Brief Notes Toward Understanding Kuhn's Importance

I. The Verification Principle

A. J. Ayer, Language, Truth, and Logic:

We say that a sentence is factually significant to any given person, if and only if, [she or] he knows how to verify the proposition which it purports to express—that is, if [she or] he knows what observations would lead [her or] him, under certain conditions, to accept the proposition as being true, or reject it as being false.

The only meaningful language is either empirically verifiable or is a mathematical tautology. Rudolf Carnap's title The Elimination of Metaphysics through Logical Analysis of Language says it all.

Ludwig Wittenstein, Tractatus Logico-Philosophicus:

4.01 A proposition is a picture of reality. A proposition is a model of reality as we imagine it.

4.02 We can see this from the fact that we understand the sense of a propositional sign without its having been explained to us. 

4.021 A proposition is a picture of reality: for if I understand a proposition, I know the situation that it represents. And I understand the proposition without having had its sense explained to me. 

4.022 A proposition shows its sense. A proposition shows how things stand if it is true. And it says that they do so stand. 

4.023 A proposition must restrict reality to two alternatives: yes or no. In order to do that, it must describe reality completely. A proposition is a description of a state of affairs. Just as a description of an object describes it by giving its external properties, so a proposition describes reality by its internal properties. A proposition constructs a world with the help of a logical scaffolding, so that one can actually see from the proposition how everything stands logically if it is true. One can draw inferences from a false proposition. 

4.024 To understand a proposition means to know what is the case if it is true. (One can understand it, therefore, without knowing whether it is true.) It is understood by anyone who understands its constituents.

At the heart of the logical positivists concerns is what is commonly called the "observational- theoretical" distinction. For the positivists, only the empirical observations of the sciences can said to be actually meaningful; their theories can strictly speaking "meaningless," though they refer to real objects and actions, so they have a utility abut them. This is often called an instrumental view of science. A variation of this is Carnap's later argument for justificationism. Granted that a theory can not be verified entirely, we are nonetheless justified or "confirmed" in holding it to be true based on the high degree of experimental support.

II. The Falsification Principle

Karl Popper pointed out,  however, that the verification principle itself cannot be verified! Likewise, something declared probably true always contains the possibility of later disproof. Instead, he proposed in its place a principle of falsification.

Karl Popper, Conjectures and Refutations:

  1. It is easy to obtain confirmations, or verifications, for nearly every theory- if we look for confirmations.
  2. Confirmations should count only if they are the result of risky predictions; that is to say, if, unenlightened by the theory in question, we should have expected an event which was incompatible with the theory  - which would have refuted the theory. 
  3. Every 'good' scientific theory is a prohibition: it forbids certain things to happen.  The more it forbids, the better it is. 
  4. A theory which is not refutable by any conceivable event is not scientific.  Irrefutability is not a virtue of a theory (as people often think), but a vice. 
  5. Every genuine test of a theory is an attempt to falsify it, or to refute it.  Testability is falsifiability; but there are degrees of testability: some theories are more testable, more exposed to refutation, than others; they take, as it were, more risks. 
  6. Confirming evidence should not count except when it is the result of a genuine test of the theory; and this means that it can be presented as a serious but unsuccessful attempt to falsify the theory…
  7. Some genuinely testable theories, when found to be false, are still upheld by their admirers - for example by introducing ad hoc in such a way that it escapes refutation.  Such a procedure is always possible, but it rescues the theory from refutation only at the price of destroying, or at least lowering its scientific status.

III. Conventionalism

Pierre Duhem has pointed out that what we often call a "single" theory in science is really built around a network of auxiliary assumptions. The central theory forms a core which then has a whole series of assumptions following from it. Given that some conclusion is derived from a set of premises (e.g. P1. . . . Pn, therefore C), even if the conclusion is found to be false, it doesn't follow that the central core is also false since the problem may be at any point along the chain of premises. In other words, a negative result for a whole theory system need not force a scientist to reject the central theory but simply to rework the chain of assumptions. So can any theory in science finally be falsifiable? The conventionalists would say, no. Theories are adopted not on the basis of their being true or false but on the basis of their observing well the conventions of science--simplicity, coherence, ingenuity, subsumptiveness, reproducibility, etc. 

IV. Conceptions of Explanation

  • Inferential: scientific explanations are logical inferences of either an inductive or deductive nature in which one hopes to provide grounds for believing the conclusions reached. These conclusions can either be of a universal or a statistical nature and are testable by experiment or by observation. 
  • Causal: while they may involve deductive or inductive arguments and may involve some explanatory claims, scientific explanations are more about understanding the underlying causal mechanisms that produce universal or statistical patterns.
  • Erotetic: scientific explanations should be understood as answers to why-questions. This involves contrasting one class of objects or phenomena with another and offering an explanation for the relevant differences.
  • Compositional: a scientific explanation is offered based on the properties of various parts of an object.
  • Evolutionary: a scientific explanation is offered by analyzing the development of objects over time, including objects within a larger system that has been successfully analyzed from a temporal framework.
  • Functional: a scientific explanation is offered by showing how a complex object or process organizes its simple component systems.
  • Transitional: a scientific explanation is offered by studying the transitional dynamic an object makes as it moves from one state to another.

V. Historical Models of Science

  1. Cumulative: Scientific fields develop through adding new knowledge to the accumulation of past knowledge. Scientific knowledge expands as new insights are added to the permanent stock of what is known.

  2. Evolutionary: Instead of a simple accumulation, new models replace older ones just as humans adapt to to their environments. New experimental testing leads to some results that contradict older ideas, and a survival of the fittest ideas ensues.

  3. Revolutionary: As theories change so do scientific fields--research programs, methods, goals, and the surrounding culture of scientific education. Scientific history is a series of revolutions in understanding and practice. Something like progress does occur over time, but there is never complete progress toward an absolute knowledge of the world.

  4. Gradualist: Yes, as theories change so do scientific fields, but these are rarely if ever revolutions that are incommensurable with previous theories. Rather, they are small changes in various fields of research that are often functionally independent, which impact each other over time. When this occurs, there are justifiable reasons for a field drawing from another field's models to self-correct its own.


Models of the Physical Universe


Ptolemaic Universe

Copernican Universe

Einstein & Space-Time

Quantum Mechanics

Calabi-Yu Manifold


"All manner of thing shall be well/ When the tongues of flame are in-folded/ Into the crowned knot of fire/ And the fire and the rose are one." -- T.S. Eliot, Little Gidding