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 , .

Working Hard on Special Biological Relativity

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

Or something.

Posted in biology, evolution, fitness, philosophy, science, Special Relativity. Tagged with , , , , , .

Occam’s Razor and Entropy

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.

Posted in economics, ontology, philosophy, physics, science.

New Quantifier Angle-I, and Agent Logic

I was thinking that upside down A and backwards E were feeling lonely.  Yes, ∀ and ∃ love each other very much, but they could really use a new friend.  Introducing Angle I:

Now, Angle I, Angle I small, is just like her friends ∀ and ∃.  She can be used in a formula such as ∀x∃yAngle I smallz(Pxyz).

But how should we understand what is going on with the failure of the quantified tertium non datur?  With that advent of a third quantifier, what’s to stop us from having a fourth, fifth or n quantifiers?

The Fregean tradition of quantifiers states that the upside down A means ‘for any” and the backwards E mean ‘there exists some’.  So ‘∀x∃yPxy’ means ‘for any x, there exists some y, such that x and y are related by property P’.  For instance we could say that for any rational number x there exists some other rational number y such that y=x/2.

If we, however, follow closer to the game-theoretic tradition of logic, then the quantifiers no longer need take on their traditional role.  The two quantifiers act like players in a game, in which the object is to make the total statement true or false.  In our above example, we would say that backwards E would win the game, because no matter what number upside down A picks, there is always some number that ∃ could find that is twice the number ∀ chose.

Under this view of quantifiers, quantifiers acting as players in a game, there is no reason why there can’t be any number of players.  (Personally, I like the idea of continuing down the list of vowels: upside-down A, backwards E, angle I, then inverted O, O, maybe angle U? Go historical with Abelard, hEloise, and then Fulbert? Suggestions?)

Now, what is it good for? Let’s play a game of Agent Logic!

The purpose of a game of Agent Logic is to determine the loyalties of the agents in that game, i.e. discover any secret agents. A game consists of a particular logical situation, as given by formulae of independence friendly logic, with at least three different agents, each of which is represented by a quantifier: ∀, ∃, angle I, inverted O, etc. Each agent has an associated ‘domain’, and for the game to be non-trivial the intersection of the domains must have at least one element.

A game of Agent Logic is played by determining the information dependencies required to derive the target formulae from the premise formulae. Once the required information dependencies are known, then the strategies and loyalties of the agents have used may be inferred. The simplest solution to a game is one in which an information dependence indicates a loyalty: if an agent has access to certain information, then that agent must have a specific loyalty.

The person running the game is the Intelligence Director, given by the quantifier angle-I. This is you! All other agents are possible opposing Intelligence Directors or secret agents of the opposing Intelligence Directors. It is your job to figure out who has given who access to information and how that agent has acted upon it. Any information or strategy that is not derivable from the premises are considered acts of treason against you, the Intelligence Director. If the target premise (conclusion) is derivable from the premises alone, no determination of loyalty can be made.

The ‘domain’ of angle-I consists of what you depend upon, i.e. what you believe to exist and what you believe the other agent’s believe to exist. (Though it is a premise itself.)  Recall that the backslash, , means ‘is dependent upon’ and the forward slash, /, means ‘is independent of’.

premise:

1. Angle I small (
∀ (a, b, c),
∀/∃,
∃ (a, b, c, d),
a, b, c, d
)

In this ‘domain’ of angle-I, the Intelligence Director is dependent upon ∀ depending upon the existence of a, b and c, and being independent of  ∃, that ∃ depends on the existence of a, b, c and d, and the director herself depends upon the existence of a, b, c, and d.

premise:

2. ∀xPx

target (conclusion):

3. Pd

Now, since angle-I depends upon ∀ not depending upon d, there is no way to derive the target from the premises. However, since ∃ does depend upon d, if ∀ depends upon ∃, then agent ∀ has access to d.

Therefore, given treason,

4. ∀ (∃(d))               [premise of treason – ∀ receives information from ∃, specifically d ]

5. Pd                                  [instantiation from 2, 4]

This shows that the conclusion can be reached if ∀ is treasonous, a secret agent of ∃, i.e. ∀ is loyal to ∃ and not angle-I.

Posted in Frege, game theory, independence friendly logic, logic, philosophy.

Special Relativistic Fitness, Preliminary Thought Experiment

Imagine two different tribes of biologists.  The first tribe is comprised of very fast people.  They survived for thousands of years by studying biology and being faster than their competitors.  The second tribe is comprised of very strong people.  They survived for thousands of years by studying biology and being stronger than their competitors.  After all this time, the first tribe is filled with very fast biologists and the second tribe is filled with very strong biologists.

