Implication and conditionality

The traditional problem of platonism is this - how can eternal extra-worldly objects affect this temporal world and vice versa.

As analysis moves up the chain the question becomes about the phenomenon of logic - reason - and the absolute notion of reason, logic.

In my terms, "reason" will refer to the actual good reasoning of human beings. "Logic" will refer only to the abstract notion of the possibilities of valid and sound inferences.

In this world, there are reasoning-events where people deduce or induce. Those reasoning-events are members of the causal or pseudo-causal chain of events of this world. They have relations to things with causal efficacy, including causal and pseudo-causal (quantum?) relations with them. I don't know the full nature of those causal and pseudo-causal chains, only that they are there.

This is true -no matter what- we say about whether or not our minds or souls or brains are part of or not part of this world - the world around us in a sense dictates to a large extent what we think about - that is, what we concern ourselves with - in the ordinary course of reason. Even "extraordinary reasoning events" - like thinking about metalogic - have their roots in physical conditions - who I am, where I am born, what my parents thought was important, what my teachers thought was important, etc., all combine to make this questioning about the notion of reason a reality for me. This is not to commit to causal determinism with respect to reason, but rather simply to note that the subject matter of our reason is to an extent subordinate to the availability of datum about which to reason. While we may be able to reason ex nihilo, in general we don't in fact. And what we're interested here preliminarily is "in fact" not the "abstract possibility" that were we disembodied eternal minds how we might then reason.

Similarly, the conclusions that we draw from a given set of circumstances appear to be to a large extent socially-determined. A child of the middle ages when seeing a sick person might make guesses as to the various humours involved in the sickness. In the early 21st century, we assume the existence of some virus or bacteria or poison is the cause of the disease. In the late 21st century, we may have determined the quantum basis of life and may attribute diseases to some field-conditions - I DON'T KNOW what we'll find out or decide obviously. Even the idea of thinking about our faculties of reason sociologically is a phenomenon of our century (Kuhn, feyerabend, etc.).

So we may call our reasoning-events "causally determined" - even the platonist won't deny the presence of a given person on earth is causally determined by their parents' mating - and without our presence, our conclusion-reaching isn't even remotely possible. Again, "causally determined" is not to be read in the sense of determinism as traditionally conceived.

Now, given that our reasoning-events are causally determined, there is a question as to their relationship to the abstraction notions of inference and validity which we (some of us anyway) have. And the question arises, what is the relationship between a given inference and it's generalized rule which makes it a "good reasoning"?

For instance, back to the math questions. We say "2 + 3 = 5" and so the correct answer to "if you have 2 cats and someone gives you three more how many cats do you have?" is 5. But here there are obviously counter-possibilities. Maybe the cats ran away during the transaction? Maybe when you add cats, they don't act like integers, but instead quintegers and are magically transported to another world. Maybe being the key word here. How will we determine from pure mathematics how many cats are in your possession? How can mathematics, indeed, decide what a cat is or how to count them.

I've said before that the concept of number is prior to set theory. I think it's also prior to mathematics generally. The questions "how to count and what to count" are more akin to what happens when a conductor and symphony interact than when a mathematician attempts an abstraction. The Conductor indicates the piece of music and tempo so that the musicians can stay together - all knowing what to count and how to count based on the movement of the baton and the conductor's gestures. This primal ability to count is in a way essential to what we do in a way evolutionarily. If a person can not repeat what its parents say eventually, it can not learn its language and it is unable to join society and be recognized as fully human. There are obviously such people. The genesis of this ability to repeat is unknown obviously, but some key elements have to be in it I think:

To repeat a phrase, someone must differentiate the phrase from other things and sounds around them, isolate it as a single thing of the kind in question (perhaps without having any thoughts of it being "single"). This happens in general with practice - hearing and testing to see which sounds produce the desired results in their environment - perhaps needed results. An infant is hungry and cries out. Eventually it learns to distinguish the hunger cry from the pain cry and indicate when the matter is settled and so the infant learns to speak eventually by identifying sounds made by their caretakers corresponding to the relevant events.

In this way also the core of "conditionals and implication" are learned. The baby learns that IF they scream such and such, they get food that they need. Then they learn that if they SAY such and such they get the specific kind of food that they need, etc. The -if-ness- is a relation between the word and the event. Eventually we learn that there are relations between words and words - our parents/siblings/teachers teach us the use of other new words not by ostension but by relations to other words. We learn to read a dictionary, etc.

