The fundamental logical concepts

Part 3 – The disjunction

Definition: A logical disjunction is an operation on both statements’ values, that produces the value false if and only if both statements’ values are false. If both statements’ values are true, and if either one of the statements’ values are true, the logical disjunction produces true.

Note that the logical ‘or’ differs from the linguistic ‘or’. The linguistic ‘(either ..) or’ usually means that the statements exclude one another: if one is true then the other is false – or reversed. Depending on the context however, the statements’ values could also be true when both their values are true.

Examples of linguistic disjunctions
– When an advertisement for a lecturing position asks ‘Applicants must have either a PhD or teaching experience’, then also someone who had both a PhD and teaching experience is included.
– When mum tells her son ‘You can either have some candy or some cake,’ she means one or the other, exclusively, and therefore not both.
Either the chauffeur did it or the butler did it’, can be read both as exclusive and inclusive disjunction.

According to S. Greenbaum in his “Adverbial”, there are 2 kinds of (linguistic) disjuncts: style disjuncts and content disjuncts.
– Style disjuncts are comments made by speakers on the style or manner in which they are speaking [or as an opinion of the speaker.]:
frankly: ‘Frankly, you have no chance of winning’ (= I am telling you this frankly);
personally;
with respect;
if I may say so;
because she told me so: She won’t be there, because she told me so (= I know that because she told me so).
– Content disjuncts comment on the content of what is being said: mostly degrees of certainty and doubt as to what is being said:
‘perhaps’ in ‘Perhaps you can help me’;
undoubtedly;
obviously.

That the logical disjunction always produces the same interpretation, may be viewed as a relief – at any rate less of a headache.

disjunction

 disjunction  meaning

A

˅

B

 The sun shines or we have a picnic

T

T

T

The sun shines and we have a picnic

T

T

F

The sun shines, (but) we have no picnic

F

T

T

(Although) the sun doesn’t shine, we have a picnic

F

F

F

It is not the case that the sun doesn’t shine and we have no picnic

So either there is son or a picnic, or both; but excluded as possible interpretation is: no sun and no picnic.

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