On a few occasions, I have been accused of saying that there is no difference between the sciences and the arts. I am somewhat puzzled by this accusation, because I certainly do not see myself as holding this view. In fact I am somewhat dismayed that such an obviously false position could be attributed to me. I must conclude, therefore, that some of the things I have said must have led to a misunderstanding, probably because I did not state my position clearly enough.

My views on the so called "science" disciplines and the "arts" disciplines can be best expressed by taking physics and history as the exemplars of the two sets of disciplines:

There are a number of similarities and differences between physics and history. The stereotype of "science" as a totally certain, infallible body of knowledge arrived at through totally objective observation and deductive reasoning is not true of physics. Conversely, the stereotype of "arts" does not apply
to history either.

The similarities and differences between sciences and arts involve a number of parameters. If we consider all these parameters, what we get is a multidimensional spectrum, not a binary classification.

In spite of the obvious differences, it is possible and useful to develop an integrated perspective on knowledge as a whole that includes both physics and history.

In what follows, I will elaborate these statements.

Classification by the Domain

The traditional institutional division of university disciplines as "Sciences", "Social Sciences" and "Arts" is in terms of their subject matter.  The term "sciences" refers to "natural sciences", which includes physical sciences (physics, chemistry, astronomy, ...) and biological sciences (human, animal and plant biology). The term "social sciences" refers to the study of the human societies (economics, politics, sociology...), and "arts" refers to disciplines like history, literature, and philosophy. I find this division very strange and difficult to understand. Why is psychology, which is the study of the human mind, a "social" science"? The kind of theoretical linguistics I do (Chomskian linguistics) defines its subject matter as the study of the mental linguistic system of human beings. Why is this classified as a "social" science?

I would like to suggest that more meaningful classification of the domains would be along the following lines:

    A. Logico-mathematical systems: logic, mathematics, computational science, ...
    B. Physical systems: physics, chemistry, astronomy, physical engineering...
    C. Biological systems: medicine, zoology, botany, genetic engineering, ...
    D. Mental systems: psychology, Chomskian linguistics, ...
    E. Social systems: sociology, sociolinguistics, political science, economics, history, ...

From the classificaion above, it would follow that a subject like "geography" can belong to category A, C or D, depending upon the approach taken by the researcher. Physical geography would belong to category A, while human geography would belong to category C or D. Linguistics, as I have indicated, can be studied as D or E.

Classification by the Dimension: historical vs. ahistorical

Another parameter of classification involves the temporal/non-temporal dimension. Any system can be studied either in terms of its evolution (changes in time) or in terms of its state at a given point of time. I will use the terms "historical" and "ahistorical" for these two approaches. (An alternative terminology would be diachronic nd synchronic.) Big bang theory, which is a theory of the evolution of the universe, is a historical, while quantum theory and relativity theory are a historical. Both belong to the physical domain. Developmental biology and evolutionary biology (biological domain) are historical, while physiology and anatomy (biological domain) are ahistorical. Language acquisition (biological domain) is historical, while the (Chomskian) study of language structure (mental domain) is ahistorical. The discipline called "history" represents the historical approach to the social domain, while sociology, economics, and politics represent the ahistorical approach to the social domain.

Why , then, is history grouped under "arts" and sociology under "social sciences"? Why is the history of the species grouped with the sciences while the history of nations is grouped with the arts? To answer this question, we should examine the methodology rather than the domain or approach.

Methodology of constructing and evaluating knowledge

The methodology of knowledge construction and evaluation involves a number of parameters.
Let us take a look at some of them.

Empirical vs. non-empirical.

Empirical disciplines make claims about what is true about the world; non-empirical disciplines do not. Physics, chemistry, biology, sociology, economics, and history are empirical disciplines, while logic, mathematics, theology, law, normative aesthetics and normative moral philosophy are non-empirical. [Point: with the exception of mathematics and computational science, science disciplines pursue empirical knowledge. However, empirical knowledge is pursued by arts disciplines as well.]

Mathematical vs. non-mathematical

General principles in subjects like physics are expressed in the formal language of mathematics. In contrast, general principles in subjects like evolutionary biology, sociology and history are not.
[Point: mathematicalizability is not a necessary condition for science.]

Quantitative vs. qualitative

Subjects like physics rely largely on quantitative data/observations, which also call for quantitative
reasoning. Subjects like chemistry and biology use a mixture of quantitative and qualitative data/observations. Subjects like Chomskian linguistics and history use qualitative data/observations, and hence qualitative reasoning ("Data" in history are called primary"sources"). The use of quantitative data and reasoning in subjects like sociology, economics and psychology depends upon what kinds of sociology, economics, and psychology one is pursuing.
[Point: "science" does not necessarily mean "quantitative".]

