Philosophy of Science

Deduction
All swans are white.
A is a swan.
Therefore, A is white.

Induction
I observe many swans, and all the swans that I have seen are white.
A is a swan.
Therefore, A is white.

Abduction or Inference to the best explanation
All swans are white with long necks.
A is white with a long neck.
Therefore, A is a swan.

Falsification
I hypothesize that all swans are white.
A is a black swan.
The hypothesis is false.

Falsifiability
I have a theory that all swans are white.
I could, in theory, find a black swan.
The theory is scientific.

I have a theory that all swans are either white or not white.
I could never find a swan that is neither white or not white.
The theory is not scientific.

Hypothetico-deductive model
Without observing any swans, I hypothesize that all swans are white.
I therefore predict that all swans are white.
I then seek to observe non-white swans and failure to find any would corroborate my hypothesis.

(Bayesian) probability
My degree of belief that all swans are white is 0.95.
In the face of new evidence, I will update my degree of belief.

Problem of induction
The principle of induction worked successfully on occasion x₁.
The principle of induction worked successfully on occasion x₂.
.........................................................................
The principle of induction worked successfully on occasion x_n.
The principle of induction always works.
The above argument — used to justify induction — relies on induction, so is therefore flawed.

New riddle of induction
Let the word "whack" be defined relative to an arbitrary time t as follows: An object satisfies the proposition "x is whack" if and only if it is examined before t and is white, or is examined after t and is black.
The problem is this. Assuming t has yet to pass, then every swan that has been observed is both white and whack. But surely we believe that swans discovered after t will be white, not whack. So it seems that a white and whack swan discovered before t is evidence only for "All swans are white", not evidence for "All swans are whack." The problem is to explain why.

Problems with falsification

• To verify that "all swans are white" requires that one falsifies an infinite number of hypotheses: "all swans are red", "all swans are blue", "all swans are green", etc.
• The existence of a single dirty white swan would erroneously lead us to reject "all swans are white" (there could be a problem with the evidence, not the theory).
• "There are white swans" cannot be falsified.
• "90% of swans are white" cannot be falsified.
• In practice, a theory will need to be augmented by auxiliary assumptions.

Popper's 'scientific method' requires an infinite number of hypotheses, yet is not robust, fails with existential statements, fails with probabilistic statements and fails in practical application due to the necessity of auxiliary assumptions. Poppers' falsification is not science at all, it is schoolboy logic.