Tautological Tautology
Niniva
Tautological Tautology
Smartteaser192
NOTA BENE:
The Fallacy of rejecting the antecedent is not a violation if the major premise involves "Sequential correlation". Here, even if the antecedent is denied in the minor premise, the conclusion remains to be valid.
e.g. If today is Monday, then tomorrow is Tuesday.
But today is not Monday.
Therefore, tomorrow is not Tuesday.
I don't know much about sequential correlation, but it seems to me that this is true because "tomorrow is Tuesday" implies that today is Monday. Would you say that the argument essentially says "p→ p"
Unfortunately what you are pointing out here is a troublesome spot in logic. Simply because on the truth table of (If P then Q) has a line in which Q is true, and P is false and yet the statement is still true simply because we cannot call it false if the anticedent is false but the consequent is true. Therefore just because today is not monday.....that does not necessarily imply that tomorrow is not tuesday.
This is absurd however. In order for logic to account for this troublesome spot we are forced to say that you cannot translate the sentence "If today is monday then tomorrow is tuesday" into the form "If P then Q" because that is not what is meant, nor what is implied by what the person saying it meant.
We must then translate it into a more complicated form that accounts for the impossibility in the english language any other day is followed directly by tuesday.
So it becomes (If P then Q) AND (If Q then P) Which is essentially the same as Q if and only if P. So no....it isn't a case of If P then P....its a case of Q....If and only if....P.
What I have said here is that based on what you have written: In the case of If P then Q....denying P has NO AFFECT on the truth of Q and so therefore (based on the law of the excluded middle) the statement is true. Think of it like this, the entire statement is considered true until such a time in which we find an example of a time when P is not directly followed by Q. But that does not mean that Q cannot ALSO be preceded by something else (in the case of multiple causes).....however because tomorrow being tuesday implies that today is monday BY DEFINITION....If P then Q is not adequate but Q if and only if P is perfectly adequate since it makes it so that there is no time that Q occurs that is not preceeded first by P.
But I would dissagree that saying "Today is monday" and saying "Tomorrow is tuesday" are saying the same thing. It seems like today being monday is implied by saying "Tomorrow is tuesday" sure, but that does not mean that they are the same. The object of the senteces....for example....is very different. So is their reference to time passing, the "thing" pointed out by the two sentences is vastly different, and so are the attitudes presented by the speaker.
So no, this is not a tautology, but If P then Q is also not an adequate translation either. Q if and only if P is the only way to say this correctly in logical form.
You're right, it should have been a biconditional instead of a conditional.
Do you think that they are not equivalent due to the sense-reference distinction? In other words are "tomorrow is Tuesday" and "today is Monday" extensionally equivalent because they both refer to Monday and intensionally inequivalent because they have different senses, being that the former takes into account an anticipated passage of time while the former says nothing of it?
Sounds like a a question for Wittgenstein and the philosopher's of language to me. *laughs*
But I believe that yes, that is one way to look at it. Another is to take into account the subject of the sentences in a purely language format. When I say "Tomorrow is tuesday" the subject of the sentence is "tomorrow" which happens to hold the name "Tuesday" which is nothing more than a descriptor or a proper name. This then, is not an existential quantifier...it is a propper name. In this case, we have given the "day" a name. So the "thing" pointed out by the sentence is not "today", or "monday", but rather "tomorrow" which is "tuesday". When you say "Today is monday" however, you are saying something vastly different. For you are not indicating those properties of monday that might imply tomorrow is tuesday....all you are ascerting here is something about right now. The subject then is "today" what do you know about today? Well.....it is called "Monday". That is quite simply ALL that the sentence ascerts. Now what is logically implied by that is of course up for debate and may, by definition, include tomorrow being tuesday, but the speaker did not ascert anything about tomorrow...or tuesday...but rather ascerted something about today. Namely...that today is monday.
In quantified form you would may use universal quantifiers for this, provided you first decide to use "monday" and "tuesday" as properties of "days" rather than names. Otherwise you will have to assign them a name and use a rather complicated (though elegant and precise) identity logic. I prefer not to (since I haven't studied identity yet) and stick with quantifiers using Monday and Tuesday as properties of "days".
I hope I answered your question. I do think time is important here though...yes. But you would still need a biconditional there. It being Monday at time T implies Tuesday at time T2 only if in EVERY instance of Monday....there follows a tuesday 24 hours later. You cannot show this without a biconditional, even if you use quntifiers or time.
In any case I have said a lot that you didn't ask about, but I think I first answered your question as to my opinion of why they refer to different things in begining of this. I don't think I need to assume Tuesday will come in order to refer to it (though some people might), in other words, to make tomorrow the subject of my sentence I do not need to know anything about today. Meaning....I may not know today is Monday in order to know tomorrow is tuesday.
Say, for example, that it really is monday, and a 3 year old who is learning their days of the week knows the name for 6 of them but always forgets the name for the day after sunday and right before tuesday. So if you asked the kid what day tomorrow was....they would refer to tomorrow as Tuesday...but if you asked them what day today was, they wouldn't say "Tomorrow is tuesday" they would say something like "I don't remember" or "I don't know" or maybe they'd be creative and say "Today is the day after Sunday!" or "Today is the day before tuesday" but in every case they purposefully refer to TODAY...and not TOMORROW as the subject for their sentence thereby picking out a definitive existential object in the universe.
I hope that provokes some thought.