Hedonium's semantic problem

12 Stuart_Armstrong 09 April 2015 11:50AM

If this argument is a re-tread of something already existing in the philosophical literature, please let me know.

I don't like Searle's Chinese Room Argument. Not really because it's wrong. But mainly because it takes an interesting and valid philosophical insight/intuition and then twists it in the wrong direction.

The valid insight I see is:

One cannot get a semantic process (ie one with meaning and understanding) purely from a syntactic process (one involving purely syntactic/algorithmic processes).

I'll illustrate both the insight and the problem with Searle's formulation via an example. And then look at what this means for hedonium and mind crimes.

 

Napoleonic exemplar

Consider the following four processes:

  1. Napoleon, at Waterloo, thinking and directing his troops.
  2. A robot, having taken the place of Napoleon at Waterloo, thinking in the same way and directing his troops in the same way.
  3. A virtual Napoleon in a simulation of Waterloo, similarly thinking and directing his virtual troops.
  4. A random Boltzmann brain springing into existence from the thermal radiation of a black hole. This Boltzmann brain is long-lasting (24 hours), and, by sheer coincidence, happens to mimic exactly the thought processes of Napoleon at Waterloo.
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Understanding Who You Really Are

7 ozziegooen 02 January 2015 08:44AM

Here are 14 ways in which you reveal who you really are. If you’re brave enough, or if you dare, aim to share who you really are, little by little, everyday, with those you trust.

- A typical 'Who You Really Are' article on Lifehack

Take a minute to consider the following questions.

Who are you?
Who are you, really?
Who do you really think you are inside?


It took me a full year to find the answer to these.  The answer was that these questions, when posed as philosophical dilemmas, were bullshit.  This post is not about ‘understanding who you really are’. It's about understanding, 'who you really are'.

“Who are you” is a question that sounds grandiose.  It’s hard to come up with a philosophically solid answer, and this makes it seem interesting.  It is not interesting.  It just lacks context.

What would you say if you were asked “who are you?” by the police?  By a doctor? By a relative? By a potential boss? By a space alien?

You should say different things, because these people would be using the same words to mean different things. 

What they really want is information about you that is of decision relevance to them.   A police cares where you are from. The doctor cares how old you are. A relative cares about who you are related to. A boss cares what skills you have. A space alien cares about your number of eyes and hands.  “Who are you?” really means, “given your understanding of my position, what simple information about yourself do you think is useful to me?”

So when a young philosopher follows up your response with, “no really, who are you?”, you should respond with asking, “what in particular would you like to know?”

Some may respond to this saying that there does exist a true self. A real self.  This is what the phrase should really mean, and this is what I personally spent a year pondering.

But first, the very idea of there being a true self is specific to a set of religions and philosophies that you may not believe in.  If you’re a empirical atheist, you shouldn’t.  David Hume fought the notion of an inner self 250 years ago. [1] Derek Parfit fought it more concretely in the last 30 years. [2]

Second, even if you do ascribe to a belief system where there is some sort of true self, this would not give you a clear way to describe it.  Should you say that you are a Capricorn inside?  Or that a small fraction of your brain believes in Libertarianism?  Or that you possess soul #988334?

Of course not.  The question of “who are you?” is wrongly worded, and the one of “who are you, really?” should be placed on hold until the questioner can figure out what they are actually trying to ask.  

 

[1] David Hume's view on Personal Identity, Skinner (2013)

[2] Reasons and Persons, Parfit (1986)

The flawed Turing test: language, understanding, and partial p-zombies

11 Stuart_Armstrong 17 May 2013 02:02PM

There is a problem with the Turing test, practically and philosophically, and I would be willing to bet that the first entity to pass the test will not be conscious, or intelligent, or have whatever spark or quality the test is supposed to measure. And I hold this position while fully embracing materialism, and rejecting p-zombies or epiphenomenalism.

The problem is Campbell's law (or Goodhart's law):

The more any quantitative social indicator is used for social decision-making, the more subject it will be to corruption pressures and the more apt it will be to distort and corrupt the social processes it is intended to monitor."

This applies to more than social indicators. To illustrate, imagine that you were a school inspector, tasked with assessing the all-round education of a group of 14-year old students. You engage them on the French revolution and they respond with pertinent contrasts between the Montagnards and Girondins. Your quizzes about the properties of prime numbers are answered with impressive speed, and, when asked, they can all play quite passable pieces from "Die Zauberflöte".

You feel tempted to give them the seal of approval... but they you learn that the principal had been expecting your questions (you don't vary them much), and that, in fact, the whole school has spent the last three years doing nothing but studying 18th century France, number theory and Mozart operas - day after day after day. Now you're less impressed. You can still conclude that the students have some technical ability, but you can't assess their all-round level of education.

