Incommensurability

Incommensurability is the thesis that world-views which scientific practice has posed throughout the ages are fundamentally different, or not comparable. An example often used a comparison between Einsteinian, Newtonian, and Quantum physics. Newton stated that mass is an entity separate from energy. Einstein's physics posits that mass is a manifestation of energy -- a possible property for energy to take on. Quantum physics, contra both Newtonian and Einsteinian physics, posits (in its first form, at least) that causality is a probabilistic construct, instead of an infinitely deterministic construct.

Usually the incommensurabile thesis is defended by pointing out dramatic changes between scientific systems. Naturally there is wiggle room for what constitutes "dramatic". Generally I take this to mean that the ontological construct of science has changed. So, we have an atomic theory, for instance, and it would not change the ontological structure of chemistry to posit another atom, or another molecule, or even a new way of bonding. There exists atoms and bonds. However, were we to posit that the universe is not composed of atoms, but waves of energy and waves of energy only, and that the atoms we reference are tools in the same sense that a meter is a tool (whereas "length" would be the ontic unit of a meter), then we'd have an instance of incommensurability. " "The universe is atoms and only atoms" and "The universe is energy waves and only energy waves" "can not be true. You have to choose one or the other, or make an adjustment that allows for both.

In playing with the incommensurability thesis, I broke open my Aristotle and wrote the following thought experiment where I interpreted spectroscopic data using Aristotle's theories.

Spectroscopic analysis would be conceived of in an entirely different way within the Aristotelian framework. Nature abhors a void so there aren't any atoms, and... (From Book II of De Anima)

"...to explain what light is.

Now there clearly is something which is transparent, and by 'transparent' I mean what is visible, and yet not visible in itself, but rather owing its visibility to the colour of something else; of this character are air, water, and many solid bodies. Neither air nor water is transparent because it is air or water; they are transparent because each of them has contained in it a certain substance which is the same in both and is also found in the eternal body which constitutes the uppermost shell of the physical Cosmos. Of this substance light is the activity-the activity of what is transparent so far forth as it has in it the determinate power of becoming transparent; where this power is present, there is also the potentiality of the contrary, viz. darkness. Light is as it were the proper colour of what is transparent, and exists whenever the potentially transparent is excited to actuality by the influence of fire or something resembling 'the uppermost body'; for fire too contains something which is one and the same with the substance in question. "

So, the differences one can obtain from a spectroscope could be explained by this transparent substance in activity with different proportionate mixtures of the elements, which is something Aristotle references often in explaining why different things are what they are (I'm just taking a guess here. But I don't think it's fair to infer, using Aristotle's work in a scientific manner, that reference to quantum energy states modeled by operator algebra explains lines on a given spectroscopic measurement). But, even more importantly, this would be the mere material cause, reflecting a samples potentiality. The actuality could only be garnered from what that material would be used for. Suppose it is a medicine. The ratio of elements would be the potential within the substance, and the shape of the sample at the time of the spectroscope would be during its coming-to-be. For the end of medicine is getting well, and when it is used would be its actuality. (I'm pulling from ideas in Aristotle's Physics and Metaphysics as well, here)


In using Aristotle, while I can find a common referent, and I even think that modern theories are better with respect to truth-value, one can come to understand the incommensurability thesis best, I think. This is because science works by inferring to the best explanation within a certain explanatory framework, and inferences, contra arguments, are actions. It's in the use of science that one understands incommensurability best, and not the "logic" of science.

Tractatus Logico-Philosophicus

I have been re-engaging Wittgenstein's Tractatus logico-philosophicus. It is one of the most difficult books I've read, and now reread, and even translated to get a bearing on my reading. With the most difficult thinkers I engage, I enjoy stopping in the middle of my writing and drawing a diagram of the argument/metaphysic in order to have a visual representation of the argument as I go along that I can modify, reconnect, and have at the end to remind myself of key points. The list of thinkers that had been on that list is now expanded by one, and Wittgenstein's diagram is the messiest version (though Kant is still the one that has forced me to start from scratch more than any other).

Last night I believe I obtained an important key to understanding this work: It ought to be read as a lament. The book claims to have solved all the problems of philosophy in its introduction, and to claim that the size of the Tractatus shows how insignificant these problems are. And so he begins:

1. The World is everything that is the case

which lays a foundation, of sorts, upon which the Tractatus digs into. I think it important to understand this as a digging downward, because the emotional feel of this work is best understood as a negative plot: the sharpness of this descent can first be sharply felt within section 3. Section 2 begins to outlay the connection between "the case", "objects", "facts", "atomic facts/states of affairs", and other common-place things which are talked of "in the world".

In 3 one can feel the descent because this is where one understands in what way we understand the world. 4 displays how thinking is connected with itself, and this is why the serious logic begins here. The outline of propositions is significantly different from the outline of atomic facts and objects. We can only mention atomic facts and objects, as we can only mention atomic propositions and their truth values. 5 shows how truth values are derived. I think the nadir occurs around proposition 5.5, but I'm being somewhat arbitrary about that. That I have a feeling for this text, now, is a significant leap forward in understanding it. I can not explain all of the text, but I have an idea of its predominant thrust.

The end of 5, right before 6, signifies an upward slope. But it isn't a hopeful upward slope. It's the beginning of building back upwards from the hole that has been dug into the foundations lain in the beginning.


6 begins to show in what way this digging and explicating, while part of what philosophy has been doing, doesn't answer what philosophy asks -- the world is understandable, but the whole is tautologous. It places mathematics and natural science in a "place" within understanding, and reflects that while some persons think these things are ultimately true that this is a sort of superstition. Science, causality, and so on is logical, and all we can know is logic. And, even more than that, I think a very important proposition for understanding the catharsis/melancholy of the ending is:

6.4 All propositions are of equal value.

From this it follows that the important questions, important to Witty at least, can not be answered. They have no sense. Or that this is the answer to the important questions: That the question, having no answer, can't even be sensibly formulated -- and so the secret to immortality and happiness lies not in philosophical speculation, but in a mental nowness: Which is entirely unsatisfying.

This is why I think one needs to read Wittgenstein's "correct method" as sort of tongue-in-cheek preperation for his final proposition. If "correct philosophy" consists in correcting the errors of metaphysical speculation, and others feel that they are not then learning philosophy, then how is philosophy philosophy? Why is it that philosophy is, correctly done, unphilosophical?

Naturally the ending is a bit enigmatic, but I think the final proposition in 6 can be understood in that all what has been said is senseless -- in Wittgenstein's specific way of using this word. The outline that the Tractatus is has no reference. As the entire thing does not refer to "the case", and one finds that out by the time they begin to build "the world" back into a whole from which it has been disassembled, there can't actually be a sense to any of these propositions. However, if we, after having crawled through, on, and over these propositions, one would be wise, having reached the limit of our world at the barrier of language, to throw the ladder down. What has been taken apart is no longer needed -- it is senseless, and with that understanding of senselessness, the world is made right.

However, There is proposition 7. I get the feeling that Wittgenstein did not take his own advice. He did not "see the world right". The entire book is a detailed struggle to understand ethics and related philosophical problems, and it ends in failure. It's horribly dissapointing, and with 7 we see that Wittgenstein will not give up that chase -- he will simply remain silent, and melancholy.


Man, I'm probably going to reread the Tractatus, as I'm not entirely certain on what everything in it means -- but the effort I've spent in reading and rereading this book has been well worth it. Once I seemed to "Get it"... it was an absolutely incredible feeling.