Tag Archives: wittgenstein

An Introduction to the Game Theoretic Semantics view of Scientific Theory

What is a scientific theory?  In an abstract sense, a scientific theory is a group of statements about the world.  For instance the Special Theory of Relativity has, “The speed of light in a vacuum is invariant,” as a core statement, among others, about the world.  This statement is scientific because, in part, it is meant to hold in a ‘law-like’ fashion: it holds across time, space and observer.

The Popperian view is that we have scientific theories and we test those theories with experiments.  This means that given a scientific theory, a set of scientific statements about phenomena, we can deductively generate predictions.  These predictions are further statements about the world.  If our experiments yield results that run counter to what the theory predicts — the experiments generate statements that contradict the predictions, the theory did not hold across time, space or observer — then the theory eventually becomes falsified.  Else the theory may be considered ‘true’ (or at least not falsified) and it lives to fight another day.

The game theoretic semantics (GTS) view is that truth is the existence of a winning strategy in a game.  In terms of the philosophy of science, this means that our theories are strategic games (of imperfect information) played between ourselves and Nature.  Each statement of a theory is a description of a certain way the world is, or could be.  An experiment is a certain set of moves — a strategy for setting up the world in a certain way — that yields predicted situations according to the statements of the theory.  If our theory is true and an experiment is run, then this means that there is no way for Nature to do anything other than yield the predicted situation.  Said slightly differently: truth of a scientific theory is knowing a guaranteed strategy for obtaining a predicted Natural outcome by performing experiments.  If the strategy is executed and the predicted situations do not obtain, then this means that Nature has found a way around our theory, our strategy.  Hence there is no guaranteed strategy for obtaining those predictions and the theory is not true.

An example:

Take Galileo’s famous experiment of dropping masses off the Tower of Pisa.  Galileo’s theory was that objects of different mass fall at equal rates, opposing the older Aristotelian view that objects of greater mass fall faster.

According to the Popperian view Galileo inferred from his theory that if he dropped the two balls of different mass off the tower at the same time, they would hit the ground at the same time.  When he executed the experiment, the balls did hit the ground at the same time, falsifying the Aristotelian theory and lending support to his theory.

The GTS view is that dropping balls of unequal mass off a tower is a strategic game setup.  This experimental game setup is an instance of a strategy to force Nature to act in a certain way, namely to have the masses hit at the same time or not.  According to Galilean theory, when we are playing this game with Nature, Nature has no choice other than to force the two masses to hit the ground at the same time.  According to Aristotelian theory, when playing this game, Nature will force the more massive ball to hit the ground first.  History has shown that every time this game is played, the two masses hit the ground at the same time.  This means that there is a strategy to force Nature to act in the same way every time, that there is a ‘winning strategy’ for obtaining this outcome in this game with Nature.  Hence the Galilean theory is true: it got a win over the Aristotelian theory.

Why you might want to consider doing things the GTS way:

GTS handles scientific practice in a relatively straightforward way.  Theories compete against Nature for results and against each other for explanatory power.  Everything is handled by the same underlying logic-game structure.

GTS is a powerful system.  It has application to  game theory, computer science, decision theory, communication and more.

If you are sympathetic to a Wittgensteinian language game view of the world, GTS is in the language game tradition.

More on GTS:

http://plato.stanford.edu/entries/logic-games/
https://en.wikipedia.org/wiki/Game_semantics

Posted in game theory, logic, philosophy, science. Tagged with , , , , .

For the Classy Wittgensteinian

Stylish Wine Filled Fly-Bottle


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Wittgenstein and Sun Tzu (on throwing the ladder away)

Wittgenstein, Tractatus Logico-Philosophicus #6.54

My Propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them — as steps — to climb beyond them.  (He must, so to speak, throw away the ladder after he has climbed up it.)

He must overcome these propositions, and then he will see the world aright.

