In common usage, people sometimes tend to use the words rational and logical somewhat interchangeably. The purpose of this post is to distinguish between these.


Logic is the set of rules that allows me to evaluate an arguement independent of its content, purely from its structure. Just as I use grammar to parse a sentence and determine the relationships between the words in the sentence, I use logic to parse an arguement and determine the relationships between the statements in the arguement. Just as a grammatical sentence may be meaningless (Colorless green ideas sleep furiously), a logical arguement may be meaningless or irrelevant. However, the analogy with grammar only goes so far. There are many different grammars and all of them are equally valid within the context of their application – a given language. Any consistently applied way of meaningfully combining words in a sentence forms a grammar. Grammar is a matter of convention. The same is not true of logic. The word itself has no plural. This is a striking fact. Think about it. It indicates that man cannot even conceive of a plural for logic. There can be no such thing as my logic vs your logic. Logic is the structure of coherant thought. It is a part of the mental apparatus that man is born with. It is implicit in the capacity to think. By implicit, I mean that I cannot choose to think illogically (though I may make mistakes). To identify mistakes in thinking, the implicit rules of logic need to be made explicit by identifying them. This is a science. Like all sciences, the science of logic also presupposes several things. In particular, it presupposes man’s ability to use logic (implicitly). Whether the word logic refers to the implicit set of rules or to the science which deals with identifying them depends on context. In this post, I am going to use the word logic to refer to the implicit set of rules.


Reason is the faculty of understanding and integrating sensory material into knowledge. Reason does not work automatically. To reason, man has to consciously choose to think and to direct his thoughts to achieve understanding. By directing thoughts, I mean preventing thoughts from wandering by staying focussed. Reasoning involves the use of logic. It also involves several other techniques. “Reason employs methods. Reason can use sense-perception, integration, differentiation, reduction, induction, deduction, philosophical detection, and so forth in any combination as a chosen method in solving a particular problem.” [Burgess Laughlin in a comment on an old post] Deduction obviously uses logic. I believe induction does too but the science on inductive logic is nowhere as well developed as it is on deductive logic. Sense-perception, integration and differentiation don’t use logic (Note: integration and differentiation refer to grasping the similarities and differences between various things). Reason then is not simply the faculty of using logic.


“Rationality is man’s basic virtue, the source of all his other virtues… The virtue of rationality means the recognition and acceptance of reason as one’s only source of knowledge, one’s only judge of values and one’s only guide to action.” [Ayn Rand, in The Virtue of Selfishness]

In the discussion that motivated this post, a colleague argued that if the use of reason does not guarantee correct decisions, it cannot be one’s only guide to action. A gut feeling or intuition might sometimes be a better guide to action. There are two separate issues here – the fact that the use of reason cannot guarantee correct decisions and the claim that intuition can be an alternative guide to action.

Consider intuition first. Intuition is an involuntary automatic evaluation of the available choices. There is no conscious awareness of the reasons for the evaluation. Intuition is a learnt response from previous experience. As such intuition is extremely helpful in any decision making process. However, the fact remains that in every voluntary decision – the sort of decision where there is enough time to reason – intuition is only one of the inputs to the use of reason. As long as I make a decision consciously and deliberately, reason remains the only guide to action. The only alternative is to evade the responsibility of a choice. Relying upon intuition is not irrational in itself. I might decide that I do not have sufficient knowledge to reach a decision and choose to rely upon intuition instead. As long as I identify the lack of knowledge, my decision is fully rational. Identifying the lack of knowledge (and hopefully doing something about it) will actually allow me to learn from the new experience and improve my intuitions for future use. Blindly relying on intuition – by default instead of by choice – will actually weaken my intuition in the long run. Intuition is one of the most valuable tools for decision making but it needs to be carefully cultivated by the use of reason for it to be good or useful.

It is important to stress that rationality (in the context of making a decision) involves the use of all my knowledge to the best of my ability. In particular, this includes knowledge of the time available, the relevance of prior experience and any known gaps in knowledge. It is this last aspect of rationality – the use of known gaps in knowledge – that is the motivation for the field of probability. Probability is about quantifying uncertainty by making use of all known information and postulating equal likelihood where no information is available. The consistent use of the equal likelihood postulate is at the heart of probability theory and it is what gives probability its precise mathematical characteristics. In modeling an outcome for an uncertain event, I start with a uniform distribution (every outcome is equally likely) and use available information to transform it into a more appropriate distribution. The parameters of the transformation represent a quantitative use of known information. The shape of the final distribution represent a qualitative use of the known information.

