Category Archives: science
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.
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:
Philosophy is disparaged often enough, and by people who ought to know better. As of late, every time this happens I think of this scene — but with the text (something like) below…..
Oh. Okay. I see.
You think this has nothing to do with you.
You go to your desk and you select, I don’t know, some statistical mathematical model, for instance, because you’re trying to show the world that you take science seriously and follow what you think are established scientific practices.
But what you don’t know is that that mathematical model is not just established science.
It’s not a data model. It’s not a model of phenomena.
It’s actually a deductive nomological model.
And you’re also blithely unaware of the fact that in 1277, the Bishop of Paris proclaimed that a multiplicity of worlds could exist.
And then I think it was Pascal, wasn’t it, who argued that probabilistic mathematics could be applied to situations?
And then mathematical models quickly showed up in many different philosophies.
And then it, uh, filtered down through to natural philosophy and then trickled on down into some basic handbook of science, where you, no doubt, adopted it without another thought.
However, that statistical model represents millions of hours and countless lives. And it’s sort of comical how you think that you’ve made a choice that exempts you from philosophy, when, in fact, you’re using ideas that were selected for you by the people in this room.
Mohan Matthen’s post Teleology in Big Systems brought up two options explaining how someone — Tom Nagel in Mind and Cosmos — would choose a teleological explanation over a naturalistic one. The first, below, got me thinking:
First, he might be saying that though it is physically possible (by a fluke series of mutations, for example) for mentality to have come about, it would be better explained by teleology. (Let’s call this the “intelligibility” argument.)
Though Matthen was referring to doubts about Darwinism being sufficient to lead to consciousness, there is another way to understand this intelligibility argument. If we grant that consciousness is something very special, though not unphysical, someone might consider the laws of physics to be constructed, teleologically, to permit consciousness. This is to say that our physics is teleogically directed to account for consciousness. The claim is not that consciousness was necessitated by our physics, but that our physics must conform to allow the possibility of consciousness. What is one philosopher’s Nature is another’s Teleology.
Now, I can’t see any philosophical motivation for this outside of a very deep belief that consciousness is exceptionally special. But if we grant exceptional status to consciousness, then it wouldn’t be ridiculous to consider that our physics must somehow be subject to the requirements of consciousness instead of the other way around. Whereas there may be infinite other possible physics that do not allow for the possibility of consciousness, we live under a physics that does.
My immediate, knee jerk response to this sort of move is that it is just a semantic shift about the meanings of teleology and nature, nothing deeper. If what the teleologist means by teleology is what others mean by nature, then there is no difference of opinion, only word use.
However, this semantic response does not engage the motivation for the teleological argument. The motivation is that consciousness is exceptional. So, if the naturalist believes that consciousness is exceptional and entirely natural, then the naturalist is left with no natural explanation for why it is so exceptional. However the teleologist may say that consciousness is exceptional, subject to the laws of physics, but unsurprising, since the laws of physics itself are directed to allow for consciousness. Since the teleological account does a better job at explaining something as special as consciousness, it is preferable.
This conclusion about preferring the teleological explanation to the naturalistic one is based on the absolute assumption that consciousness is exceptional. But how exceptional must it be? Since we are making physics, and presumably the rest of science, subject to our assumption, then the reasons for our assumptions must then be ontologically more basic and more certain than our entire scientific understanding of the world.
Personally I do not have any basis for thinking consciousness is so special that all of science must be made to account for it. From my perspective, claiming that science must conform to consciousness is a post hoc ergo propter hoc fallacy, since I’d have to arbitrarily assume consciousness to be a fundamental substance and science to be constructed to allow for it.
However, there could be people who do have beliefs that strong. For them, they would not be arbitrarily assuming consciousness to be the more fundamental substance in the universe and hence it would follow that science should conform to it. Instead it would be a direct causal link: consciousness, therefore science that teleologically allows for consciousness. This kind of teleological naturalism is special in that it does not appeal to the unlikelihood or complexity of consciousness evolving, as is wont to happen nowadays, but is based on an ontological claim about consciousness. I don’t know if this is more defensible than the Intelligibility Argument based on likelihood, but, as it is different, perhaps it has a chance to fair better.
If we try to represent tossing a coin or a die, or picking a card out of a deck at random, in logic, how should we do it?
Tossing a coin might look like:
Toss(coin) → (Heads or Tails)
Tossing a die might be:
Toss(die) → (1 or 2 or 3 or 4 or 5 or 6)
Picking a card:
Pick(52 card deck) → (1♣ or 2♣ or … or k♥)
This begs asking, do these statements make sense? For instance look what happens if we try to abstract:
such that ‘Toss’ represents a random selection of the given object.
