Karl Popper (1902-1994) had been a leading theoretician of the origin of scientific thought and its demarcation from non-scientific thought in his native Austria before he was forced to leave because of the Nazi ascension to power. After World War II, he first went to teach and research in New Zealand, and then became a professor of philosophy at the London School of Economics. His theory of science relied heavily on the following idea: a scientific theory it scientific because it has met attempts to refute it. Refutability is key to the notion of being scientific.
To fully understand Popper's point of view, some basics of what is known as sentential logic is needed. We are especially interested in this context with the logic of implication -- statements involving "if" and "then". Some preliminary definitions of terminology are required:
Statements, some of which are implications, can be combined to form arguments:
We must now identify, among the syllogisms involving "If A then B" as the first (or major premise), those that are valid and those that are invalid. This will then lead on to a discussion of how Popper applies logic to his theory of science.
Intuitively, that is to say from the point of view of common sense, the following type of syllogism is valid:
If I study hard, then I'll succeed
I study hard
Therefore, I'll succeed
The logical form of this argument is:
If A then B
A
Therefore, B
This type of argument is usually referred to by its Latin name, "modus ponens" (or the mode of affirming), or by its English name, "affirming the antecedent" -- since as you can see, the second premise affirms the antecedent.
Similarly, we should all readily agree that the following syllogism is valid:
If I study hard, then I'll succeed
I didn't succeed
Therefore, I didn't study hard.
The logical form of this argument is:
If A then B
not-A
Therefore, not-B
This type of argument is usually referred to by its Latin name, "modus tollens" (the mode of denying), or by its English name, "denying the consequent" -- since as you can see, the second premise denies the consequent.
These arguments are valid because we cannot possibly have a situation where the premises are true, yet (and simultaneously) the conclusion is false.
But there are syllogisms with an implication as its major premise which are invalid. Consider:
If I work hard, then I'll be wealthy
I'm wealthy
Therefore, I work hard.
The problem here is that given the two premisses as true, it is possible that the conclusion could be false. Perhaps I don't work at all, but inherited my money from a wealthy relative.
The logical form of this argument is:
If A then B
B
Therefore, A
This type of argument is invalid and is termed, "the fallacy of affirming the consequent" -- since as you can see, the second premise affirms the consequent. This "mimics" the valid modus tollens argument form, but notice the significant difference: modus ponens affirms the antecedent, whereas the invalid form affirms the consequent.
A second invalid argument form is the following:
If A then B
not-A
Therefore, not-B
An example of this in words is:
If I win the lottery, then I'll be happy
I didn't win the lottery
Therefore, I'm not happy.
Again, the problem is that I may indeed be happy, but for reasons other than having won the lottery; for example, I may not have won the lottery, but still be happy because I did well at my studies.
This type of argument is invalid and is termed, "the fallacy of denying the antecedent" -- since as you can see, the second premise denies the antecedent. This "mimics" the valid modus tollens argument form, but notice the significant difference: modus tollens denis the consequent, whereas the invalid form denies the antecedent. We now have the following tableau of valid and invalid forms:
|
Modus Ponens
If A then B (major premiss) |
Affirming the Consequent
If A then B |
|
Modus Tollens
If A then B |
Denying the Antecedent
If A then B |
Now we can go on and see how Popper uses these logical conclusions to inform his theory of science.
Commonly, we assume a scientific theory is "true" because it has been "proven" through experiment. Popper made central to his theory the critique of a logical fallacy in this argument: If theory A predicts phenomenon p, and phenomenon p is observed through experiment, this does not "prove" that A is true. The reasoning is formally as follows:
If A then p;
p;
Therefore A.
This is a fallacy of reasoning, for p might occur for reasons other than A. However, Popper pointed out that the following reasoning is valid:
If A then p;
not-p;
Therefore, not-A.
In other words, a theory can be refuted by a negative instance of its predictions, but cannot be proved by positive ones. In this latter case, the theory can only be "confirmed" (and the more often predictions are true, and the more surprising they are, the more the theory is confirmed; even if it can never be fully proven).
Consequently, Popper concluded:
In Popper's view, a scientist tests his or her theory by subjecting it to attempts to refute it. If the theory stands the test -- is not refuted -- it can be provisionally accepted; the more so if the test is difficult. But a scientific theory is never fully proved -- only mathematical, not scientific propositions can be proved, and even they are dependent on the axiom system upon which they are based.
When a scientific theory is refuted, it is time to replace it. The cycle of provisional acceptance and eventual refutation make for theory progress.