Experimental vs. non-experimental

The empirical bases of subjects like physics and chemistry are typically experimental findings. In contrast, the empirical bases of subjects like astronomy and history is non-experimental.
[Point: "science" does not necessarily mean "experimental"]

Amalgamative vs. non-amalgamative knowledge

If you look at the history of the notions of atom and element from the Greek times to the modern times, you will get a picture of a large community of people retaining some of the ideas of the past, rejecting some of the other ideas, modifying yet other ideas, and finally adding new ideas to the pool, such that knowledge evolves in a manner very similar to biological evolution.

This strategy of amalgamation/integration is also a part of disciplines like history and linguistics. As far as I can tell, it is not a striking feature of, say, philosophy of literary criticism where knoweldge tends to be spread in a horizontal direction.  (Please correct me if I am wrong.)
[Point: science disciplines involve amalgamative knowledge, but so do some of the arts disciplines.]

Revisable vs. unrevisable

A theory in empirical disciplines like physics is revisable in the sense that an established theory or pieces of a theory can turn out to be wrong at a later stage. (e.g. Dalton thought that atoms were indivisible, and that a molecule of water has one atom of oxygen, but subsequent science rejected these hypotheses.] In contrast, mathematical theorems are non-revisable in the sense that a mathematical theorem, once proved, cannot be disproved. (I am using "revisable" in the same sense as "defeasible".) We can find evidence for theories in physics, but they cannot be proved. As far as I can see, theology is unrevisable, since the scriptures on which theological knowledge is based are finite and are unrevisable. In contrast to modern medicine, knowledge in Ayurveda (ancient system of medicine in India) appears to be unrevisable since the practitioners are not allowed to say that the classical text was wrong. (Forgive me if my impression of Ayurveda is incorrect.).

In subjects like philosophy and literary criticism, ideas of the past are not generally banished from the knowledge pool. Thus, Aristotle's philosophy and literary criticism continue living in the modern world, but most of Aristotle's physics and biology are replaced by more reliable ideas. With respect to this property, history behaves like physics.
[Point: with the exception of mathematics, knowledge in science disciplines is revisable, but revisability is not an exclusive property of science.]

Explicit vs. non-explicit  knowledge

The knowledge of an engineer is largely explicit. In contrast, the knowledge of a wine taster or a tracker in the forest is largely explicit. The knowledge of medical doctors is probably somewhere in between. [Point: knowledge in science disciplines is mostly explicit, but so is knowledge in most academic subjects.]

Explicit vs. implicit standards of evaluation

In physics, the criteria (standards/cannons) for evaluating the success of knowledge claims is relatively explicit (and hence shared by the community). These criteria include consistency with observations (correct prediction), internal consistency (between two propositions within a theory), external consistency (between the propositions of different theories), simplicity, generality, and so on. In contrast, the criteria of evaluating the success of knowledge claims is generally implicit in literary criticism. When different individuals or communities subscribe to different canons of evaluation, it results in what philosopher Kuhn called "incommensurability". The criteria of critical evaluation are largely explicit in a science subject like physics, but I have my doubts about science subjects like paleontology. [Point: Not all science disciplines have explicit criteria of critical evaluation.]

Differences among standards

Whether implicit or explicit, it is clear that knowledge claims in subjects like history are not evaluated on the basis of the correctness of predictions or simplicity, unlike knowledge claims in physics. Evaluation of knowledge claims in medicine and biology do involve correctness of predictions, but it is my impression that these subjects do not resort to the simplicity criterion. (Again, forgive me if this impression is incorrect.).
[Point: Even within science disciplines, we may find differences in the standards of critical evaluation.]

What is "Science"? Back to Physics vs. History

Is "History" a "science"? Can history be studied using the strategies of physics? The answer to the question depends on what we mean by the word "science". Clearly, there are huge differences between the two subjects with respect to the domain, approach, and methodology. However, there are also a number of similarities. Depending on which set of features we choose as the defining features of science, we can get either "yes" or "no" as an answer.

Perhaps it is useful to ask a different question. If you have an undergraduate degree in physics, can you be said to have imbibed (a part of) science? The answer depends upon how we use the word "science". Take, for instance, the following alternative definitions:

    Sense 1: Science =  a body of knowledge claims that the scientific community has
                                  accepted as correct.
    Sense 2: Science = a way of knowledge building and knowledge construction that
                                 involves   the skeptical and tentative attitude towards knowledge,
                                 willingness and ability to critically evaluate knowledge claims, and
                               willingness and ability to revise knowledge on the basis of
                                 new experience.

Under sense 1, a physics major has imbibed a part of science. Under sense 2, however, having a degree in physics is not sufficient for imbibing science. I have an undergraduate degree in physics, but I learnt nothing about science in sense 2 from my physics education. Furthermore, the majority of "science" graduates that I have come across are scientifically"uneducated" in science with respect to sense 2.

Let me raise one more question. With respect to sense 2, which subject is more amenable to the teaching of science, history or physics? My own personal choice would be history. This may sound preposterous to you, but please reserve your judgment and reflect on it for a while. If you accept the proposition that I am not a lunatic or an idiot, there must be a grain of truth in what I am saying.  [Why I subscribe to this idea is a different topic.]