Sun Tzu, The Art of War, Chapter XI #38

At the critical moment, the leader of an army acts like one who has climbed up a height and then kicks away the ladder behind him.  He carries his men deep into hostile territory before he shows his hand.

I haven’t heard or seen too many uses of the concept of “throwing away the ladder.”  It seems interesting, though coincidental, that it shows up in these two places.

Wittgenstein is discussing the end of philosophy, how once you understand his statements in the Tractatus, you will understand how to move beyond thinking in those terms.  And then everything will be solved.

Sun Tzu, on the other hand, is discussing how a leader can get the most out of those under her command by preventing retreat.  The famous examples are of Hsiang Yu, and later Cortez, who burnt their ships behind them to prevent mutiny and ensure that their troops would fight as if their lives depended upon it (because they did).

Sun Tzu and Wittgenstein may be two of the most commented upon authors of all time.  However, I don’t think either could have the other’s meaning in these passages, or at least I’ve never seen any commentary to that effect.  However, this does not mean there is nothing to be learned:

For Wittgenstein, the recognition of the nonsensical is what is doing the work.  His words are nonsensical and the realization of this is what allows you to move beyond them, to something better (says he).  So by doing as he says, by recognizing his words as nonsensical, your retreat is prevented, because no one, save a mad man, would willingly return to a nonsensical philosophy when a better one exists.  By climbing the ladder, you also discard it.

Compare this to Philosophical Investigations #309:

What is the aim in philosophy?– To shew the fly the way out of the fly-bottle.

The fly-bottle, a supposedly one way process, Wittgenstein is trying to walk back…  In the Philosophical Investigations he’s trying to climb down the discarded ladder.

Posted in game theory, random idiocy, wittgenstein. Tagged with , .

Disrespect

If there were a verb meaning ‘to believe falsely’, it would not have any significant first person present indicative.

Wittgenstein, Philosophical Investigations, II x

Interesting that there is no significant first person present indicative of self disrespect.  Consider, with Moore’s Paradox in mind:  ‘I disrespect myself by sitting here, but I am doing it anyway.’

* * * * *

Considering disrespect”s relation to Moore’s Paradox at issue here, it begs the question, ‘What is the analysis of Moore’s Paradox?’  For given an answer to that, we might have a parallel answer for disrespect.

My stance is that a person’s statements about the truth are indistinguishable from statements of how he or she is going to act.  Also, statements about a person’s beliefs are about how that person plans on acting.  So Moore’s Paradox breaks down to saying that you are going to act one way but then planning on acting a different way, yielding a contradiction.

This suggests that if you believe that Moore’s Paradox has something to do with predicting how the speaker will act, then the similar form of self-disrespect may likewise be about self-knowledge.

Venturing a tentative opinion, let’s assume that respect has something to do with capabilities.  You have to respect the strengths of your enemies;  they are capable of fighting back.  You have to treat dangerous objects with respect because they can hurt you.  You respect people you like because they have done or can do things that are difficult.

Disrespecting someone is to treat that person as incapable when they are not.

Disrespecting yourself would be to treat yourself as incapable when you are not.  So in any case that you could say you were disrespecting yourself, you would know you were capable of greater things and yet not changing.  Hence it makes sense that there is no first person present indicative of self-disrespect on this analysis.

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Of Duckrabbits and Identity

Of late I’ve become increasingly concerned with the meaning of identity.  When we say, ‘x = x,’ we don’t mean that the x on the left is exactly identical to the x on the right because the x on the left is just that, on the left, and the x on the right is on the right, not the left.  Since equality would be useless without having 2 different objects (try to imagine the use of a reflexive identity symbol, i.e., one that for whatever object it is applies to, indicates that the object  is identical with itself), there is something mysterious about the use of identity.

But what is the mystery?  It cannot be anything to do with the subjects being declared identical: these objects are arbitrary to the particular topic being discussed.  For example if I say ‘the morning star = the evening star’ then we are talking about planets, and if I say that ‘3 = y’ then I am talking about numbers.  The identity sign is the same in both, even though the objects being discussed are rather different.

