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SCIE1000 Python

§7.7. POPPERIAN SCIENCE Lecture 19: Third Philosophy Lecture
According to Popper, science proceeds by conjectures (hypotheses) and refutations (de- ductive inferences that show the hypothesis to be false) — hypothesis and deduction (hence the name hypothetico-deductivism. Rather than trying to prove universal laws that constitute scientific knowledge by induction from observational evidence, as the in- ductivist would have us believe, science is in the business of proposing bold conjectures as laws describing what we see around us and then subjecting these conjectures to stringent tests to see if the law can withstand attempts to falsify it (hence the alternative name falsificationism). If it can withstand the tests then, though we are not in a position to claim it as true (when are we ever in such a position? — this is the force of the problem of induction) we may claim it as the best “law” currently available and so rational to believe, at least for the time being.
The popular notion that science is a body of established fact is entirely mistaken; con- jectured scientific laws are, at any given time, those which have not yet been shown to be false and, on balance, are the best we currently can conceive of to account for the nature of the world around us.
7.7.2 Inductive Proof vs. Falsification
Popper’s proposed solution to the problem of induction derives its force from a logical difference between the (supposedly inductive) proof of a universal claim and the (clearly deductive) falsification or disproof of a universal. Consider the claim ‘All metal expands when heated’. No number of instances of metals expanding when heated can be sufficient to prove the claim true yet a single instance of a metal not expanding when heated will be enough to prove the claim false — i.e. “falsify” it. The claim says that all As are B yet, if we can find a single A that is not B then the universal claim will be shown to be false. Unlike inductive proof, this is uncontroversial.
The falsity of a universal statement can be conclusively inferred from certain singular (particular) statements. Thus there is a clear and uncontroversial logical relation between singular and universal statements: singular statements, though they cannot inductively prove universal ones, can falsify them. It is this justifiable logical relation that Popper

§7.7. POPPERIAN SCIENCE Lecture 19: Third Philosophy Lecture
relies on to explain how it is that observation and scientific data relates to scientific laws
and theories.
Laws are not justified by being proved by the data, they are justified by being not disproved by the data.
Falsifiability
Let us look more closely at just what we mean when we describe some statement as falsifiable. The following claims are all falsifiable in the Popperian sense:
1. ‘It never rains on Wednesdays.’
2. ‘All metals expand when heated.’
3. ‘Heavy objects fall straight downwards if not impeded.’
4. ‘When a ray of light is reflected from a plane mirror, the angle of incidence is equal to the angle of reflection.’
Claim (1) can be falsified if the world is observed to be such that it rains on some Wednesday. Claim (2) can be falsified if at some particular time a metal is observed not to expand under heating. Claim (3) can be falsified if a heavy object, which was not impeded in any way, was observed not to fall straight downwards. Claim (4) would be falsified if some ray of light at some time were observed to be reflected from a plane mirror in such a way that the angle of incidence was different from the angle of reflection.
The definition of “falsifiability” then is the following: an hypothesis is falsifiable if there exists a logically possible observation statement or set of observation statements that are inconsistent with it — i.e., which if established as true would falsify the hypothesis.
Scientific laws then (given the requirement that they be falsifiable) are testable in spite of their being unprovable; they can be tested by systematic attempts to falsify them.
Examples of claims that are not falsifiable are:
Logical Truths — e.g. ‘Either it is raining or it is not raining.’ Definitional Truths — e.g. ‘All bachelors are unmarried males.’ Mathematical Truths — e.g. ‘2 + 2 = 4’
Certain Modal Truths — e.g. ‘Luck is possible in sporting situations.’
This latter example is the stock-in-trade of many fortune-tellers and newspaper astrolo- gists. Such claims can never be shown to be false because they are not capable of being falsified.

§7.7. POPPERIAN SCIENCE Lecture 19: Third Philosophy Lecture As further examples of seemingly unfalsifiable claims, consider the following:
1. ‘The cosmos doubled in size overnight.’
2. ‘God created the earth 6,000 years ago complete with fossil record.’ (To test our faith perhaps — in this way, it is argued, we can consistently argue for creationism.)
3. ‘The world came into existence only five minutes ago, complete with a “history”.’