Now imagine that two biologists, one from each tribe, are evaluating the fitness of two organisms.  One of the organisms is fast, the other is of average speed.  Other than the difference in speed, they are identical.  The strong biologist recognizes that one is faster than the other, but does not find this to be significant and assigns the two organisms equal fitness.  The fast biologist recognizes that one is faster and assigns it a slightly higher fitness because of its speed advantage.

Is the difference in fitness evaluations a matter of scientific opinion?  If it were an opinion that the fast organism was fitter, this would be a scientific opinion based upon environmental and competitive factors.  Given different competition and environment, the evaluation would have come out differently.  However, the fast biologist and her entire tribe have survived by being faster than their competition.  Her evaluation is not only scientifically based but also partly based upon her evolutionary heritage and Weltanschung that is finely attuned to how speed is beneficial.  It is these factors, unique to people of this tribe, that give more weight to speed as evolutionarily significant and makes it more than just a case of scientific disagreement.

Is the fast biologist unfairly biased? If we consider the perspective of the strong biologist, we can see that the strong biologist has no greater claim to her appraisal of an organism’s fitness: strength is just as arbitrary a trait as speed and this thought experiment could have equally been set up with two organisms that only differed in strength.  Hence the fast biologist could equally claim the strong biologist is unfairly biased toward strength and away from speed.  Generalizing, we can say that no one perspective, be it speed, strength, sight, etc., or any combination of traits, is privileged.  Hence their is no unfair bias because every scientific perspective based upon evolutionary heritage and an associated Weltanschung is as legitimate as any other.

Lastly, consider that every biologist will recognize the same amount of phenotypic difference between two organisms;  difference in phenotype does not permit variation in interpretation.  Therefore any difference in fitness evaluation is not due to a perceived physical difference by the biologists in the organisms studied.

Therefore this thought experiment implies that our determinations of fitness are not independent of the evolutionary history of the biologist(s) making those determinations.   Insofar as we cannot escape our own biology and how it shapes our views, it will determine the fitness value we assign to organisms, if only to a small extent.

Consequences:

In one sense everything on Earth has been evolving for the exact same amount of time, since the dawn of life, and hence no organism alive is any more evolved than any other.

However, from the perspective of the fast biologists, the fast organism is more evolved.  Insofar as the fast biologists believe that life is evolving towards moving faster, the organism that moves faster has adapted before the other organisms.  So, in the special circumstance of a population perceiving evolution to move regularly towards a trait, an organism with that trait can be considered more evolved.

—– the analogs —–
evolutionary significant events are specific adaptations :: physically significant events are light flashes
regular evolutionary change is a population with trait selection :: regular motion is a non-accelerating inertial frame
difference in phenotype does not permit variation in interpretation, regardless of observer :: failure of addition of velocities of light, regardless of observer.
upper limit to adaptation- by definition, no jumps :: speed of light in vacuum defined as c

Posted in biology, evolution, fitness, philosophy, Special Relativity. Tagged with , , , , , .

Job

Dear readers, I’ve decided to try to get myself paid for my efforts.  If you know of people or programs (graduate or otherwise) that would want someone like me, please let me know.

What I want to do is write up my theories about the causal structure in evolution;  it will get done regardless, but it will get done faster and better if I have help.  So I am looking for a place that does philosophy of science, biology and physics, but anywhere willing to fund my writing about these topics will be considered.

Any and all information, thoughts, wishes, questions, condemnations, etc., are encouraged.  Leave a comment below or send me an email at noahgreenstein@noahgreenstein.com.

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

Deriving Natural Selection = Fitness × Acceleration

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.

If you want to see the paper as it stands now, you can access it here or below.[6in/120mm ebook formatted]

Posted in biology, evolution, fitness, General Relativity, philosophy, physics, Relativity, science. Tagged with , , , , , , .

Natural Selection = Fitness × Acceleration

Natural Selection is the force that changes species.

Fitness is the resistance to change in the rate of change of the species.

Acceleration is change in the rate of change of the species.

Natural Selection = Fitness × Acceleration

Posted in biology, evolution, fitness, philosophy, science. Tagged with , , , , .

Water Water Everywhere

Running water is one of the most amazing things in this world. Turn a knob, water flows.

But even here in America we are starting to have problems:

Soon enough we are all going to have to decide between water and power. What really worries me is I have no idea who is going to make that decision.

blogactionday.change.org

Posted in internet.