allzermalmer

Truth suffers from too much analysis

False Hypotheses & True Predictions

Posted by allzermalmer on June 23, 2016

In logic, a conjunction is a logical connective that connects two separate propositions. For example, say we have the propositions ‘The Golden State Warriors won the Western Conference Championship of the NBA in 2016’ and ‘The Cleveland Cavaliers won the Eastern  Conference Championship of the NBA in 2016’. We can represent each of those propositions, respectively, as P and Q.

The logical connective of conjunction would combine each of these two separate propositions together. Each of these propositions would be known as a conjunct that makes up a conjunction. Conjunct of P and conjunct of Q make up the conjunction of ‘Both The Golden State Warriors won the Western Conference Championship of the NBA in 2016 & The Cleveland Cavaliers won the Eastern Conference Championship of the NBA in 2016’. This can be represented as ‘P&Q’.

A conjunction is only true when each conjunct is true. A conjunction is false when either one of the conjuncts is false or both conjuncts are false. In the example presented, it is true that both teams won the Conference championships in 2016. So the conjunction is a true proposition.

Logic tells us that from false hypotheses, or hypothesis, that true predictions follow from it.  Suppose that P means ‘The Golden State Warriors won the NBA Championship in 2015’ and that Q means ‘The Golden State Warriors won the NBA Championship in 2016’. From these two propositions, we can form the conjunction of ‘Both The Golden State Warriors won the NBA Championship in 2015 & The Golden State Warriors won the NBA Championship in 2016’. This can be represented as ‘P&Q’.

Taking ‘P&Q’ as a hypothesis, we can prove that some propositions follow from that hypothesis. One of these propositions that follow is P.  So from the hypothesis of ‘Both The Golden State Warriors won the NBA Championship in 2015 & The Golden State Warriors won the NBA Championship in 2016’ that it necessarily follows by rules of logic that ‘The Golden State Warriors won the NBA Championship in 2015’.

Suppose ‘P&Q’ then necessarily follows ‘P’.

The hypothesis presented is false, P&Q is false. One of the conjuncts is false, Q is false. One of the conjuncts is true, P is true. So the conjunction is false. But from this false hypothesis, we find that a true conclusion follows from it.

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