Form vs. Meaning in Logic

Read my theory: http://www.mm-theory.com


One learns in the study of logic that what determines the adherence to rules (rules like modus ponens, DeMorgan's law, excluded middle, etc.) is form - that is, the form taken by the propositions involved.

All Xs are Ys.
This is an X.
Therefore, this is a Y.

From Aristotle down to present day logicians, the tradition has been to recognize in syllogisms such as the above, as well as other common logical structures, the form of the argument as the one distinguishing feature that justifies drawing the conclusion from the premises. We don't know what Xs and Ys are - they are meaningless terms in this case - and so it can't be meaning that justifies the argument. All we have a right to discern here is its form.

Of course, this disagrees very sharply with one of the basic tenets of MM-Theory - namely, that what justifies drawing the conclusion from the premises is meaning through-and-through - that it is only in virtue of what the premises mean that the conclusion can be drawn. Therefore, I must take it upon myself to rectify this contentious point and defend MM-Theory against this tradition in the field of logic.

The point I would like to make is not so much that form is not a determining factor, not even the determining factor, but that by 'form', one should not understand something contrary to 'meaning' as MM-Theory defines it. This nevertheless does require some defense as the tradition has been to place form in contradistinction to meaning. The point has traditionally been that where only the form of a logical argument is evident, meaning is absent. What I wish to show, however, is that were meaning truly absent, not a single trace of it to be found, not even form would be left.

To start with, compare the following

All Xs are Ys.

with

zupe diva ectongle arba

We could suppose that the latter is a statement expressed in a hypothetical language. Now I ask: which statement strikes us as truly meaningless? I would expect the answer to be: the latter. For at least we get something from the former, some minimal information that tells us more than the latter. What is this minimal information? Is it form? One could say so, but how do we know that the latter - making sense in our hypothetical language keep in mind - doesn't adhere to the same form? Of course, one could say that the latter indeed may adhere to form, but if only we understood the language, we could then demonstrate it. But does not this supposition presuppose that, by 'understand', we mean 'to apprehend the meaning of'? Does it not follow from this that in order to determine the form of a proposition, we must at least determine some meaning therein?

So the question becomes: What about the former statement allows us to apprehend (or impose?) meaning on it such that the latter doesn't? The most obvious answer that comes to mind is that there are units of language present in the former statement that are absent (at least in English) from the latter - namely, units such as 'all' and 'are'. These are English words. They have a meaning. What they tell us is, not so much what things Xs or Ys are, but what kind of words they are - that is, what function they perform in our language. For example, to say "All Xs" seems to indicate that the term X is a noun. This further implies that Xs are 'things' - perhaps abstract things, but things in some sense. It can further be deduced that Ys are also things. In particular, the pluralizing of the term 'Ys' rules out the interpretation that the term is an adjective (for without pluralizing, the statement becomes "All Xs are Y" which shares the form with "All men are mortal"), as well as the interpretation that it is a verb (as that would share the form with "All men are living" - though the latter interpretation could be secured with the suffix 'ing' - as in "All Xs are Ying"). Needless to say, the term 'are' also adds some substance to the meaning of the statement, for the term Y would clearly become a verb should the statement read "All Xs Y" (or grammatically incoherent should Y remain pluralized as in "All Xs Ys").

Thus, form, should it require at least a few clearly defined language units such as 'all', 'are', 'my', 'not', 'if', 'then', 'some', 'at least one', 'This is a' and so on, must also supply us with a rudimentary level of meaning - and in fact must do so in order to serve its very function of form (for without doing so, there is no form to be gleaned as the latter statement above evinces).

Now I say that this rudimentary level of meaning still leaves us wanting for something more substantial for apprehending what Xs and Ys are. We still don't know what kind of things they are. But insofar as the grammatical form of the statement tells us that they are things, this is the beginning of meaning. It has much potential to be developed and refined, but we must acknowledge that we have something meaningful to start with. So long as the right units of language are supplied - the 'all's, the 'are's, the 'like's, etc. - the form of an argument manifests for all who speak the language to see. Without these units, one cannot make heads or tails of its form:

All Xs are Ys.
This is an X.
Therefore, this is a Y.

zupe diva ectongle arba
Tet vi pip diva.
Idavox, tet vi pip arba.

And of course, it goes without saying that the meaning supplied to these terms - Xs and Ys - as rudimentary as they are - also supplies meaning to the overall statement - perhaps also rudimentary, but meaningful nonetheless. Thus, the meaning of the premises overall allows for, and entails, meaning in the conclusion.

It should also be noted that the meaning gleaned from such statements depends not so much on what practiced users of the language know it to mean (in the sense that a statement can have a 'right' meaning), but simply on whether we can glean a meaning (right or wrong). The point here is that insofar as we can glean some meaning, whether or not users of the language correct us, this affects how we recognize the form of the argument overall and whether or not that form is proper. This, after all, is the central argument we want to make: we wish to say that insofar as the mind apprehends some meaning, it is able to make use of that meaning towards entailing further meaning - that is, towards instigating the flow of experience (thought in this case), towards drawing conclusions from the premises in what it takes to be a logical manner. If it is mistaken in this pursuit, it would not be on account of an illusion of meaning (for it creates its own meaning), but on account of disagreement with a majority of others.


Read my theory: http://www.mm-theory.com