With this brief treatment of probability, I can now address the obvious fact that the use of reason cannot guarantee correct decisions. Consider an example. I have historical data for the exchange rate between a pair of currencies. I also have market quoted prices for various financial instruments involving the currency pair. To model the exchange rate at some future time with a probability distribution, I can use the historical data to establish the shape of the distribution and the market quoted prices to obtain the parameters of the distribution. If I had more information (say a model for other parameters that affect the exchange rate), I could incorporate that too. A decision based on such a model would be a rational decision. On the other hand, I could say that since the model does not guarantee success, I will simply use a uniform distribution (Ouch!! That is not even possible since the range for the exchange rate is unbounded. Let me simply restrict the range to an intuitive upper bound) with the arguement that the uniform distribution might actually turn out to be better. Yes, it might turn out to be better, but the arguement that it should be used is still invalid (Consequentialism is invalid and I am not going to argue this). Not all decisions can be formulated with precise mathematics like this, but the principle is the same. It is always better to use all my knowledge to the best of my ability.

Another aspect of the original discussion remains unaddressed – the claim that rationality is subjective. Since this post has already got long enough, I will just stress here that there is a difference between context-dependent and subjective.

Probability – 2

In a comment on my previous post arguing that probability is arbitrary, Stephen Bourque wrote 

Probability is an empirical measurement of an ensemble of events. It means: Given a set of N independent events, the probability of a specific event is, to a degree of certainty, the number of times the specific event occurred divided by the total N, as N becomes large. By “a degree of certainty,” it is meant simply that the uncertainty in the measurement can be made smaller and smaller by increasing N. (Since this is an inductive process, it has the characteristics of induction, including the requirement of objectively determining when N is large enough to achieve certainty of the probability measure.)

Let me work out the math to calculate the degree of certainty. Consider a coin tossed N times. Suppose that M tosses resulted in a ‘heads’ (H) outcome. To simplify the math (by keeping it in the discrete domain), suppose I know that the coin has been designed to have a “true” heads probability ‘r’ for a single toss of either ‘p’ or ‘q’. Let HM,N denote the event of obtaining M heads from N tosses. Let P(A/B) denote the conditional probability of A given B.

Using Bayes’ theorem,
P(r = p / HM,N) = P(HM,N / r = p) P(r = p) /

[P(HM,N / r = p) P(r = p) + P(HM,N / r = q) P(r = q)]


P(HM,N / r = p) = NCM rM(1-r)N-M


P(HM,N / r = q) = NCM qM(1-q)N-M

If one knows P(r = p), the probability of the true probability being p, one can calculate P(r = p / HM,N), the degree of certainty for the probability estimate of r = p given the empirical data. The problem is that to calculate the degree of certainty of a probability estimate based on empirical data, one needs another probability number. To take a concrete example, suppose I know that my coin has a ‘true’ probability of either 0.3 or 0.4 for a single toss. I toss the coin 100 times and get 33 heads, so that N = 100, M = 33, p = 0.3, q = 0.4. If I use P(r = 0.3) to be 0.5, then the degree of certainty works out to be 69.7 %. The problem is that the value of 0.5 for P(r = 0.3) is still arbitrary. It has no basis in empirical data.

One can extend this to the continuous domain, where r may take any value between 0 and 1. To get a degree of certainty measure, one will need a prior probability distribution for the “true” probability and this distribution will have to be arbitrary. Just as I used a value of 0.5 in my concrete example, one may take this distribution to be the uniform distribution. I have not worked out the math for this case, but it should be easy to do so.

