Logical Positivism

Logical Positivism was an attempt to apply the powerful methods of symbolic logic in developing an Empiricist view of our scientific knowledge of the world. Empiricism is the view that all of our knowledge of the world is ultimately justified in terms of our sensory experience. The Positivists were heavily influenced by the work of David Hume, an 18th century British Empiricist.

Progress in symbolic logic towards the end of the 19th century in the work of Gottlob Frege and at the outset of the 20th century in the work of Bertrand Russell and Alfred North Whitehead provided the positivists with powerful new tools for developing Empiricist views of scientific knowledge. Opposed to Empricism is Rationalism, the view that at least some knowledge is either innate or known through reason alone. Mathematics had long served as the Rationalist's paradigm case of knowledge justified through reason alone. Russell and Whitehead, in their work Principia Mathematica made a strong case for grounding mathematical truths in terms of logic (and set theory). According to the argument of Principia Mathematica the only truths that need to be justified independent of experience are logical truths. And merely logical truths are trivial in the sense that they tell us nothing about the nature of the world (Any sentence of the form 'Either P or not P', for instance, is a basic logical truth. But, like all merely logical truths sentences having this form assert nothing about how the world is.)

We will consider four central projects taken on by the Positivists in developing their Empiricist view of scientific knowledge. These are (1) the demarkation problem, the problem of distinguishing science from non-science, (2) developing a view about what a scientific theory is, (3) developing views about what laws of nature are and how laws are known, and (4) giving an account of scientific explanation. The Positivists utilize the resources of symbolic logic in each of these projects.

1) The Demarkation Problem

Among the main tasks the Positivists set for themselves was that of distinguishing legitimate science from other rather suspect fields and methods of human inquiry. Specifically, they wanted to distinguish science from religion, metaphysics (concieved of as an attempt in philosophy to defend views about the nature of reality through reason alone), and pseudo-science like astrology. This had to be done without making the unobservable theoretical entities of genuine science unintelligible.

19th century speculative metaphysics involved attempts to reason about such obscure notions as 'the absolute', or the nature of 'the nothing'. Such metaphysics needed to be distinguished from genuine science. We also see appeal to obscure empirically contentless entities and forces in science such as the 'vital force' to explain life, or the 'dormative virtue' a mysterious power of opium to cause sleep. Such mysterious forces needed to be eliminated from genuine scientific explanation.

While metaphysics and talk of obscure forces in science were to be distinguished from genuine science, the Positivists needed to preserve a role for unobservable theoretical entities like atoms. You can have good empirical reasons for accepting the existence of some unobservable entities, like atoms, electrons, etc. The rejection of metaphysics and obscure forces must not undermine the legitimate role for theoretical entities.

The Positivists employed Empiricism in their proposed solution to the demarkation problem. Empiricism, again, is just the view that our sense experience is the ultimate source of justification for all of our factual knowledge of the world. The Postivists extend Empiricism to cover not just the justification of knowledge, but the meaningfulness of language. That is, they take the source of all meaning to ultimately be our sense experience. Only meaningful statements can be true or false. So, only statements whose meaning can ultimately be given in observational terms can be true or false. This doctrine about meaning is called the Verificationist Theory of Meaning.

In brief, the Verificationist Theory of Meaning holds that the significance of a claim is given in the possible observable conditions that would lead us to accept the claim as true or reject it as false. According to this view, words are meaningful only if they meet one of the three following conditions:

1) They are part of the language of logic and mathematics

2) They are observation terms defined by ostension (pointing). For example "By 'blue' I mean these things have in common (pointing at various blue things)"

3) They are theoretical terms defined in terms of observational terms plus logic and math by 'Correspondence Rules'.

Correspondence Rules have the following form: For all x, x is T if and only if x is O. In a correspondence rule, T will be a theoretical term and O will be a complex predicate that defines that theoretical term in observational terms. For example "a conductor is in a state of 'electrical charge' iff if an electrical meter were attached to it, the meter would register voltage".

According to the Positivists, only legitimate scientific discourse and logical analysis of scientific discourse will count as meaningful on the Verifiability theory of meaning. On this view, all of philosophy is replaced by the logical analysis of scientific discourse. Philosophy (other than that aimed at the logical analysis of science), pseudo science, religion, literature etc. are, strictly speaking, meaningless. Being meaningless, religion, pseudo science, literature etc. is neither true nor false. While these things cannot be true or false, according to Positivist's criteria for meaningfulness, they may provide helpful expressions of human emotions, attitudes towards life, etc.

2) The Positivists Account of Theories

Understanding the Positivists view of theories requires that we say a few things about formal languages. The symbolic logic developed in Russell and Whitehead's Principia Mathematica is a formal language. Computer languages are also formal languages. A formal language is precisely specified artificial language. A formal language is specified by doing three things:

1) identifying the languages vocabulary.

2) identifying what counts as a well formed expression of that language.

3) giving axioms or rules of inference that allow you to transforming certain kinds of well formed expressions into other kinds of well formed expressions.

Scientific Theories are formal languages according to the Positivists. A theory consists of the formal language of first order predicate logic with quantifiers (the logic developed first by Frege and then in greater detail by Russell and Whitehead) supplemented with correspondence rules and statements of laws.

3) The Positivist's Account of Laws

According to the positivists, scientific laws are statements of regularity having the following form

For all things x, if x is P, then x is Q

The quantifier phrase "for all things x" should be understood as ranging over things in the very broadest sense. That is, x can refer to any entity whatsoever. So, to say that it is a law that the speed of light is 186,000 miles per second is to say:

For all things x, if x is light (electromagnetic radiation), then x travels at 186,000 miles per second.

We have now identified the logical form of laws as general exceptionless regularities. But we need to fill in some constraints on their content. Not every claim with the logical form attributed to laws above counts as a law. For instance, "all of the coins in my pocket are dimes" has the logical form we've attributed to laws. But this sentence does not express a law of nature. To fix this problem, we can specify that the terms given in laws make no reference to specific things places or times. The term 'my pocket' in "All of the coins in my pocket are dimes" refers to a specific thing. So, with this added condition, claims about the coins in my pocket will not count as laws. We will, however find other counterexamples to this account of laws when we consider objections to positivism.

4) The Positivist’s Account of Explanation

The Logical Positivist Carl Hempel developed the Deductive Nomological model of explanation. According to this view of scientific explanations, an explanation has the form of a deductively valid argument where the fact to be explained, the explanandum, occupies the position of the conclusion and the premises consist of laws and statements of conditions which in conjunction with the laws, deductively entail the explanandum. For example:

F = GM1M2/r2Newton's law of universal gravitation

The rock was released within the gravitational field of the earth.

The rock has mass of 1 Kg.

No forces prevented the rock from falling to the earth.

The rock fell to the earth