. We propose scraping Russell's plan in favor of a substantially more promiscus ontology allowing us to imaging all manner of 'things'

We start by observing that our mental images of 'imaginary' things cannot be structurally different from out mental images of 'real' things, for if this were true our archectecture would have to be able to distinguish between the 'real' and the 'imaginary' and this leaves no room for error or invention.

The conversion of incomesurable (irrational) numbers into actual numbers or the realization that accepting 'imaginary' numbers into the canon are clear examples of imaginary 'things' becoming 'real' (assuming you imagine that numbers are in fact 'real' things to begin with).

THIS BRINGS US TO 'SLITHY TOVES'. What are they? And how does a 'slithy' tove differ from any other tove? The mere fact that these questions seem to make sense means that our minds contain something that might reasonably be called our mental image of a tove. The using the word 'imaginary' about a thing, already suggests that we have some sort of 'image' of it.

This also occurs when we hear 'round square' and 'the current king of France'. It is a prerequisite for a discussion of their existance that we have some mental image that 'anchors' our discussion.

If we think about this in symbolic terms the question might be: what might be our mental image of something that satisfies the conjunction

  (AND (ROUND? x) (SQUARE? x))

Reasonable models of this formula might conclude that there are no x's that can satisfy

 (AND
   (IMPLIES (ROUND? x) (NOT (SQUARE? x)))
   (IMPLIES (SQUARE? x) (NOT (ROUND? x)))
 )

but this begs the issue of what's in our head when we hear 'round square'.

I propose we handle this thus:

When we hear 'round square' we form a mental image of type [round-square] which has two properties. ROUND? and SQUARE?. In IBML we might write this

 (*EXA* (|shape| . (*finite-set* |aset|
   (DB . |current-context|)
   (TI . |round-square|)
   (|properties|
    (|  | . |round|)
    (|  | . |square|)
   )

)))