Anyway, it turns out that as one increases the values of N and M proportionately, the degree of certainty for the probability estimate r = M / N, rises to 100% very fast irrespective of the arbitrarily chosen prior probabilities. Practically, this is a very useful feature and this is what Stephen refers to when he writes that the uncertainty in the measurement can be made smaller and smaller by increasing N. But does it change the epistemological status of probability calculations? I don’t think so. As long as N is finite – that is, always – the degree of certainty is arbitrary. At some level, probability calculations always depend on an arbitrary choice of equal likelihood. To see this, just consider Bayes’ theorem above. It uses a weighted average where the weights are prior (or unconditional) probabilities. These unconditional probabilities are usually themselves estimated with other empirical data. Regardless, the calculation of an average assumes an equality of significance of the numbers being averaged. My position is that this assumption of equality is an arbitrary assumption. By using more and more empirical data, one can drive this assumption deeper and deeper, but unless one develops a physical theory – a cause and effect relationship – one cannot get rid of it.

If you make x private…

T.R. asks a question that begins with “If you make education private”

The question should be the other way round, “if you make education <i>public</i>…”
Education is just a service rendered by some people (teachers, school administrators) for others (students). Like any other service, it has to be paid for in some form. The default is (should be) for the service beneficiaries to pay the service providers. The default is <i>not</i> to have a service public. My point is that you are starting from a socialist framework (where everything is public). But that is not a natural framework to start with. A framework (when it is explicitly created by interactions of men) needs justification. Your question already assumes that there is some justification to have education be public.
You should start from the natural state of affairs, where education like other services is a private service. Now ask “Should this service be made public?” Immediately several questions arise: How is this service (education) different in principle from other services? What sort of differences require a service to be public? Who decides what these differences are? What happens in the case of a disagreement? Note that none of these questions arise when the service is private. Individuals make all the decisions themselves, with no physical force being used.

Suppose, for the moment, that you find the answers to these questions. Several other questions now arise. What constitutes a proper education? Should mathematics be a part of this education? Should astrology be a part of this education? Should religious teachings be a part of this education? What sort of clothing is acceptable for students (or teachers)? What costs are acceptable? What compensation is acceptable for the service providers? Should parents who do not accept the public answers to these questions be allowed to teach their own children? Should they then still be taxed? Note that I am not making up any of these questions. They are all actual issues that have come up at one time or the other. There have been petitions claiming that maths should be optional. There has been a court case regarding the inclusion of astrology. The issue of teaching creationism (or intelligent design) keeps coming up in the U.S. There are court cases in places like France, U.K and Turkey about scarves, turbans and burkhas. There are teachers unions in some places in India. I remember reading about a teachers association in the U.S. that does a lot of lobbying in the government. There is an active homeschooling movement in the U.S. I remember there was a proposition about tax credits for homeschooling parents (I don’t know if it was passed). Again, note that none of these questions arise when the service is private. If a parent does not like a particular school, he can choose another one or maybe not choose any school at all.

Once you think it through, it is obvious that any answers (no matter what political process is used to arrive at it) to these questions will involve the initiation of physical force against individuals. You might argue that I am mixing up examples from the U.S. (a developed country) and India (a developing country). That India needs public education (even if it involves some force) if it is to develop. Note that (in its somewhat credible form) this is a variant of the benevolent dictator arguement (For the democratic form, look at today’s frontpage of The Times of India). The problem with that arguement is it ignores man’s nature and the conditions required for progress. Why is India a developing country (despite decades of public education) while the U.S. achieved near universal literacy with mostly private schools (according to this article in Wikipedia – “The school system remained largely private and unorganized until the 1840s. In fact, the first national census conducted in 1840 indicated that near-universal (about 97%) literacy among the white population had been achieved.”)? The benevolent dictator arguement mixes up causes and effects. Freedom is the cause, progress (of which education is an indicator) is the effect (look at the history of Europe for example). The two cannot be interchanged. India will remain a “developing” country until people realize the value of freedom. Just compare the results of 60 years of public education and 20 years of limited economic freedom. Which of the two have caused progress?

Social planning

In a response to a forwarded post, a friend made the following argument (I am putting only its essence and in my own words, since I have not taken permission to make it public)

Market forces can produce outcomes that are worse off for everyone in the system. A social planner can, (in some cases at least) improve on the efficiency of the market. Pigouvian tax is an example.

In his response, he acknowledges that it might be difficult in practice for the social planner to obtain all the information required, but says that it would be very surprising if the social planners actions could never lead to efficiency improvement.

Consider the crux of the argument (emphasized above). There are three aspects to it that should be considered.