The Turing test functions in the same way. Imagine no-one had heard of the test, and someone created a putative AI, designing it to, say, track rats efficiently across the city. You sit this anti-rat-AI down and give it a Turing test - and, to your astonishment, it passes. You could now conclude that it was (very likely) a genuinely conscious or intelligent entity.

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Logic: the science of algorithm evaluating algorithms

6 Christian_Szegedy 22 February 2012 06:13PM

"Mathematical logic is the science of algorithm evaluating algorithms."

Do you think that this is an overly generalizing, far fetched proposition or an almost trivial statement? Wait, don't cast your vote before the end of this short essay!

It is hard to dispute that logic is the science of drawing correct conclusions. It studies theoretically falsifiable rules the lead to derivations which are verifiable in a finite amount of mechanical steps, even by machines.

Let's dig a bit deeper by starting to focusing on the "drawing correct conclusions" part, first. It implies the logic deals both with abstract rules: "drawing" and their meaning: "conclusions".

Logic is not just about mindless following of certain rules (that's algebra :P) its conclusions must have truth values that refer to some "model". Take for example De Morgan's law:

not (a and b) = (not a) or (not  b).

It can be checked for each four possible substitutions of boolean values: a = false, b = false; a = false, b = true; .... If we agreed upon the standard meaning of the logical not, or and and operators, then we must conclude that the De Morgan's rule is perfect. On the other hand: the similar looking rule

not (a and b) = (not a) and (not b)

can be easily refuted by evaluating for the counterexample a = false, b = true.

Generally: in any useful mathematical system, logical conclusions should work in some interesting model.

However, in general, total verifiability is way too much to ask. As Karl Popper pointed out: often one must be satisfied with falsifiability of scientific statements as a criterion. For example, the following logical rule

not (for each x: F(x)) <=> exists x : not F(x)

is impossible to check for every formula F.  Not directly checkable statements include all those where the set of all possible substitutions is (potentially) infinite.

This observation could be formalized by saying that a mapping from abstract to concrete is required. This thinking can be made precise by formalizing further: logicians study the connection between axiom systems and their models.

But wait a minute: is not there something fishy here? How could the process of formalization be formalized? Is not this so kind of circular reasoning? In fact, it is deeply circular on different levels. The most popular way of dealing with this Gordian knot is simply by cutting it using some kind of naive set theory in which the topmost level of arguments are concluded.

This may be good enough for educational purposes, but if one in the following questions should always be asked: What is the basis of those top level rules? Could there be any mistake there? Falsifiability always implies an (at least theoretical) possibility of our rules being wrong even at the topmost level. Does using a meta-level set theory mean that there is some unquestionable rule we have to accept as God given, at least there?

Fortunately, the falsifiability of axioms has another implication: it requires only a simple discrete and finite process to refute them: an axiom or rule is either falsified or not. Checking counterexamples is like experimental physics: any violation must be observable and reproducable. There are no fuzzy, continuous measurements, here. There are only discrete manipulations. If no mistakes were made and some counterexample is found, then one of the involved logical rules or axioms had to be wrong.

Let's squint our eyes a bit and look the at whole topic from a different perspective: In traditional view, axiom systems are considered to be sets of rules that allow for drawing conclusions. This can also be rephrased as: Axiom systems can be cast into programs that take chains of arguments as parameter and test them for correctness.

This seems good enough for the the formal rules, but what about the semantics (their meaning)?

In order to define the semantics, there need to be map to something else formally checkable, ruled by symbolics, which is just information processing, again. Following that path, we end up with with the answer: A logical system is a program that checks that certain logical statements hold for the behavior of another program (model).

This is just the first simplification and we will see how the notions of "check", "logical statement", and "holds" can also be dropped and replaced by something more generic and natural, but first let's get concrete and let us look at the two most basic examples:

  1. Logical Formulas: The model is the set of all logical formulas given in terms of binary and, or and the not function. The axiom system consists of a few logical rules like the commutativity, associativity and distributivity of and and or, the De Morgan laws as well as not rule not (not a)=a. (The exact choice of the axiom system is somewhat arbitrary and is not really important here.) This traditional description can be turned into: The model is a program that takes a boolean formulas as input and evaluates them on given (input) substitutions. The axiom system can be turned as a program that given a chain of derivations of equality of boolean formulas checks that each step some rewritten in terms of one of the predetermined axioms, "proving" the equality of the formulas at the beginning and end of the conclusion chain. Note that given two supposedly equal boolean formulas ("equality proven using the axioms"), a straightforward loop around the model could check that those formulas are really equivalent and therefore our anticipated semantic relationship between the axiom system and its model is clearly falsifiable.
  2. Natural numbers: Our model is the set of all arithmetic expressions using +, *, - on natural numbers, predicates using < and = on arithmetic expressions and any logical combination of predicates. For the axiom system, we can choose the set of Peano axioms. Again: We can turn the model into a program by evaluating any valid formula in the model. The axiom system can again be turned into a program that checks the correctness of logic chains of derivations. Although we can not check verify the correctness of every Peano formula in the model by substituting each possible value, we still can have an infinite loop where we could arrive at every substitution within a finite amount of steps. That is: falsifiability still holds.

