Exploring Ontology

It's all about the deep questions.

Second Principle on the Structure of Possible Worlds: A Solution to Hume’s Problem of Induction

1. An Allegorical Tale

Imagine that you have been taken prisoner. The judge of this imaginary prison, however, decides that your fate will be decided by chance in the following manner. Every morning during your stay at this prison a card will be drawn from a hat. Within this hat, 100 cards are placed. Furthermore, you are told that 99 of them have the word “death” written on them while 1 of them has the word “life” written on it. If one of the 99 are drawn on a particular morning, you will be killed that morning. If the “life” card is drawn, you will be spared. Not surprisingly, the very moment that you are told this, you expect to die the following day. Luckily, you don’t. This doesn’t take away your dread, however. The rest of the day is just as nerve-wracking as the previous one. However, the next morning, you are spared again. This cycle of dread and redemption continues on for days, then weeks. Gradually, the feeling of dread begins to wane and subconsciously you begin to expect to live to another day. Moreover, this feeling is justified. As long as you were not 100% confident that the judge was telling the truth with respect to the hats contents, the more days you live the more confident you are licensed to believe that the probability distribution of cards in the hat is not 99% chance of death and 1% life, but something much more skewed in the direction of life (this can be argued mathematically with conditional probabilities and Bayes’ theorem). As the months approach a year, you begin to wonder if there were any “death” cards in the hat at all.  Read more of this post


Against Deep Questions

(FYI: This post should probably considered to come prior to the “what it is to know” post)

Many philosophical questions are considered so deep, that it is often the case that one doesn’t know where to begin. Take the seemingly deep question, what is the nature of X? Don’t we just “point” at what the concept of X means? If one asks what is a bachelor, most people wouldn’t want to take that question too seriously, but if one asks what is morality, one is often taken very seriously. What really is the difference between these two questions? Well, since the only difference in the two sentences is the words “bachelor” and “morality” then the culprit has to lie in those two words. Two vital distinctions need to be made to address this question.

A first distinction can be made between precise and imprecise words. The best example of a precise word is that of a mathematical definition introduced within an axiomatic framework. The standard words used in every day english usually fall far short of this standard. Take the word “chair”. There are some cases where it is clear whether a certain object should be referred to as a chair. In other cases, two different people may disagree on whether a certain object should be called a chair; the cases cease to be so easy. So, should we deem the question “what is the nature of chairness” a deep, philosophical question? After all, its answer doesn’t seem to be straightforward, and for most (if not all) definitions we propose for “chair”, there would be someone who disagreed. Most of us would answer no, asking the nature of what it is to be a chair is not a profound philosophical question. The problem is that the concept “chair” is an imprecise one and hence defective for an in-depth debate of the nature of chairs. When two people utter the word “chair”, they might have two slightly different meanings in mind. We can distinguish the different meanings that chair might have as chair1, chair2, …, chairn, etc. Now, when asking “what is the nature of chairn?” The endless counterexamples of proposed definitions cease to exist. Once we stipulate a precise definition, the answer is in front of our faces. In summary, a precise word is one in which there exists unambiguous necessary and sufficient conditions for its application, an imprecise word is one where there does not exist unambiguous necessary and sufficient conditions. The vast majority of english words are imprecise [Note: Vague concepts are not meant to be necessarily imprecise. One could say red = (exact levels of gradation as to how red something is at particular wavelengths.) This concept of red can be discussed with perfect preciseness.] Read more of this post

The First Principle on the Structure of Possible Worlds: An A Priori “Falsification” of Occam’s Razor

This is the first post in the philosophical project motivated by the “What it is to Know” blog post. (If you haven’t read it, you should probably start with that post.)

Imagine all of the possible metaphysical theories (corresponding to possible worlds) that account for (are consistent with) the observations of a particular phenomenon. Now line them up according to their ontological commitments on a ray. The beginning of the ray will be the theory with the least ontological commitments, with precisely none. In other words, the phenomenon can be explained with recourse to the ontological commitments we already have prior to philosophizing on the phenomenon. Just above the beginning point, the theories with the smallest and simplest ontological commitments will lie. Continuing on, the distance from the beginning point will correspond to the complexity of the theory.