But this is weird because Toss is a randomized function and x is not selected randomly in this formula. Perhaps if we added another variable, we could generate the right sort of function:
∀y ∃x Toss(yx)
Then x would be a function of y: we would select x with respect to y. The problem is still that a Toss involves randomness. So this setup is incorrect because treating x as a function of y is not randomized, because y is not random.
How can we represent randomness in logic?
As noted, functions alone will not work. Variables and interpreted objects cannot invoke randomness. Perhaps we can modify some part of our logic to accommodate randomness. The connectives for negation and conjunction haven’t anything to do with randomness either.
But, if we use the game theoretic interpretation of logic, then we can conceive of each quantifier as representing a player in a game. Players can be thought of as acting irrationally or randomly.
Therefore, let’s introduce a new quantifier: Я. Я is like the other quantifiers in that it instantiates a variable.
- Яx T(x)
However, Я is out of our (or anyone’s) control. It does instantiate variables when it is it’s turn (just like other quantifiers) but it instantiates randomly. So we have three players, Abelard, Eloise and Random (or the Verifier, Falsifier and Randomizer).
But more is still needed. We need a random selection between specific options, be it between heads and tails, 1-6, cards, numbers, or anything else. One way of doing this would be to create a special domain just for the random choices. Я would only instantiate from this domain, and if there are multiple random selections, we will require multiple indexed domains.
Hence, given Di(Heads, Tails),
represents a coin flip since Я randomly instantiates out of the domain containing only Heads and Tails.
I prefer to use an artifact of Independence Friendly logic, the dependence indicator: a forward slash, /. The dependence indicator means that the quantifier only depends on those objects, variables, quantifiers or formulas specified. Hence
means that the variable x is randomly instantiated to Heads or Tails, since the only things that Яx is logically aware of are Heads and Tails. Therefore this too represents a coin flip, without having multiple domains.)
Now that we have an instantiation rule for Я we also need a negation rule for it. If some object is not selected at random, then it must have been individually selected. In this case the only other players that could have selected the object are ∀ and ∃. Hence the negation rule for Я is just like the negation rule for the other quantifiers: negating a quantifier means that a different player is responsible for instantiation of the variable. If neither player is responsible, it can be considered random: ¬Яx ↔ (∀x or ∃x). We can leave the basic negation rule for ∀ and ∃ the way it is.
Therefore, given the additions of the new quantifier and domain (or slash notation), we can represent randomness within logic.
See “Propositional Logics for Three” by Tulenheimo and Venema in Dialogues, Logics And Other Strange Things by Cedric Degremont (Editor) College Publications 2008, for a generalized framework for logics with 3 quantifiers. Since the above logic requires either indexed domains or dependence operators, Яandom Logic is a bit different, but it is a good discussion.
The Genial Gene: Deconstructing Darwinian Selfishness by Joan Roughgarden
In The Genial Gene Joan Roughgarden seeks to replace the competitive understanding of evolution, known as sexual selection, with a cooperative one. The first sentence of her book reads, “This book is about whether selfishness and individuality, rather than kindness and cooperation, are basic to biological nature” (p. 1).
So what is the argument? Taking this first line, she wants to conclude something about basic biological nature. To do this, one can either define what basic biological nature is and then use that definition to derive conclusions, or else survey the natural world and find the best interpretation for whatever empirical results were found. She opts for the latter strategy.
To this end she first surveys and compiles examples of what people consider to be evidence for sexual selection and argues that this evidence has been misconstrued or simply does not support the theory of sexual selection. Then she offers a few logical arguments against sexual selection with the aim to highlight contradictions within the theory.
She then develops her alternative, called Social Selection. Social Selection is fundamentally based upon cooperation, not competition, and she proceeds to reinterpret the empirical research with respect to cooperation. Given the results of this reinterpretation, she concludes that the cooperative approach provides a more accurate picture of the empirical data than the competitive approach. Therefore social selection, not sexual selection, is fundamental to biological nature.
Can this argument be maintained?
Her argument fundamentally turns on the interpretation of the empirical research. (If her logical arguments were strong enough to undermine sexual selection on their own, she would have dedicated more space to them. At best, in my opinion, they could raise questions about sexual selection, but are not inherently damaging enough, even if they are accepted uncontested, to force a major revision to sexual selection.) She interprets the research in terms of cooperation and her opponents are those who interpret the research in terms of competition. Roughgarden claims her interpretation is the correct one.
Insofar as she is making an inference saying her interpretation is the best conclusion, her argument fails. She readily admits that the defenders of sexual selection are able to consistently create explanatory fixes for apparent contradictions in the empirical research. Since they are able to explain the data, the fact that she is unsatisfied by their explanations (and likes her own better) is no grounds for convincing her opponents to give up their explanations. After all, they have history and authority on their side. Her coming up with better numbers, that is, having formulas that (she says) more accurately represent the research, is not a sufficient reason for discarding a theory that has held up for many years, especially one that continues to be an area of active research. So, she has not successfully argued that social selection should replace sexual selection.
