Q].I repeat the main menu:
Just click on the links for headline advice.
The message encoded by 'Although it was very hot, Her Majesty wore a cardigan' is formalized as a conjunction:
P: It was very hot
Q: Her Majesty wore a cardigan.
And we formalize as [P Q].
In the mistaken framework of the boy Hodges, we say that '--although--' operates as a truth-functor.
The message encoded by 'Because it was very hot, Her Majesty stripped off' cannot be adequately formalized. We can extract something weaker, namely the conjunction of its prior messages:
P: It was very hot
Q: Her Majesty stripped off.
And we can extract the conjunctive information [P Q].
In the mistaken framework of Hodges, we say that '-- because--' does not operate as a truth-functor.
The message encoded by 'Since there are no trees in Orkney, it is a desolate place' cannot be adequately formalized. Nonetheless, the usual point of such a message in an argument is to affirm the independent message, and throw in a reason for accepting it, as a little sub-argument. So we can at least extract a single proposition:
Q: Orkney is a desolate place.
And we can formalize as: Q.
Nota Very Bene Indeed: This does not capture what is going on in the full message , which does something really quite complicated. It announces a premise, performs a deduction, and affirms the conclusion of that deduction. And be sure to get very clear how 'since' differs from 'if'. 'If' does not affirm a premise as true, and then draw a conclusion. Instead 'if' accords the dependent message the status of an hypothesis, and announces that it is being treated as true, whether or not it really is, and deduces the conclusion thus hypothetically. The proponent of such a message helps himself to the inference whilst avoiding commitment to the truth of it's premise. The proponent of a 'since'-message is committed to the truth of that premise.The message encoded by 'Unless I am mistaken, the answer is 42' is formalized as a disjunction:
P: I have made a mistake
Q: The answer is 42.
And we formalize as [P 
Q].
In the mistaken framework of the boy Hodges, we say that '--unless--' operates as a truth-functor.
The message encoded by 'Whether or not you like them, carrots are good for you' is formalized as a single proposition:
Q: Carrots are good for you.
And we formalize as: Q.
In the mistaken framework of the boy Hodges, we say that '--whether or not--' operates as a truth-functor.
The message encoded by 'Despite the fact that Mike Tyson is a convicted rapist, this administration let him in' is formalized as a conjunction:
P: Mike Tyson is a convicted rapist
Q: This administration let him in.
And we formalize as: [P Q]
In the mistaken framework of the boy Hodges, we say that '--despite the fact that--' operates as a truth-functor.
The message encoded by 'If Oswald did'nt shoot Kennedy, somebody else did' cannot be adequately formalized. Nonetheless we can settle for an ersatz, which will not do too much damage most of the time. We formalize as a disjunction:
P: Oswald didn't kill Kennedy
Q: Somebody else did.
And we formalize as: [
P Q]. Or, if you prefer to use the arrow functor, as [P 
Q] .
But NEVER, EVER read this 'arrow' formulation as 'if'. ALWAYS think of it as 'arrow', and ALWAYS REMEMBER that [P Q] is just a convenient shorthand for [P Q]. Otherwise, I guarantee, you will get into all kinds of tangles.
In the mistaken framework of the boy Hodges, we say that '--if--' does not operate as a truth-functor, but that we are going to pretend that it does.
The message encoded by 'Even if Granny was gunned down in the street this morning, she's chirpy enough now' is formalized as a single proposition:
Q: She's chirpy enough now.
And we formalize as: Q.
In the mistaken framework of the boy Hodges, we say that '--even if--' operates as a truth-functor.
And there it it, and there you are, and there you have it. It remains only for Francis to say farewell:-