It is easy enough to believe that by paying attention to the different objects being declared identical we can know how to act (some sort of context principle *cringe*).  But this doesn’t address the question specifically: although we can know how to use the identity symbol in specific instances, this tells us nothing about how identity works or what it means.

Take a look at this:

drthumb = drthumb

The picture is the same save for location on the webpage.

———–

But what if we call the one on the left a duck and the one on the right a rabbit: what is different?  The features obviously don’t change, only the way we are seeing (perceiving? apprehending? looking at? interpreting?)  the two images.

(Triple bonus points to anyone who can look at the two pictures at once and see one as a duck and the other as a rabbit. Hint- it is easier for me to do it if I try to see the one on the left as a rabbit and the one on the right as a duck… focus on the mouths.)

In this example, as opposed to the others discussed above, a decision was required to be made – to see one picture one way and the other another way – before the differences even existed.  Now, in the above examples it appeared that there was a difference of knowledge: at one point we didn’t know that the evening star and morning star were one and the same, or that y was equal to 3.  This isn’t the case when looking at identical duckrabbit pictures because there is nothing about the two pictures that is different; the difference is entirely in the mind.

Let me make a suggestion about how to describe the phenomenon of being able to see one image two different ways: the image can be instantiated in two different ways, i.e. it has an associated universe with a population of two.  There are two possible descriptions associated with this image and until we make a decision about how to describe it, the image is like an uninstantiated formula.

Identity, then, is an indication that the two associated objects are things that can be generalized to the same formula.  The picture of the duck and the picture of the rabbit can be called identical because they both have a single general formula (the duckrabbit picture) that can be instantiated into either.  The identity symbol indicates that the two associated objects are two instantiations of the same general thing, be it a number, planet or image (but not objects in space-time because that would be self-contradictory… space-time and instantiation, a topic for another day).

How identity works can now be identified: it is to instantiate and generalize.  Consider the mystery of how we see the duckrabbit one way or the other: no one can tell you how you are able to see the image one way or the other.  However, you are able to instantiate the image in one way and then another, and recognize that both the duck and rabbit are shown by the same image.

Instantiation and generalization are skills and the identity symbol between the two images above indicates that you have to use that skill to generalized both to one formula.  Most of the time it is non-trivial to instantiate or generalize in order to show two things (formulas) to be equal.  In the case of the duckrabbit it is trivial because the work went into the instantiation process (to see the images one way or the other); in the other examples the situation is reversed, such that we had the instantiations but not the general formula.  In all cases, though, only when we can go back and forth between different instantiations and a single generalization do we claim two things identical.

Posted in epistemology, metaphysics, ontology, philosophy, wittgenstein. Tagged with , , , , .

the lowest desires of modern people

… Another alternative would have been to give you what’s called a popular scientific lecture, that is a lecture intended to make you believe that you understand a thing which actually you don’t understand, and to gratify what I believe to be one of the lowest desires of modern people, namely the superficial curiosity about the latest discoveries of science.

This quote is from the beginning of Wittgenstein’s “A Lecture on Ethics” or whatever the untitled transcript of the talk he gave to The Heretics Society is called.  I’ve seen this part of the lecture omitted; admittedly it has little to do with his later arguments.  However, I always felt that this barb was something interesting.

The quote has little force as an argument: it is merely his opinion that a superficial curiosity about the latest discoveries of science is bad.  No contradictions or other nonsense is pointed out, nor does it even evoke a parallel between those he is disparaging and some accepted foul thing.

But it is clear, concise and otherwise totally unlike everything else that Wittgenstein is known for, while touching upon the topics of belief, understanding, science, and desire.  Odd, no?

What the quote is, is a smear; it is an insult:  Calling something a lowest desire, without reason, is merely to insult it.  What’s going on here?