However, if we consider a more modest conclusion, then Roughgarden may be able to maintain part of her argument. She makes the point that the core Darwinian theory does not include sexual selection; it is a later contribution (ppg. 3-4). This suggest that there may be theoretical room for cooperation in addition to competition. But how much room?
Now the interpretive problem that she set up cuts the other way. Instead of her trying to convince us that her cooperative interpetation of the empirical research is the correct one, we ask the competitive interpretation why it is the best one. Empirical research alone cannot support one conclusion over another: the data must first be interpreted before a conclusion can be reached. As mentioned above, sexual selection has history and authority on its side, but age and endorsements are not arguments for being the sole fundamental methodology of biological nature. Without history and authority, sexual selection proponents only have their ability to explain bioogical research, which is no more than Roughgarden has. Therefore, advocates of sexual selection have no further theoretical resources to support their claim that sexual selection is the fundamental method working in evolution.
This means that Roughgarden does succeed in part. Based on the arguments she provides she is unable to maintain that kindness and cooperation underpin evolution, but she is able to cut sexual selection down to her size. She has shown that it is possible to reinterpret biological research in terms that do not rely upon competition and that sexual selection has no special theoretical privelege. Therefore sexual selection proponents can no longer claim to be fundamental biological reality: even though Roughgarden was unable to fell their theory, they won’t be able to down her either, and so she has established theoretical room for cooperation in Darwinian theory.
I’ve been working hard on Special Biological Relativity and it is taking up most of my blogging energy. However, I do have some fun results:
Define Biological Energy as the ability to do work, the ability to change the environment. Then Fitness can be related to Energy because the higher the fitness the greater the ability to change the environment.
E ∝ f
If we consider an organism that lives in a place with infinite resources – a Garden of Eden – and also replicates at the speed of the chemical reaction of replication – there is no maturation process, it immediately starts to replicated as soon as it is created – then it’s life is identical to it’s replication process. Define d to be the speed of the chemical process of replication. Then the ability of this organism to change the environment is given by it’s fitness, the rate it replicates at and it’s life:
E = fd2
I was trying to understand Occam’s Razor, specifically I wanted to know its justification. There are posts over at Wikipedia and the Stanford Encyclopedia of Philosophy worth looking at, but neither left me satisfied.
Instead, I came up with “Death Implies Economy”. What this means is that we are fundamentally limited in time and resources, and hence we cannot afford to waste what little we have on unnecessary complication. DIE is a metaphysical justification of ontological parsimony: regardless of how we come to the knowledge of death, the principle only requires that we are fundamentally limited and is agnostic as to how we come to understand this of ourselves. [One may revise the principle to ‘Demise Implies Economy’ without problem or changing acronym.]
Now, the reason I wanted to figure out Occam’s Razor was because I thought it might help me understand entropy better. Entropy seems to be this force or cause that basically is always at work and does whatever we don’t want it to. Jerk. Of course the universe has no reason to conform to our way of doing things, or worse, my way of viewing the world, but entropy just seems to be excessive: why should our physical science be subject to a form of energy loss? This makes me think it is our fault. No, not ‘fault’, but intrinsic part of how we go about our science. My apologies to the universe for calling it a jerk.
So, back to Occam’s Razor and DIE. If DIE underpins Occam’s Razor, then we are metaphysically bound to proceed in a piecemeal manner. Even our most radical theories are not developed by immortals with no care for time. So, in some sense, our theories are also fundamentally limited and hence will always admit some unknown factors as a metaphysical consequence.
It is fair to ask if this is all just a fancy way of stating pessimistic induction, “Since we haven’t gotten theories perfect in the past, we shouldn’t expect to in the future”? How can I make the claim that we will never succeed in this scientific endeavor?
My answer is that these questions raise legitimate issues, but the specific question at hand is not to speculate on what will happen with future theory but how we are to understand entropy and simplicity now. And to question whether our adherence to ontological parsimony has the theoretical consequence of an unresolvable force. Since we must believe the theories we have, at least to some extent, whatever these theories do not describe must be left in an accordingly deep mystery– as the result of an unexplained force at least as powerful as the forces we do explain. Therefore I have to conclude that, given a metaphysical understanding of Occam’s Razor such as DIE, there is a legitimate concern of inevitable unresolvable causal consequences which could manifest as various forms of entropy.
As you can see from my previous post, I now have postulated a direct relation between Natural Selection and Fitness (N.S.=F.×A.). This relation follows from the theory.
The short short short version of the theory is this general postulate: one organism’s traits are another’s environment and vice versa. Hence all competition can be viewed as environmental phenomena. This gives Natural Selection as a result of Fitness and an environmental factor, which I refer to as Acceleration.