"Imagine some Scottish chauvinist settled down one Sunday morning with this customary copy of The News of the World. He reads the story under the headline, 'Sidcup Sex Maniac Strikes Again'. Our reader is, as he confidently expected, agreeably shocked: 'No Scot would do such a thing!' Yet the very next Sunday he finds in that same favourite source a report of the even more scandalous on goings of Mr Angus MacSporran in Aberdeen. This clearly constitutes a counter example, which definitvely falsifies the universal proposition originally put forward. ('Falsifies' here is, of course, simply the opposite of 'verifies'; and it therefore means 'shows to be false'.) Allowing that this is indeed such a counter example, he ought to withdraw; retreating perhaps to a rather weaker claim about most or some. But even an imaginary Scot is, like the rest of us, human; and we none of us always do what we ought to do. So what in fact he says is: 'No true Scotsman would do such a thing!'." -Antony Flew in "Evasion and Falsification"
The philosopher Antony Flew presents what is to be the "No True Scotsman" fallacy. If the reasoner re-characterizes the situation solely in order to escape refutation of the proposition, then this error is a type of ad hoc rescue of one's generalization.
All arguments or discussions are between at least two individuals or at least two positions. In all arguments, there are at least two positions being argued or discussed. Take an argument between an individual who believes that absolute physics of Newton is true & another individual who believes that relative physics of Einstein is true, or "there exists a law of nature" or "there doesn't exist a law of nature". The argument is based on two propositions, which are that "absolute physics of Newton is true" & "absolute physics of Newton isn't true". The argument is based on the foundation of P & ~P. But logic forbids that P & ~P are true, or forbids the truth of "absolute physics of Newton is true & absolute physics of Newton isn't true".
Structure of Discussion
(1) P; (2) ~P; (3) P&~P; (4) ~(P&~P); (5) Pv~P [Standard Notation of Symbolic Logic]
(1) p; (2) Np; (3) KpNp; (4) NKpNp; (5) ApNp [Polish Notation of Symbolic Logic]
Step One: An individual proposes that (1) is true. p.
Step Two: Another individual proposes that (2) is true. Np.
Step Three: Discussion between both individuals contain (3). KpNp.
Step Four: Discussions can't contain (3) because discussion follows (4). NKpNp.
Step Five: Discussions must contain either (2) or (3) because discussions follows (5). ApNp
Step Six: Examine if both (1) and (2) are Falsifiable.
The processes of discussion or arguments, so far, show that there is a problem to be solved by the individuals in the discussion. One of the propositions must be rejected & the argument doesn't show which proposition must be rejected. We may either reject "absolute physics of Newton is true" or we may reject "relative physics of Einstein is true"; We may either reject "there is a law of nature is true" or we may reject "there isn't a law of nature is true". But nothing shows which one, in the argument, is to be discarded as false. Is "relative physics of Einstein is true" false or is "there exists a law of nature is true" false?
No True Scotsman fallacy can't be committed when propositions are analytic and necessary. Analytic and necessary propositions are impossible to be false. No True Scotsman fallacy can be committed when propositions are synthetic and contingent, or so one would think.
There is a criterion of demarcation between empirical propositions and non-empirical propositions. Empirical propositions are synthetic and contingent & falsifiable. Non-empirical propositions are synthetic and contingent & not falsifiable. "Absolute physics of Newton is true" is an empirical propositions, so it is synthetic, contingent, and falsifiable. "There exists a law of nature is true" is a non-empirical proposition, so it is synthetic, contingent, and not falsifiable.
Empirical propositions can't be shown true & empirical propositions can be shown false. Non-empirical propositions can't be shown true & non-empirical propositions can't be shown false. But both propositions are synthetic and contingent, because they are both possibly true and possibly false. Both propositions can't be demonstrated that they are actually true instead of possibly true, but empirical propositions can be demonstrated that they are actually false instead of possibly true and non-empirical propositions can't be demonstrated that they are actually false instead of possibly false.
"Absolute physics of Newton is true" is possibly true and possibly false; It can't be demonstrated that it is actually true; It can be demonstrated that it is actually false; So "absolute physics of Newton is true" is falsifiable.