This second kind of implication - semantic implication - is somewhat related to the first. We say "only use bald when someone has no hair on their heads" but we define "hair on the head" by ostension (sometimes). So while "bald" comes to have a specific semantic relation to "hair on the head" upon its first use, it becomes when used this way "linked" in a special way to no-hair-on-head (e.g. the phenomenon underlying "there is no hair on that person's head" when spoken and understood as true). By systematically relating words to each other (say by providing a dictionary or set of definitions) we can create a closed system of definitions - we'll come back to this.

Meanwhile, it remains possible to detach baldness from "no-hair-on-head" and we learn this after a short time. There are a million varieties of baldness - thinning, thinning in just the crown, shaving the head, partial shaving of the head, etc. Not all of them or even any of them need be immediately related to having "no hair on the head" (which it turns out is very seldom associated with baldness if you take it too literally - everybody has hair on their heads). In fact, learning to detach "no-hair-on-head" given by the first ostension is critical to learning what "baldness" really is - so that baldness becomes a phenomenon of its own.

In this way, I think, all such semantic implication dissolves - when we learn to use "2" we also learn to semantically detach it from "1 + 1" or "count and stop at the second one" or whatever. We learn that 2 is special and that its PURELY SEMANTIC relations with other things dissolve the more we understand the phenomenon of two-ness. The argument is simple. If two is "by definition" 1 + 1, then what is the meaning of "I have two legs"? In what way are my legs added together? Are my legs subject to the union axiom? Of course we can try to tell such a story but that story gets wilder and wilder the more detail required of it. When stories about why something is the way it is become too wild, we have a tendency to start thinking of them either as literally false or as metaphorical.

And so we start looking for the base of the metaphor - that is, trying to understand the Phenomenon of Two-ness. By this I mean distinguishing the specific circumstances in which "2" is the appropriate descriptive modifier - and so we return to finding out what we are counting and how we should count it/them. So we have not "two mashed potatoes" even if we have two potatoes that are mashed, for instance - because we've learned that 2-ness is nevertheless a phenomenon of the nature of our speaking without it being therefore a purely semantic phenomenon.

Thus detached from pure semantic relations, I think, the temptation toward platonism is removed. If we understand the nature of semantic relations (e.g. relations between human communicative devices) and look at them for what they are (words, talking, singing, pointing, etc.) rather than what they should be (purely logical entities with absolute meanings) we come to be able to understand how things IN FACT have semantic relationships without therefore being extra-worldly.

These semantic relationships, though, then don't have the implication-force we're used to assigning to them. In the platonist system of thinking, implications are absolute because the predicates are introduced with purely semantic relationships - all bald men have no hair on their head in the platonic world BECAUSE to be bald is to not have hair on your head by definition. Again, though, if we recognize that such introductions by definition only go so far, then we're able to understand what the word "bald" really means phenomenally.

IN FACT, if we insist on the purely semantic meaning of bald, we are simply unable to understand real discourse about the word "balding" or "bald". "The difference between living things and non-living things is that living things are still moving". This saying isn't true (the sun is moving, isn't it?) but the idea behind it is - and it applies to words as well. If our words become "rigorously defined" they become useless because they are unable to cope the with ongoing phenomenon of the world around us.

So finally to the notions of implication and conditionality. There is a certain kind of conditionality which is primordial for our language - the ability to associate words with situations and phenomenon pragmatically to produce behavior in our parents. Without a notional similar to "If I scream, they'll come" the screaming ceases (and this is a tested fact - either the baby dies or learns some other way to get the attention it needs or learns that it doesn't need the attention it thought it did), language is impossible - because there's no associating linguistic phenomena (the screaming) with other phenomena (the help). THIS variety of implication though, is not what we call "semantic implication" - the relations between words and words defined by them, though. That relation - the relations between words and their definitions - has to be regarded as an heuristic tool for learning languages more quickly. A person who has never been exposed to the phenomenon of baldness can nevertheless get a sense of what it would be like by pure word-definitions and will make a variety of assumptions about a person described as bald. HOWEVER, these assumptions will never be completely accurate as they are unable to provide DEDUCTIVE CERTAINTY.

But we do have still implication - phenomenal implication - implications which are presumed by the notion of the possibility of semantic implication. These phenomenal implications we also call "reason" and in some cases "common sense" - and while known to be fallible, are also capable of being thought of as revealing real relations between real things, as opposed to their semantic counterparts.

So we have two notions corresponding to our initial "logic" and "reason". We have a notion of implication - semantic implication - for which a statement must be regarded as true because so defined - and a notion of conditionality - for which a notion must be regarded as true because it is the underlying phenomenon for the possibility of a semantic structure. To give another example - my own existence must be regarded as conditionally related to this email because it is a member of its underlying phenomenon that make it possible.