Logic: The 'is-ought' problem

A seemingly simple question:
Can we infer an ought statement from an is statement?

And one example of such derivation was given by amiya :

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EXAMPLE
Premises: 1. John eats chocolates.
2. John does what he ought to do.

Conclusion: Therefore John ought to eat chocolates.

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Neat indeed!
I appreciate the way the above example has been constructed.

However, if inference is being used in this question as in logic, then one should first state what logic is being used, what an is-statement is and what an ought-statement is.

First order logic, for example, does not have anything to do with the structure of statements except those introduced by its own connectives, quantifiers, inference rules etc.

Therefore, the discussion will not be meaningful until the terms involved in the question are defined. Or, at least, explained with some clarity.

Now, I will myself jump the gun. That is, I will add to this discussion without myself attempting what I have asked for (the definitions).

An ought-statement cannot be inferred unless there is an ought within the premises or in the rules of inference. This is, of course, obvious. Because, if the ought-clause is already there in a complex proposition, it may be possible to infer it in a valid way. But, if the premises do not contain either an implicit or an explicit ought-clause, there has to be a rule of inference that allows ought to be inferred from is.

Also, ought is about an imperative and is applicable where, seemingly, the opposite of what has been asserted as an ought is a likely course of action. On the face of it, a choice among various course of actions can be justified by inference only if the consequences or the circumstances related to choices can be arranged in some order of preference. This ordering is then a premise in our argument, and the inference would require, in addition to the aforesaid premise, another premise of the form: "The choice of action ought to be in accord with the most preferred item in the ordering (mentioned above)."

Or this last statement will be a rule of inferring the choice of action. But with this rule, we have a new species of logic. On this, I will say nothing further.

But, in ordinary english, let us be clear that the justification of a choice of action from is-statements has more to do with rationality than logic.

Inferences as to what a rational person would under the given is-premises itself involves a lot many unstated assumptions which implicitly depend upon some mutually agreed upon ordering of the kind mentioned above.

Metaphysics: Existence of Unobserved Events

Someone wrote:
"Just because we hear an alarm clock when we are in hearing distance of it doesnt mean that it still makes a noise when we can't hear it."
________________
That is a neat and sound argument. The question is whether it is correct to infer/hypothesize the existence/occurence of events that are not observed. Let us call such inferences by the name "inference X".

Let us begin with asking why we infer that events have happened/will happen even in the absence of observation. Irrespective of the nature of the real world, or whether there is any reality beyond our perceptions, etc. the inference of events without observation yields a simple and fairly consistent picture/theory of the world (of reality/of perceptions?) making it easy for us to comprehend and understand it. To this most of us will agree. Thus, we know the usefulness of the inference X. And, therefore, inference X can be used until it is falsified even though it may not be verifiable.

Now, having admitted the utility of inference X, are these inferences correct? Clearly, the answer will depend upon the verification of the inferred event. Since the observer has not directly perceived the event and only inferred it, he/she must depend upon other means of verifying. Then we are led to the question: what are the other sources (i.e., other than one's own perceiving something) on which one can rely on as an evidence to the occurence of some event ?

I will not attempt a reply to this question. Because an answer to it will vary according to what sources we trust? But let it be clear that holding perception of the event by oneself as a reliable evidence of the occurence of that event is questionable too. That is, I could just as well express the doubt: just because I hear an alarm clock does not mean that the alarm clock is making the noise. The doubt, as can be seen, will turn out to be important in case of observers with hearing aberrations.

However, in raising this doubt I am not merely thinking of some stray pathological cases. Philosophically, the doubt is even more important. The manner in which you resolve it determines the kind of picture/theory that you prefer to have about this universe. And the incorrectness of that theory will be determined if it leads to some incorrect fact (which in turn should be verified/falsified using the methods consistent with the theory being tested). Meanwhile, there is no denying the possibility of the existence of many competing theories. In some of these, the alarm clock will sound when you can't hear it. In others, it won't.

Logic: Affirming the Consequent

I will begin with a slightly edited quote from a discussion on modus ponens or affirming the consequent from www.ephilosopher.com.

------Start of Quote---------

ARGUMENT #1 (modus ponens):
Where A is any well-formed formula (WFF) and B is any WFF:
1) If A then B
2) A
3) Therefore, B


ARGUMENT #2 (affirming the consequent):
Where A is any WFF and B is any WFF:
1) If A then B
2) B
3) Therefore, A

Suppose, however, that A and B are the same WFF-- call it "S". The resulting argument looks like this:

ARGUMENT #3:

1) If S then S
2) S
3) Therefore, S

What is the best description of argument #3? Is it modus ponens, affirming the consequent, or something else?

