It is fairly well-known that scientific theories can be falsified or corroborated, but it is a far more intriguing fact that they cannot be truthified. In other words: while it is wholly possible to prove a scientific theory false (viz. disprove it), it is impossible to prove a scientific theory true. Discouraging as this latter could potentially be, rather than calling it quits we respond by interpreting any lack of disproof as a positive result and refer to it as corroboration.
Falsification via modus tollens
The rule of logic known as modus tollens states that given a conditional as well as the negation of its consequent, we are allowed to deduce the negation of its antecedent. In the case of falsification the antecedent is the scientific theory (T) and the consequent is an event (E) predicted by the theory. Subsequently, because the event is not observed (¬E) we are allowed to deduce the falsity of the theory (¬T):
T → E
¬E
∴ ¬T
Such a deduction is valid because the contrapositive (¬E→¬T) and the conditional from which it is derived (T→E) are logically equivalent [i.e. in a truth table both statements have identical truth values].
Fallacy of affirming the consequent
If instead the predicted event does end up being observed (E), although oftentimes in the mainstream media this is put forth as proof of the theory, it is actually not valid to deduce that T is true. The invalidity of that deduction is due to the fact that the converse (E→T) and the conditional from which it is derived (T→E) are not logically equivalent. To illustrate why, let A equal 'birds are flying' and B equal 'birds can fly'. In this case the conditional (A→B) is true whereas its converse (B→A) is not. In other words, the act of flying implies the ability to fly but not vice versa. Alternatively, its contrapositive ¬B→¬A [if birds cannot fly then birds are not flying] is true.
Corroboration: a tautological compromise
What is actually deducible when the event predicted occurs is the tautology "either the theory is true or it is false".
T → E
E
∴ T ∨ ¬T
What is significant about corroboration is that the observed evidence has not falsified the theory. However, since tautologies are true regardless of the truth value of their components, a corroboration constitutes a far weaker assertion − epistemologically speaking − than a falsification.
A Question of Interpretation
Why is it that logic allows us to verify the falsity of a scientific theory with the force of a deduction, and yet we are limited to mere tautology when attempting to verify its truth? Is there a reason that falsification is allowed to operate with the strength of modus tollens while truthification is not even allowed to exist?
It is interesting that logic so straightforwardly backs up the negative result in this case. It could be that logic is an inherently negative undertaking [essentially having its origins in negation] and this is why falsification comes so easily. Or it could simply be nature nudging us toward skepticism in the face of anything purporting itself to be scientific truth.
Either way, it is prudent to keep in mind that our methods of truth-verification and falsehood-verification with regard to scientific theories do not stand on equal ground, they are asymmetric. So if you hear that a theory has been disproved you ought to have no qualms about believing that, but if you hear that a theory has been proved then you can be sure that someone is greatly overestimating the power of corroboration.
Falsification via modus tollens
The rule of logic known as modus tollens states that given a conditional as well as the negation of its consequent, we are allowed to deduce the negation of its antecedent. In the case of falsification the antecedent is the scientific theory (T) and the consequent is an event (E) predicted by the theory. Subsequently, because the event is not observed (¬E) we are allowed to deduce the falsity of the theory (¬T):
T → E
¬E
∴ ¬T
Such a deduction is valid because the contrapositive (¬E→¬T) and the conditional from which it is derived (T→E) are logically equivalent [i.e. in a truth table both statements have identical truth values].
Fallacy of affirming the consequent
If instead the predicted event does end up being observed (E), although oftentimes in the mainstream media this is put forth as proof of the theory, it is actually not valid to deduce that T is true. The invalidity of that deduction is due to the fact that the converse (E→T) and the conditional from which it is derived (T→E) are not logically equivalent. To illustrate why, let A equal 'birds are flying' and B equal 'birds can fly'. In this case the conditional (A→B) is true whereas its converse (B→A) is not. In other words, the act of flying implies the ability to fly but not vice versa. Alternatively, its contrapositive ¬B→¬A [if birds cannot fly then birds are not flying] is true.
Corroboration: a tautological compromise
What is actually deducible when the event predicted occurs is the tautology "either the theory is true or it is false".
T → E
E
∴ T ∨ ¬T
What is significant about corroboration is that the observed evidence has not falsified the theory. However, since tautologies are true regardless of the truth value of their components, a corroboration constitutes a far weaker assertion − epistemologically speaking − than a falsification.
A Question of Interpretation
Why is it that logic allows us to verify the falsity of a scientific theory with the force of a deduction, and yet we are limited to mere tautology when attempting to verify its truth? Is there a reason that falsification is allowed to operate with the strength of modus tollens while truthification is not even allowed to exist?
It is interesting that logic so straightforwardly backs up the negative result in this case. It could be that logic is an inherently negative undertaking [essentially having its origins in negation] and this is why falsification comes so easily. Or it could simply be nature nudging us toward skepticism in the face of anything purporting itself to be scientific truth.
Either way, it is prudent to keep in mind that our methods of truth-verification and falsehood-verification with regard to scientific theories do not stand on equal ground, they are asymmetric. So if you hear that a theory has been disproved you ought to have no qualms about believing that, but if you hear that a theory has been proved then you can be sure that someone is greatly overestimating the power of corroboration.
To read more about this and other related phenomena, check out Aamrgan.