Say I have a superficial curiosity about the latest discoveries of science.  So what?  If the latest scientific research has little to do with my profession, say I’m a restaurateur, then what harm is there in having a passing interest in what other smart people do?  It might even be considered commendable that I make such an effort.

Now Wittgenstein is saying that my earnest effort is nowhere near commendable, but all the way at the bottom, the basest, of desire.  Since he accusing “modern people” it is not just ‘me’, but everyone.  This is insulting and unwarranted.

However, this isn’t exactly what Wittgenstein was after: he disliked superficial curiosity in scientific discoveries not because of the impulse of people to learn and take interest in others, but because it made people believe that they understood a thing which actually they didn’t understand.  Understanding difficult things is an accomplishment, and scientific research is difficult. In enjoying a superficial curiosity about the latest discoveries of science, he is accusing us of feeling a sense of accomplishment when we have done nothing to merit it: he is accusing us of mental masturbation.  Ouch.

We can also now understand why this criticism is “modern”.  Before  modern times, there was no way to have a “popular scientific lecture”: only in the last century or so have we had the communications technology and an available public which allows for such a thing.  You couldn’t expect feudal peasants to leave their farms or be educated enough to appreciate such a lecture.  But by November 1929, the date of this lecture, mass media was in full swing with the wide distribution of newspapers and books, and the start of national radio broadcasts.  Only with widespread media distribution did the danger of popular science becoming a narcotic exist.

Wittgenstein saw that with the modern increase in information distribution capability came a danger of intellectual drugging of the population.  It disgusted him that people would take pleasure from the feeling that they understood difficult theories with which they only had the most superficial engagement.  Unfortunately he had no argument or solution to prevent this, and so he resorted, as we all do when we are out of good arguments, to insults.

One can only think that the internet has made this an even more pervasive problem.  It blows our information distribution capability off the charts.  And we are, unsurprisingly, completely addicted to it.  It’s too bad dear Ludwig never really commented more on modernity, he seems to have been rather perceptive.

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It was just a matter of time…

[via]

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Positive and Negative Biological Time

In my biorelativity series I used mutations per generation as a measurement of distance. However, with my recent historical/generative musings, specifically the post on the logical foundations of biorelativity (the logic of which is at the foundation of how I arrived at biorelativity), I fear I may have ignored the distinction between a mutation and an adaptation.

Consider an organism with some feature. The feature can be considered both a mutation or an adaptation depending on what the organism is being compared to. If the organism is being compared to another organism, then the feature is likely to be called a mutation. If the organism is being discussed in reference to the ecosystem, then the feature will be referred to as an adaptation.

Now I am sure that there may be some technical properties/definitions having to do with genetics or whatnot that distinguish mutation and adaptation. This is not my concern, though, because in my arguments the two can be used interchangeably.

What does concern me is that there are different sets of related concepts associated with the two words. An adaptation is, to my ear, always a positive thing. A mutation can be good or bad, e.g. mutant freak. By this line of thought adaptations are useful mutations, a subset.

Since mutation is the measurement of time and adaptation is only those mutations which are useful, then we can use adaptation to signify the forward motion of biological time (and forward change of a species as adaptations per generation) which will almost always be what people are discussing (“as time marches on, as things adapt…”). Conversely, to describe biological time going backwards, we could say something like ‘unmutating’.

——

On a slightly different note it is interesting that that there is no word for adapting in the opposite direction: it’s a significant gap. Unadapting? This could imply mere stagnation; the idea here is to think of what it would mean to be adapting in a way to specifically undo previous adaptations. I think a word like this does not nor cannot meaningfully exist: the logical/grammatical structure of adaptation presupposes forward progress.

Consider, “If there were a verb meaning ‘to believe falsely’, it would not have any significant first person present indicative.” (Philosophical Investigations Part II Section x)

“The species is currently *counteradapting*” — It just makes no sense.

Posted in biology, evolution, logic, measurement, philosophy, science, time, wittgenstein. Tagged with , , , , , , , , , .