Truth functional 'if'

If the number of infections is in the high twenty thousands for five consecutive days, tough restrictions on personal freedoms will be introduced.

The statement (or a very similar one) by the Polish prime minister has been seized upon by the opposition as a lie because tough restrictions have been introduced while the number of cases, at the time of writing, is in the low ten thousands. Politics aside, in terms of first-order logic, the facts do not actually make the statement false. The sentence is not the best candidate for truth-functional analysis because it is phrased as a hypothesis rather than an observation, but it will do to show the ‘weak’ force of a logical conditional. Thus:

 

If the government does as it says, the statement will be true. No problem there.

 

If the number of cases is in the high twenty thousands for five consecutive days, and the government does not introduce tougher restrictions, the statement will be false. No problem there either.

 

If the number of cases is in the low ten thousands, and the government introduces tougher restrictions, the statement will be true too. Why? Because in saying what it says, the original statement does not rule out this scenario, it merely doesn’t mention it.

 

If the number of cases is in the low ten thousands, and the government has not introduced tougher restrictions, the original statement is true as well. Why? The reason is the same as in the preceding scenario. This scenario also appeases the critics – low number of cases, therefore no restrictions – but logically it is immaterial.