[FOM] Restricted Quantification

Michael Lee Finney michael.finney at metachaos.net
Tue Jan 19 14:50:47 EST 2010

I have made a draft copy of a paper available that analyzes restricted
quantification and derives a set of axioms that implements it. The
paper shows that classical logic does not fully implement restricted
logic and cannot without triviality. The paper assumes the existence
of a logic containing restricted quantification and then deduces the
characteristics of a connective that can be used to implement it. The
paper spends a good bit of space showing what does not work which is
of some interest in its own right.

Then a set of axioms are chosen from amoung the assumptions and theses
that have been determined to be admissible. All of the expected
features of restricted quantification are then derived. One notable
aspect is that reasoning in empty domains is fully acceptable, but the
logic is not a free logic. Implementing restricted quantification
using the axioms in the paper can be done with any logic slightly
weaker than B, so it is suitable for all relevant logics.

I welcome comments and corrections.

The paper is available at two URLs


The first URL is for browsers capable of handling dynamically loaded,
embedded fonts. The following browers are supported.

   Internet Explorer 6.0 and later
   Firefox 3.5 and later
   Opera 10 and later
   Safari 3.2 and later

The second URL should work with any browser.

For the first URL only Internet Explorer and Opera can print the paper
correctly. I have found that some installations of IE 6 have occassional
display glitches.

For the second URL, that version of the paper is larger, will not
scale as well and is slower to load on some browsers. Firefox 2.0 is
notable in that it takes several minutes to finish displaying the
paper, most of the other browsers load only slightly slower than the
main version of the paper.

Michael Lee Finney
michael.finney at metachaos.net

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