The Rationality Cone

There are different sorts of constraints on thought.  We forget things, we fail to infer consequences of our beliefs and we have features of perception, like blind spots, that affect our understanding of our surroundings.  We also can be greatly affected by our emotions: when we are angry — when we see red — we are unable to see the anything but the things that are making us mad; when we are infatuated we are, conversely, unable to see anything wrong with our object of desire.

This account of emotional states — moods — is interesting because moods affect our overall reasoning ability.  Given one mood, we will be able to make certain inferences; given another, we will make different inferences.  Moreover, what seems to be a rational inference in one mood may be irrational in another mood.

At this point we have thought, which is comprised of our knowledge, perception and deductions we make, and mood, which modifies and constrains thought.  If we consider the situation over time, then at any point a person has a history of thoughts and moods, which has led up to the current state, and a potential future of moods and thoughts based on where that person is now.   Going from one mood to another, or one thought to another, can only be done within a limited range, i.e. no thoughts or moods can be completely detached from prior thoughts or moods.  This gives us a perspective on the relation between rationality, consciousness and thought:

Considering a person’s consciousness at some point, we can map what we consider rational and irrational based upon the potential mood and thought changes.  Any possible future belief (a combination of thought and mood) will be a combination of changes in prior moods and thoughts.  Beliefs that require too great a change in both thought or mood may be outside the realm of rationality for a person, while beliefs that require little effort will fall within the realm of rationality.  Hence, the rationality cone

Rationality Cone Diagram

The Future Rationality Cone illustrates how, given changes in thought or mood, a person’s beliefs can become different from their current beliefs.  The edge of the cone is the limit of what that person could possibly rationally believe:  anything outside the edge requires too great a jump in thought or mood from where they currently are.  Any point inside the cone represents a set of beliefs that the person could rationally have, given different circumstances.  The bottom half of diagram shows the past rational states that could have led up to the current state, as represented by the Past Rationality Cone.

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If the above scheme is familiar, it is because it is modeled on the Light Cone from physics; the diagram is from the linked Wikipedia page.  I always found it fascinating that the light cone implies that there is part of the universe immediately surrounding each of us that we can never physically access.  Likewise, there are thoughts and moods that are just like our own that appear irrational to us—even if they are not—because they fall outside our capabilities.  Other people could, however, have these thoughts because their rationality cones are not exactly aligned with our own, or they started from another location, which enabled them to access that part of the mental universe.

Posted in metaphysics, mind, philosophy, physics.

Яandom Logic

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:

∀x Toss(x)

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.

  1. Яx T(x)
  2. Tb

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),
Яix
represents a coin flip since Я randomly instantiates out of the domain containing only Heads and Tails.

(aside:
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

Яx/(Heads, Tails)

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.

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

new york

Posted in news, NYC. Tagged with .

Book Review: The Genial Gene

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.

Posted in biology, evolution, measurement, science. Tagged with , , , .

Philosophy Carnival #2

Well, it’s the second philosophy carnival I’ve hosted.  So let’s get started.

Counterfactuals and time traveling cold-blooded murderers!  Why is it we always want to see what happens when we kill ourselves (or others) when time traveling?  Does time travel make one murderous?  Anyway, besides  the weird questions that occur to me, the discussion over at Kadri Vihvelin’s philosophy blog does try to tackle Counterfactuals, Indicatives and What Time Travelers Can’t Do.

If that isn’t your cup-o-tea, maybe you like smoking pipes.  But apparently not the pipe if you are from Utah.

And if you don’t like smoking pipes, nor counterfactual time travelers, then perhaps you like the movies.  Over at Pirates and Revolutionaries we have durationless movies that involve no time flow.    Lot’s of YouTube clips — which I did actually watch (most of them at least) and you should too. Because what good is anything without pictures or conversation?

Well, if you don’t like the movies, pipes or homicidal time travelers, try the news.  But not if you read the New York Times’ Stone, apparently, because over at The Consternation of Philosophy, Matt says they got the foundation of human rights wrong.  He writes that the reasons that are given not only do not show a foundation for secular human rights, they actually lead to dogmatism.

But maybe you like dogmatism.  I bet there are secretly lots of philosophers out there who, while publicly decrying dogmatism, are secretly delighted with their own.  I’m probably one of these people.  Then, perhaps we should be epistemological anarchists, as is suggested over at the Kindly Ones.  Paul writes on Feyerabend’s reductio directed at rationalist conceptions of scientific method, which concludes with: Anything Goes.  You should read this- it’s something I dogmatically recommend.

Fine, be that way.  Don’t do what I recommend.  Instead sit around and listen to the radio for all I care.  Actually, we’ve got some high quality internet radio going down at the Partially Examined Life: Pat Churchland on the Neurobiology of Morality (Plus Hume’s Ethics).  I surprised myself and listened to the whole thing.  Good talk.  Also, a book for sale.

If none of this armchair stuff has impressed you, I guess you might be one of those “go out and do stuff types.” [yeah right]  If that is the case, go check out some Experimental Philosophy.  Justin writes, ask not “what the history of philosophy can do for us, but rather what we can do for the history of philosophy.”  That’s the attitude!  (The post is actually on the place of x-phi in a historical and cultural setting.  Good stuff just the same.)

Or maybe you are just at The Ends of Thought, so frustrated with the difficulties that you’re left wondering where a lot of us went wrong (and I’m not saying who has gone wrong; you’ll have to read the post to see who Roman says did).

Lastly, zombies, because philosophers like zombies.

Posted in fun, philosophy.

Philosophy Carnival 8 August

I’m hosting the next philosophy carnival, on August 8th.  If  anyone is thinking about submitting to the next philosophy carnival, I have a preference for philosophy of science, though feel free to submit on any topic.  Also, I like to be entertained by my academic philosophy, so the more off the wall the better.

Posted in news, philosophy. Tagged with , .

The SEP on the Kindle

Reading on a computer screen is often not pleasant, especially when a lot of reading has to  be done. This is a general problem for philosophy since nearly everything is in PDF format and if you don’t want to print out a tree’s worth of paper you are stuck.

I got a Kindle.  Kindles can handle PDFs, but what I just found out is that Kindles can do the Stanford Encyclopedia of Philosophy quite well.  KindleI downloaded the webpage and then deleted the content from the top of the page down to the start of the article.  Then I used Calibre to convert the webpage into Kindle format.  It looks great and the images come out well.

So I did some poking around, and found out that if you use a Firefox extension called “Download Them All” you can download a webpage and all the links on that webpage, i.e. you could go the contents page of the SEP and then download all the articles linked there.  Basically you could have the entire SEP on your Kindle and be good to go.

Posted in philosophy, products, technology. Tagged with , , .

Spell Sorites. No really.

Since none of the other philosophy blogs I follow have mentioned it, one of the final round contestants of the National Spelling Bee was eliminated last night by misspelling “sorites.”   I believe the contestant put a ‘p’ in front of the word.  It makes me wonder if these kids know how to do anything other than spell words.

Posted in argumentation, news, random idiocy. Tagged with , .

IF Logic and Cogito Ergo Sum

(∃x∃x) → ∃x

Descartes Law

If something has informational dependence upon itself, then that thing exists.  For example, thinking that you are thinking is informationally self dependent and therefore a thinking thing (you) exists.

Posted in epistemology, independence friendly logic, logic. Tagged with , .

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 , .