Now, for any specified level of ontological commitment (except for the zero level, in which case there will only be one) there will be multiple metaphysical theories with the same rough level of complexity. To represent this, the ray’s width at a particular distance from the beginning will correspond to the number of metaphysical theories that are observationally adequate at that specific level of complexity. Now, I take a stronger statement of the first crucial step in the argument to be intuitively clear: at more austere levels of simplicity in ontology fewer metaphysical theories are ideally imaginable, and those levels of ontology with increasing complexity have “more to work with” so to say, and therefore have more ideally imaginable metaphysical theories at their disposal. Here, an example might serve to elucidate things. In constructing a theory of the world, it may or may not be true that God sustains every event that happens and he is the “grounding” for causation and physical law and such. However, one can easily increase the complexity of this picture. One can say there are two gods sustaining the world; one is in charge of events of type A and the other of events of type B. And one can do this for as high a number as one wishes. Also, one can give the Gods certain psychological traits, names and so on, so that the number of possible metaphysical theories of the grounding of the universe would increase exponentially as complexity is increased. These theories would all furthermore be consistent with all observations. However, for this argument to work, it is more than sufficient to claim that the higher levels of complexity have at least an equal number of potential theories than the simpler ones. This claim makes up one kernel of the argument. Read more of this post

What it is to Know – The Beginning of a Philosophical Project

So, if my goal is knowledge, I must first ask myself what it is to know. If a proposition had less than a probability of one, would I know that p? What I take to be knowledge is this: take all possible worlds in which the evidence for a proposition holds, if that proposition is true in all of these possible worlds, then, I take it, that evidence allows me to say that I have knowledge of that proposition. Now, what about someone who contests that this does not mesh well our intuitive grasping of the word knowledge? That person must then be committed to the claim that it is perfectly well for someone to say, “For all I know it could be the case that p is false, but I still know that p is true.” I take this to be a reductio ad absurdum. Therefore, knowledge requires absolute certainty.

One question to ask is: does this definition of knowledge perserve closure? So, say that by some reasons R, I am justified in knowing a proposition P. Furthermore, let it be true that P implies Q. Well, if P is true of all the possible worlds I can be in, so it is the case that Q is true of all the possible worlds I can be in. Therefore, knowledge must be closed under implication.

So, lets try to find out things that I know. Well, for starters, I know it is not the case that nothing exists. Since, any sensory evidence whatsoever would rule out the one possible world in which nothing does exist. I, obviously, know all the truths that are true by convention, but those are uninteresting (mathematical truths seem to be of this form). I know all truths of the form, “I am having sensory experience X”, since, by the definition of knowledge, I must take all possible worlds in which I have a sensory experience X and ask whether it is true that I am having sensory experience X. Obviously, the verdict comes down on the side of knowledge. Now, although this is somewhat substantial, it still hasn’t taken us anywhere useful. Going to have knowledge of things “outside” of my experience, however, cannot be done since I can imagine a possible world with nothing outside. (A caveat here: as an axiom prior to wherever my philosophizing takes me, I must assume that whatever is producing my thoughts does so in a rational matter. Not exactly that is perfectly rational in every sense of the word, but that it is capable of rationality. If it is the case that it isn’t, then there is nothing that I can do since my thoughts cannot be produced by anything other than what is creating my thoughts.) Clearly, this definition of knowledge cannot take us very far. This makes me a skeptic with regards to knowledge.

What I must therefore look to is probable beliefs, rather than beliefs that are absolutely true. What would make a belief probable? Ideally, we could apply the same definition: reasons R maks a belief B have probablility X iff the probability of being in a world where B is true, where the set of possible worlds in question is restricted to those in which R holds, is precisely X. The problem with this definition is that I am less than a perfectly imaginative being. I do not have a perfect grasping of the “probability space” of possible worlds. Since all beliefs hinge on this idea, the most worthwhile philosophical project is to flesh out as much as possible the space of possible worlds.