The above two examples can be easily generalized to saying that: "A logical system is a program that checks that certain kinds of logical statements can be derived for the behavior of another program (model)."

Let us simplify this a bit further. We can easily replace the checking part altogether by noticing that given a statement, the axiom system checker program can loop over all possible chains of derivations for the statement and its negation. If that program stops then the logical correctness of the statement (or its negation) was established, otherwise it is can neither be proven nor refuted by those axioms. (That is: it was independent of those axioms.)

Therefore, we end up just saying: "A logical system is program that correctly evaluates whether a certain logical statement holds for the behavior of another program, (whenever the evaluator program halts.)"

Unfortunately, we still have the relatively fuzzy "logical statement" term in our description. Is this necessary?

In fact, quantifiers in logical statements can be easily replaced by loops around the evaluating program that check for the corresponding substitutions. Functions and relations can be resolved similarly. So we can extend the model program from a simply substitution method to one searching for some solution by adding suitable loops around it. The main problem is that those loops may be infinite. Still, they always loop over a countable set. Whenever there is a matching substitution, the search program will find it. We have at least falsifiability, again. For example, the statement of Fermat's Last Theorem is equivalent to the statement that program the searches for its solution never stops.

In short: the statement "logical statement S holds for a program P" can always be replaced by either "program P' stops" or "program P' does not stop" (where P' is a suitable program using P as subroutine, depending on the logical statement). That is we finally arrive at our original statement:

"Mathematical logic is the science of algorithm evaluating algorithms [with the purpose making predictions on their (stopping) behavior.]"

Simple enough, isn't it? But can this be argued backward? Can the stopping problem always be re-cast as a model theoretic problem on some model? In fact, it can. Logic is powerful and the semantics of the the working of a programs is easily axiomatized. There really is a relatively straightforward  one-to-one correspondence between model theory and algorithms taking the programs as arguments to predict their (stopping) behavior.

Still, what can be gained anything by having such an algorithmic view?

First of all: it has a remarkable symmetry not explicitly apparent by the traditional view point: It is much less important which program is the model and which is the "predictor". Prediction goes both ways: the roles of the programs are mostly interchangeable. The distinction between concrete and abstract vanishes.

Another point is the conceptual simplicity: the need for a assuming a meta-system vanishes. We treat the algorithmic behavior as the single source of everything and look for symmetric correlations between the behavior of programs instead of postulating higher and higher levels of meta-theories.

Also, the algorithmic view has quite a bit of simplifying power due to its generality:

Turing's halting theorem is conceptually very simple. (Seems almost too simple to be interesting.) Goedel's theorem, on the other hand, looks more technical and involved. Still, by the above correspondence, Turing's halting theorem is basically just a more general version Goedel's theorem. By the correspondence between the algorithmic and logical view, Turing's theorem can be translated to: every generic enough axiom system (corresponding to a Turing complete language) has at least one undecidable statement (input program, for which the checking program does not stop.) The only technically involved part of Goedel's theorem is to check that its corresponding program is Turing complete. However, having the right goal in mind, it is not hard to check at all.

Sense, Denotation and Semantics

9 Vladimir_Nesov 11 August 2009 12:47PM

J. Y. Girard, et al. (1989). Proofs and types. Cambridge University Press, New York, NY, USA. (PDF)

I found introductory description of a number of ideas given in the beginning of this book very intuitively clear, and these ideas should be relevant to our discussion, preoccupied with the meaning of meaning as we are. Though the book itself is quite technical, the first chapter should be accessible to many readers.

From the beginning of the chapter:

Let us start with an example. There is a standard procedure for multiplication, which yields for the inputs 27 and 37 the result 999. What can we say about that?

A first attempt is to say that we have an equality

27 × 37 = 999

This equality makes sense in the mainstream of mathematics by saying that the two sides denote the same integer and that × is a function in the Cantorian sense of a graph.

This is the denotational aspect, which is undoubtedly correct, but it misses the essential point:

There is a finite computation process which shows that the denotations are equal. It is an abuse (and this is not cheap philosophy — it is a concrete question) to say that 27 × 37 equals 999, since if the two things we have were the same then we would never feel the need to state their equality. Concretely we ask a question, 27 × 37, and get an answer, 999. The two expressions have different senses and we must do something (make a proof or a calculation, or at least look in an encyclopedia) to show that these two senses have the same denotation.

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