----End of Quote----



Interesting question! First let me say something about the question itself.
It is obvious to everyone that arguments #1(modus ponens) and #2 (affirming the consequent) quoted above are templates wherein A and B stand for any two (not necessarily distinct) WFF. Determining whether argument #3 is derived from argument #1 or argument #2 is important only because in the former case it must be correct (because arg #1 is correct) but in the latter case it must be wrong (because arg #2 is wrong). Had both argument #1 and #2 been correct, the question would have been neither important nor interesting.

Argument #3 quoted above fits both the templates when A = B. And, therefore, the puzzle whether the third form of argument has been derived from the first or the second template cannot be resolved in favour of just one of these arguments. Since, resolving is required let us follow the following attempts which I will call solutions:

Solution 1: If one adds the restriction in argument #1 and argument #2 that A and B cannot be the same WFF then argument 3 is clearly something else. And then argument #3 could be called a simple tautology. In fact, as stated already nobody would bother to offer such an argument.

Solution 2,3: Similarly, the restriction mentioned above could be applied to just one of the arguments #1 or #2 and then argument #3 would be derivable from just one argument (the one to which the restriction has not been applied). In these cases too, the problem would be resolved.

However, I do not favour these solutions unless there are other grounds to add such restrictions too. Let us examine these grounds if they exist.

In so far as argument #3 is derivable from modus ponens, no problem arises. That is so because modus ponens is correct whether A=B or not. So we will assert that argument #3 is modus ponens.

What about the argument #2? Clearly, it is a wrong form of argument only when "B does not imply A". Then, any substitution of A and B with some WFF such that "B implies A" will allow the inference A and the argument will look like affirming the consequent. I say "look like" because the hidden "B implies A" has been employed. It surely may happen that "B implies A" takes the same form as WFF (1) or WFF(2) of the argument #3. With this in mind, I propose the following solution:

Solution Final:
Argument #2 should be modified as follows to be true in general:

--------------------
Where A is any WFF and B is any WFF such that "B does not imply A":

ARGUMENT #2 (affirming the consequent)

1) If A then B
2) B
3) Therefore, A
--------------------
With this modification, argument #3 is modus ponens.

Logic: The Wittgenstein problem

This is a problem which should have puzzled every person who has ever ventured into philosophy of any flavour.

The following is a slightly edited and altered text quoted from a post by Bollinger, which he calls The Wittgenstein problem.

"The central questions are:

1. How do we manage to coherently label the world into particular objects through the use of language?

2. (a) And if labelling is a purely conscious process then why can't I explain how I manage this labelling?
(b) In other words how can I not know something I am doing consciously?

This I call the Wittgenstein problem in honour of the great Austrian thinker who posed these types of questions in his work 'Philosophical investigations'."

(Before beginning, I must congratulate "Bollinger" at www.ephilosopher.com for a very clear statement of the questions.)

These are two beautiful questions that have always puzzled me. And I must admit that I am in no position to give a definite answer to them. I do agree that we, in general, manage to coherently label the objects we observe; and that we have difficulty explaining how we manage to do this labelling.

I think I encountered this problem quite a few years back when I started wondering about what to call a living thing. That was during my schooldays when I had started pondering over the subject of artificial intelligence and artificial life. To be able to create what could be termed living or to even explain the origin of life, one must have a clear conception of what a living thing is. Such a concept or definition I have failed to arrive at.

Similarly, one could consider even the simpler objects and still stumble upon the same hurdle. To define X as a class of all the objects that are labelled X serves no great purpose. Because this definition would not guide you whether a new object that you come across could be labelled as X or not. Also, such a definition will keep getting revised each time a new object (i.e., one that is not already in the class) is labelled X.

I will not go into detail of how the difficulty of explaining the method of labelling arises. Anybody who has given some thought to this subject will easily understand this and raise the above questions. However, a clearer idea of the problem can be obtained by reading the first post in the discussion on The Wittgenstein problem.

Let me repeat that I am not suggesting a solution. I will try to show one way in which it is possible for us to coherently label without managing to explain how.

Consider a very complex neural network N1 that is designed to be able to classify things which it may be able to do quite satisfactorily. Let N1 also have a feedback mechanism by which it can occasionally tell that its classification was wrong and, at times, it can make corrections too. But N1 is not designed to output the exact configuration of weights that allows it to do the classification. The result is that N1 can coherently classify the objects (and hence, label them) without being able to explain how it does so.