"There exists a law of nature is true" is possibly true and possibly false; It can't be demonstrated that it is actually true; It can't be demonstrated that it is actually false; So "there is a law of nature is true" isn't falsifiable.
Falsifiability can be summed up with Modus Tollens:
(1) If p then q :: Cpq or (p-->q)
(2) ~q :: Nq or ~q
(3) ~p :: Np or ~p
Here is an example, based on Flew's example, of Modus Tollens:
(1) No Scotsman are a sex maniac.
(2) Mr. Angus MacSporran is a Scotsman and a sex maniac.
(3) Therefore, Not all Scotsman are not sex maniac.
(1) 'No Scotsman are sex maniac' is logically equivalent to 'All Scotsman are not sex maniac'. No p are q is equivalent to All p are not q. One can't be true and the other is false, if one is true then the other is true or if one is false then the other is false. The truth value of one is dependent on the truth value of the other. They must have the same truth value, and it would be contradictory for them to have different truth values.
Falsifiability follows the logical form of Modus Tollens. Falsifiability works with a hypothesis and an observation. Falsifiability works with hypothesis that are possibly false, but works to show that the hypothesis is actually false. Falsifiability shows that a hypothesis is actually false by an observation being accepted as true and the observation contradicts the hypothesis.
(1) For all things, if a thing exists then the thing isn't a law of nature.
(2) There exists a thing, such that the thing exists and the thing is a law of nature.
(3) Not all things, if a thing exists then thing isn't a law of nature.
(1) is the hypothesis and (2) is the observation. Through Modus Tollens, one would have to accept (3). However, if we reject (2), then we wouldn't have to accept (3). However, the hypothesis presented in (1) isn't a falsifiable statement because only (2) can possibly show that (1) is actually false. But, (2) can't be obtained by falsifiability. So, we learn that we don't have to accept (3) by logical implication.
Some would object that you must accept (2) as obviously true or accept that there does exist a law of nature, thus you are committing the "No True Scotsman" fallacy.
But such a statement would be a non-metaphysical statement. We can't show that the statement is not only possibly true but also that it is actually true. If a law of nature exists is true, it can't be shown empirically that it is true. This is because such a thing being true is possible, but empirically impossible to show that actually true. And since it isn't an empirical proposition, it is a non-empirical statement. And non-empirical statements can't be shown false.
This is where the Crux of the No True Scotsman lies. It is between empirical statements & non-empirical statements. Or, to put another way, the crux is between scientific statements & metaphysical statements.
Falsifiability would only accept scientific statements to be placed within the premises of Modus Tollens inference. Premise 1 and Premise 2 must be scientific statements, so that neither premise has a metaphysical statement. If there is at least one premise is a metaphysical statement, then No True Scotsman can't occur.
Now moving back to Flew's example, we show this even further.
(1) No Scotsman are a sex maniac.
(2) Mr. Angus MacSporran is a Scotsman and a sex maniac.
(3) Therefore, Not all Scotsman are not sex maniac.
Suppose that (2) is a metaphysical statement and (1) is an empirical statement. It would follow that (3) doesn't have to be accepted. But some people would complain that (2) is obviously true and so you must accept (3) follows from (1). Thus, the No True Scotsman fallacy would be invoked when faced with a falsification & the individual is performing an Ad hoc rescue to escape the proof of falsity of statement.But no such fallacy has occurred, because the individual proclaiming that the fallacy has failed to recognize that one of the statements accepted is a metaphysical statement.
Conclusion:
S1: An individual proposes that (1) is true. p.
S2: Another individual proposes that (2) is true. Np.
S3: Discussion between both individuals contain (3). KpNp.
S4: Discussions can't contain (3) because discussion follows (4). NKpNp.
S5: Discussions must contain either (2) or (3) because discussions follows (5). ApNp
S6: Examine if both (1) and (2) are Falsifiable.
If (1) & (2) are falsifiable then not accepting (2) & (3) violates (4), so No True Scotsman Fallacy has occurred.
If either (1) or (2) aren't falsifiable then not accepting (2) & (3) doesn't violate (4), so No True Scotsman Fallacy hasn't occurred.
If neither (1) nor (2) are falsifiable then not accepting (2) & (3) possibly does violate (4), so No True Scotsman Fallacy might have occurred.
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