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I can guess it is because I am a penguin is false, and t->f is false. But isn't "I am a penguin" by itself just a proposition and is not inherently true or false. Can't it be true that "I am a penguin"? Then why is the above implication false?

null
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    Are you a penguin, though? – sardoj Mar 07 '15 at 14:22
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    Of course "I am a penguin" can't be literally true. Are you daft? – MPW Mar 07 '15 at 14:27
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    If you are going to assert that every statement is just a proposition, not determined to be true or false, then of course you can't determine the truth value of compound statements, except for the case when the statement is a tautology. Indeed, saying $P\implies Q$ is false implies that we know $P$ is true and $Q$ is false... – Thomas Andrews Mar 07 '15 at 15:15
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    Why not @MPW? I'm a duck. – RubberDuck Mar 08 '15 at 00:06

3 Answers3

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A proposition is an expression that have a definite truth value.

Thus "Napoleon is a penguin" is a proposition, because it has a truth-value, and it is false.

Expression with indexicals are more complicated, because they need a "context" to be understood.

If I (mauro) am uttering it, because I (mauro) am not a penguin, then the expression "I'm not a penguin" is true.

The same (presumibely) if it is uttered by you (null).

But if the statement is uttered by Mumble (the protagonist of Happy Feet), in this case it is true.

Thus, following Demosthene's comment, the statement :

“If Tuesday is a day of the week, then I am a penguin”

can be true, if uttered by Mumble.

Mauro ALLEGRANZA
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    So, to answer OP's question, it is not a "false implication" - and as OP rightly pointed out, it depends on the truth-value of "I am a penguin". – Demosthene Mar 07 '15 at 14:41
  • @Demosthene - I would prefer to say : "the truth-value of ... depends on the context", but YES, can be a true statement. – Mauro ALLEGRANZA Mar 07 '15 at 14:44
  • What I'd like to know, is if contextualism also applies to "Tuesday is a day of the week". Say, for example, that in my country, "Tuesday" doesn't exist - neither as "second day of the week" nor as its translation from English to my language. Maybe I don't use the concept of week, and count directly in days and months. Is "Tuesday is a day of the week" still true? – Demosthene Mar 07 '15 at 14:52
  • @Demosthene - you are complicating things ... See Rigid Designators and Saul Kripke, Naming and Necessity (1980). – Mauro ALLEGRANZA Mar 07 '15 at 14:56
  • It's worth noting that the vast majority of example statements from natural language used in texts and courses on formal logic suffer from flaws like this. Take for example all of the outdated assumptions that (human) reproduction involves one male parent and one female parent. People teaching this stuff really need to stick to sets/natural numbers/abstract boolean values rather than trying to tie it to natural language in ways that are doomed to be wrong. – R.. GitHub STOP HELPING ICE Mar 07 '15 at 15:15
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The truth table for the implication logic $A \rightarrow B$:

  A     B    result
======================
  T     T       T
  T     F       F
  F     T       T
  F     F       T

As $A$: "Tuesday is a day of the week" is always true, and $B$: "I am a penguin" is false (as long as it is said by a human being, or any animal except a penguin). Therefore the result is false (second case of the above table). But, as pointed out by other replies, if this sentence is said by a penguin (meaning $B$ is true), then the result becomes true (the first case of the above table).

LaBird
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This depends on how you define an implication. If by $A\implies B$ you mean ~A v B (the truth table definition), then this is false... unless the proposer is a penguin. If this is uttered by a penguin, it would be true.

There is another way to define an implication though, that cannot be captured solely in terms of truth tables(and can cause some philosophical difficulties that I won't go into), $A\implies B$ could mean that A causes B, or that B follows from A regardless of the actual truth values of A and B, in this case, it would be quite a stretch of the imagination to say that the existance of a day we call Tuesday is the cause of my inherent penguinness, even if I was a penguin. In this case, the implication would be false no matter what the truth values of A and B are because there is no (apparent) relation between the two.

SE318
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