In mathematical logic we have iff: if and only if. As an example of this for my classes I realised that in sworn oaths there are three statements for telling:

1: the truth,

2: the whole truth, and

3: nothing but the truth.

The first two of these I rewrite as follows:

Statement 1: If I say something, then that something is true.

Statement 2: If something is true, then I will say that something.

Together these two statements are enough, since they imply what you say if and only if it is true. Hence the third statement is superfluous.

So my questions is: why is this third phrase included in the oath?

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    Sometimes they just say "the whole truth and nothing but the truth". – Michael Hardy Sep 4 '17 at 17:33
  • The second two clauses clarify what was intended by the first clause which summarizes the commitment made by the person taking the oath. It is also a deliberate poetic and archaic phrasing intended to reflect its antiquity and authority. – ohwilleke Feb 21 '18 at 22:33

Your translation of the first statement is not correct. Saying that one promises to tell the truth is not saying that one promises to not tell a falsehood. If telling truth and telling falsehood are items labeled T and F, then this is a logical statement

~(T > ~F)

for ~ negation and > implication.

The combination of the first and third statements is necessary to obtain what you have called Statement 1, while the combination of the first and second statements is necessary to obtain what you call Statement 2.

It could also be argued that the first statement is not even necessary, as it is just a less strict version of the second statement (and a less desirable one at that, if one values the honest sharing of complete knowledge), but the redundancy does not harm the meaning or impact of the following statements.

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Your translations aren't actually statements in mathematical or formal logic, they are more akin to classical Aristotelian logic.

Vowing to tell "the truth" is subsumed under telling "the whole truth", and thus could be dispensed with. If you vow to tell the whole truth, then you vow that you will say everything that is true. That does not preclude also telling a falsehood. If you vow to tell nothing but the truth, then you vow that you not say anything untrue. Both of these conditions are desiderata for testimony.

Of course, you obviously cannot comply with the literal requirement to tell the whole truth. First, there may be things that you don't know which are part of the truth. Second, there are many truths that you know that are utterly irrelevant to the question. Compliance with the first part of the oath is not entirely required by law. The reason why you say something is that the law punishes people who lie under oath. The content of the oath is not itself the bearer of the punishment for perjury, and actually can take many shapes. See this or this. Wording is recycled, until a compelling reason is found to change it.

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Boolean logic was invented in the 19th century: the oath as we know it was in use in the 13th -

It has been used in English law courts since the Middle Ages, possibly from time immemorial (that's technically the year 1189, by the way); it certainly was in use by the 13th century. Nobody is credited with having invented it; it probably just evolved as the simplest and most satisfactory formula. (VSD)

The former has no relevance to the latter.

Today it is a traditional anachronism. In previous centuries binding yourself to everlasting divine punishment if you lied may have ensured you told the truth: in these more secular times, not so much.

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    Formal logic has existed since Aristotle. More importantly, whatever the view of the early clerks may have been, the oath is not Christian. Strict Christianity forbids any oath, so much so that I recall a (Catholic) bishop called to the witness box choosing to affirm rather than swear. – Tim Lymington Feb 21 '18 at 18:59

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