Why is the implication “If Tuesday is a day of the week, then I am a penguin.” a false implication? 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?
 A: 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).
A: 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.
A: 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.