What are the lessons one can draw from N1? If our brains and the associated paraphernalia are designed/wired/evolved to coherently label things (among other faculties) but not to bother about the design then it explains how the two questions arise. The N1 example has been kept very simple to illustrate the essential elements only. Better examples can be formed without adding much.

However, N1 misses one part of the question completely. That is, "if labelling things is a conscious exercise, how can one not know how I label things".

The introduction of the term "conscious" (and its related forms) into the question necessitates understanding consciousness and its capabilities.

Consider a very complex neural network N-omega (many generations higher than N1) which can, of course, classify and label objects. N-omega can also do some maths. But what distinguishes N-omega from other generations of neural networks is that it also asserts an identity in its communication with its human users. Assume that this assertion of identity results due to its high level of complexity (I am not sure if that is possible).

It then follows from the design of N-omega that it can label things, and it asserts that it is conscious when it does such labelling. But it may still not know how its consciousness works. To be conscious of a process is quite different from understanding that process.

In stating all this I am not saying that this is how the brain works and hence the questions. What I am saying is that such questions can co-exist in certain scenarios, one of which is rudimentarily shown above.
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Conclusion
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1. The ability to coherently label things could be a result, among other things, of
(a) knowing explicitly the criteria to be followed in doing so and then using the classifying apparatus (brain, neural network, computer etc.) to algorithmically (or otherwise) put the object to the test of the given criteria, or
(b) only the structure and complexity of the classifying apparatus.

2. If the criteria is explicit, there is no difficulty in explaining how the coherent labelling is possible. But, if the labelling is a result of only the structure and complexity of the apparatus then it will be difficult to tell how the labelling is managed so coherently. The degree of difficulty should increase with the complexity. As you can see, this difficulty has nothing to do with being conscious of the process or otherwise.

Also, to be conscious of a process is quite different from understanding that process. Therefore, the only knowledge that can be inferred from being conscious of a process is the knowledge that one is conscious of that process. Being conscious alone does not imply any further knowledge about that process.
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Logic: Do fictional characters exist?

Recently, I was confronted with a question that can be briefly phrased as follows-:

--------Question
how to deal with things like Santa and purple cows in logic. If they do not exist, then how are we supposed to represent them in predicate logic.
--------end of Question

The following is an attempt at an answer.

There would be no problem here if we did not insist upon the "existence" of all entities for them to be true, etc. When I say that "the number 2461 exists", the existence implied is different from that which is implied by my saying that "in my pocket, a pencil exists". For the latter existence, the verification has to be done empirically in the spacetime of my pocket. But the existence of the number 2461 or any other is a matter of pure logic. That is, if 2461 ia an member of the class of numbers, then one might say it exists. This kind of usage is uncommon but I have introduced here with a purpose. Consider the following:

---------ILLUSTRATION 1:

X is an entity satisfying the following:
1. X belongs to the class A.
2. X belongs to the class B.

Then, does X exist? The answer can be given by looking for a member of the class A which is also a member of the class B. If such a member can be found then X exists, else it does not.

---------end of ILLUSTRATION 1

If you agree with the above illustration, then we can come to the question of the entity called Santa. To know what is Santa, we need to know the complete list of those attributes which when satisfied by an entity, the entity can be said to be Santa. Call this list of properties/attributes P. Then, to verify whether Santa exists or not one just has to look for an object that satisfies all those properties. If one finds any, Santa exists; otherwise, he does not.

The problem arises from the fact that when listing the attributes in P, one generally leaves a lot to be assumed. Suppose P included the attribute f: "Santa belongs to the class of characters in fictions" along with the other attributes, then depending upon what those other attributes are Santa may , or may not, exist. But if P included the attribute f': "Santa is not a fictional character" then one would probably assume that Santa's verification would require to look for him in the physical world.

To summarize the above, from the point of view of logic it is unnecessary to maintain a difference between entities depending upon whether they satisfy the attribute f ("is a fictional character") or its opposite f' ("is not a fictional character"). Therefore, there appears to be no reason why the fictional characters (that do not exist in the physical world) should be treated any differently from others. Also, they would not require a different representation in predicate logic unless the representation is unnecessarily made dependent upon the attribute f.

Fictional characters exist on the same footing as the concepts, ideas, etc. exist. The difference between fictional and physical begins to show when one moves from the world of pure logic to that of verification of existence. The verification could end up being entirely within logic as in the case of contradictions and tautologies, or it could cross the boundary of logic into the empirical sciences.