Dear George,
thank you so much for your reply and the link you gave. Fortunately the video interview is available as a transcript and i eagerly read it - because my flash video does not work for this site. I am happy that we have you here on FQXi, since you take the deep questions seriously, you aren't philosophically naïve but a deep thinker.
Let me contribute some thoughts that came into my mind during reading the transcript.
First of all, i am happy that you take logics seriously, last but not least by simply arguing logically when it comes to questions which are at the borders of physics and metaphysics (or beyond).
Let's assume for the arguments i will make, that logics is our main explanation system for tackling the deep questions. Since we know from Gödel, Russell and Whitehead, although a given explanation system may claim to explain all sorts of things in the world, one thing remains unexplainable, namely the explanation system itself. One has to take it as an axiom.
Thinking logically about logics being a necessary axiom not only for science, but also for philosophy, and furthermore realizing that logical connections are also implemented in the structure of the brain, we can with some significance say that the axiom of logics being a more fundamental thing than lower level physics and matter does make overall sense. Only by assuming that logics and all the rest merely 'originated' - without some logical cause (and therefore with no cause) - from something else in an unpredictable and causless manner can one deny the power and universal applicability of logics.
For the sake of my arguments i do not presuppose here the necessary existence of a platonic realm, but leave this question open. How can one then explain the ontological status of logics itself? Firstly, one can explain it by itself, simply saying that it is logical that logics has to exist. This may be true at first glance, but we easily can imagine some situation / world where things happen without any logical connections whatsoever, regardless of how much time we spend as (hypothetical) observers to figure out some meaningful correlations between the single events.
According to you, one can't think a thought unless it is one of the thoughts which can be thought because it's a logical possible thought. I conclude from this that my imagination of some scenario without logics is a logical possible thought. But according to our main axiom, namely that logics is universally applicable and universally powerful (at least in its own domain), we must conclude that not all logically possible thoughts reflect the deep consistency and *meaning* of the full system of logics (the abstract space of all logical connections). Otherwise we end up with logics being not necessary, but simply an arbitrary accident, not able to tell us something metaphysically about reality (if at all something physically relevant from the point of ontological considerations).
With the search of science and philosophy for preferably complete insight into fundamental reality, we search for logics as well as for freedom of contradiction. By pondering about the fundamental unity of fundamental reality, we must do this in a rational manner. But no rational thought can contain itself to complete the full cirlce of the full domain of logics itself. An example was given by my imagination above. This imagination cannot contain the full domain of logics, since otherwise this domain would be deeply contradictory / arbitrary and therefore useless as a fundamental starting assumption / a fundamental axiom.
Although the mentioned thought / imagination of mine is an element within all possible logical thoughts, it does not contain nor catch up with the whole set of possible logical thoughts. It is not identical with this whole set.
The question arises what this whole set means for the ontology of every existence. Surely, it is defined as only containing possible thoughts. Nothing can ever be said about the realm beyond this set by logics and human thinking (unless we allow also impossible thoughts to happen - what then contradicts logics and can be abandoned).
So the next possible thought that came into my mind is how one can connect the - unimaginably huge - space of logically possible thoughts to a unity. Since no rational thought can contain all possible logical thoughts at once (in a contradiction-free manner), maybe only irrational thoughts can? The question to find such an irrational thought - one that is logically possible to think - seems to me to be an exciting exercise.
According to set theory and its early problems, whenever one does not strictly separate elements and the respective set to make statements which should encompass a perferably wide range of validity, we run into trouble (think of the set of all sets that are not elements of themselves). Why not use this insight to create the set of all self-referential statements (the latter is not plagued by Russell's antinomy)? Could it be at the end of the day, that the whole domain of logics, including all possible thoughts, expresses one deep thought, namely that logics originated from one deep thought - the latter expressing an ingenious purposeful idea rather than merely a technical set of possibilities? Surely, the whole space of logically possible thoughts does not only contain self-referential statements (thoughts), but also non-self-referential statements, and last but not least, also tautologies. But to deal with the rather self-referential problems concerning our search for fundamental reality, i think the most rational (or irrational, this lies in the eye of the beholder) thought is to take logics as a thing that can make some general and reliable statement about itself in a self-referential manner: It is subject to Gödel's incompleteness results and therefore there has to be another level of existence which created logics for a certain goal (otherwise logics would be abitrarily consistent without no deeper reason). And otherwise we end up with the dictum that we only know that we know nothing and even the latter is not known for sure. Let's put it this way: only because the main structure of reality is deeply logical, there can exist beings with aims and intentions to figure this out. So far i think you would agree. The additional step i take is to say that only because logics came about by the impetus of some intelligent intention (plan), (human) beings can have intelligent aims and intentions (plans). Surely, the plans of human beings do not equal the plan of the intelligent intention which brought logics into being, but i think, due to considerations about meaning in our universe and the accompanied meaning of moral / immoral behaviour, the intelligent plan encompasses the possibility that human plans and the bigger plan can converge. They must not converge, at no point in time and space, but i think the possibility is always given, some way or another.
By qualifying the whole set of logically possible thoughts, it seems that we have the choice to label this conglomerate as either a self-referential set (where many identical possible thoughts are existent, containing other identical possible thoughts, next to other possible thoughts, also self-referentially containing themselves) or as a conglomerate of mere tautologies. I suspect that on a logical basis, one has the freedom to choose, and the latter reveals that some freedom of choice is built into logics, as stringent its deductions may be. The freedom lies within the axioms, as long as one's thinking does not converge with the intelligent intentions behind logics. When this happens, one may experience that the nature of tautologies and of self-reference isn't that opposite, but mainly a question of proper perspective onto the whole. What philosophy then does is to permanently work on the space of possible thoughts to find the one thought that transcends the whole space. If done, one realizes that this space must be just a tiny fraction of some more fundamental reality, since otherwise one couldn't have transcended it with only one thought.
Best wishes,
Stefan Weckbach