1) What are market forces? They are an abstraction that refers to all the judgements made by individuals interacting with each other under some conditions. If one is talking of a free market, these conditions are the absence of any coercion. Note that for the concept of coercion to be clear, a system of property rights (at the very least) needs to be in place (More on this in 3). If one is to prove the statement above (in a mathematical sense, which is what my friend meant), these market forces need to be modeled. This leads to 2.

2) How are choices evaluated? In actuality, every individual evaluates and weighs choices in a unique manner depending on the context of his knowledge, his hierarchy of values etc. This evaluation is neither necessarily rational nor quantitative. Yet if a mathematical result is to be obtained, both the evaluations and the decisions based on these evaluations need to be quantified. The evaluation (sometimes called “utility”) is quantified by assigning a monetary value to every “variable”. The decision making process is quantified by assuming that each individual acts to maximize utility (the sum of the monetary values of the results of all his choices).

3) What is the system? In actuality, the system is the set of laws that determine the kind of interactions that occur among individuals. In the model, this translates to assumptions that certain factors will remain constant over time.

Once these three aspects are modeled, one ends up with a set of equations that can be solved to determine what utility each individual will be able to achieve. The solution represents an outcome. In certain cases, feasible outcomes may exist that are better for each individual. (This usually happens when there are “externalities” which can be considered mathematically as non-linear effects). The most obvious problem with this argument is that it involves a huge number of variables, so man variables that no human (or computer) can solve the set of equations in any meaningful time. That however, is not my argument. My friend already acknowledges this fact and claims (plausibly) that in certain cases, a social planner may find an approximate solution that is still better than the free market one. My arguement is that: The fact that a (mathematically) feasible better solution exists, does not mean that it is possible to achieve in actuality. The reason is that the sort of actions required to achieve the feasible solution change the system (point 3) that was analyzed. In actual terms, such actions necessarily involve violating the property rights of individuals, thus changing the interactions between people, the monetary values they attach to different choices and the strategies they adopt to maximize their values. In plain language, attempts to achieve the “optimum” solution are lost in a host of unintended consequences. The information that says a better solution is feasible exists not with any single individual but with a vast number of individuals. To put that information to use, even if a social planner is able to approximate it, he needs to communicate it to all the people who will need to act on it. But force (and social planning is all about force) is a very destructive way of communicating. Successful communication is done with persuation and persuation is what the free market is all about.

Now consider a much simpler moral argument. Every value that man achieves is a result of using his mind. And the essential requirement for the mind to work is freedom. When man is free to act as his mind instructs him to do and is responsible for the consequences of his actions, his mind works the best. When he is forced to act against the judgement of his mind, his mind becomes passive and he loses the motivation to use his mind (something that never figures in a mathematical model). In the most fundamental sense of the word good, force can never be good for man.

In his response, following my post on propaganda, my friend clarified that what he meant by propaganda was a one-sided presentation of an idea that does not consider all sides of an issue. The moral idea (in the paragraph above) when supplemented with the practical arguments and all the evidence of the past century becomes a fundamental political principle. And there is no other side to the issue left. As I wrote in this post, as long as one is unsure of something and has not integrated ideas into principles, it is good to be circumspect and consider all pros/cons of all sides of an issue. But on issues on which it is possible to have relevant principles, there is only one side. Fundamental principles do not allow any evaluation in shades of gray. Whether I should be free to act on my own judgement or whether I should allow a social planner to force his whims on me or whether I should become a social planner myself is not an issue where I will weigh the pros/cons of the alternatives.

Finally for the sake of completeness, consider the Pigouvian tax/subsidy to correct for externalities. The first point to be noted is that most externalities go away when property rights are properly defined and implemented. And in fact a tax on pollution is actually quite close to what a property-rights solution to the “problem” of pollution would be. As for the subsidy on education, one can just look at the state of subsidised public education in the U.S. to see how it works. Externalities cause problems in model-based economics because they are non linear effects and most models are linear (eg, price = marginal utility) (for the simple reason that non-linear models are untractable). Man’s mind is not a linear device however, and a linear model does it no justice. Just think of the salesman who negotiates a price (= marginal utility?) or the investor who depends on a virtuous cycle where increase in supply creates a non-existant demand to recover his investment.

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