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Source: p 153, Letters to a Law Student, 1 ed (2006), by McBride

Section 2 of the Theft Act 1968 (title: “ ‘Dishonestly’ ”) provides that:

(1) A person’s appropriation of property belonging to another is not to be regarded as dishonest – ...
(b) if he appropriates the property in the belief that he would have the other’s consent IF the other knew of the appropriation and the circumstances of it; ...

How do I rewrite (1)(b) as a conditional sentence (If P, then Q)? Is the clause after (b) the protasis, and the grey the apodosis? How do I simplify and understand the two ifs?
Please beware that I capitalised the second IF, for want of easier reference.

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The nesting is important. This is easiest to see with the following scenarios:

Joe will let Peter take his guitar anytime he asks and has good reason. One day, Peter takes the guitar without asking and Joe is furious--until he finds out he needed it to play for his girlfriend's younger sister's birthday party.

vs.

Joe will let Peter take his guitar anytime he asks and has good reason. One day, Peter takes the guitar without asking. Joe is furious, as Peter knew he would be, but Peter "just didn't feel like asking" this time.

The nested-if definition calls the second one dishonest appropriation, but not the first. It's

(other knows circumstances => other approves) => not-dishonest

In particular, you can't just look at Joe's reaction before he knows what Peter's reasons are.

Edit: had the outer implication backwards.

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    @MauroALLEGRANZA - It is not a definition because the quote is incomplete. See the (b) there? This is evidently one way for something to count as "not-dishonest appropriation". Also, note that it does not say that the person appropriated from does know, only that they would approve if they did. For example: "I would say please when asking for a cup of water" does not mean I am asking for a cup of water, or that I said please, or that every time I say please it means I want water.
    – Rex Kerr
    Commented Dec 5, 2014 at 18:02
  • @RexKerr, we can go a little further with regards to (a)-(last section). The way the statute reads, it seems that even if none of those conditions are met, (1) does not necessarily state that the appropriation was dishonest, only that nowhere in (1) have we found an argument that it was not dishonest. There are likely many more arguments available in the statute as to the degree of honesty.
    – Daniel
    Commented Dec 6, 2014 at 6:05
  • Also, @RexKerr, note that your implication "other knows circumstances => other approves" is always true, because, as you recognized in your comment, "other knows circumstances" is hypothetical, and in fact expected to be false. The second if, then, is not a conditional or biconditional -- it is not formal logic at all, and (b) must be taken as atomic in a simple system of logic.
    – Daniel
    Commented Dec 6, 2014 at 6:07
  • @Daniel - I agree it doesn't map well onto simple logic; by its nature it's talking about possible worlds so a modal or at least first-order formalism would be better.
    – Rex Kerr
    Commented Dec 6, 2014 at 16:41
  • I edited my post a little earlier to add a potential modal argument. It's not bad, but I still have an objection to it.
    – Daniel
    Commented Dec 7, 2014 at 0:16
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This is a simple grammatical problem. What you have is a parenthetical.

A person’s appropriation of property belonging to another is not to be regarded as dishonest

if he appropriates the property in the belief that:

he would have the other’s consent IF the other knew of the appropriation and the circumstances of it

let a be "A person’s appropriation of property belonging to another is not to be regarded as dishonest" let b be "he would have the other's consent." let c be "the other knew of the appropriation and the circumstances of it"

let d be "he appropriates the property in the belief that c -> b"

The law states, in a sense, if d then a.

However, you have to realize that the sentence:

he would have the other’s consent IF the other knew of the appropriation and the circumstances of it

Is not formal logic, and that if isn't really meant to be an implication. If, for example, I believed that the other did not know about the appropriation, c -> b would necessarily be true, whether or not he would give me permission. But the law doesn't mean that -- the law obviously assumes that the other does not know about the appropriation, but instead talks about beliefs and hypotheticals in a way that cannot be reduced to mere implication. Thus, what you're stuck with is d -> a, but where d is actually:

he appropriates the property in the belief that he would have the other’s consent IF the other knew of the appropriation and the circumstances of it

Which, despite the appearance of the loaded word "if," is effectively atomic for our purposes.

Edit: To be a little bit more thorough.

The second if, being a hypothetical if, could be read as:

necessary( c -> b )

That is to say: in whatever world may exist, if c is the case, b will also be the case. Since c is contingent, it will sometimes be true, and if we assume c and b to be logically independent (they really aren't), then the logical statement has a meaning at least similar to the law's meaning: if c ever were true, b would also be true.

The problem is that the law certainly does not demand that the belief be a necessary belief, but likely just a reasonable one. If you believe that you would very, very likely have the owner's consent, but are not certain, I'm sure the appropriation would still not be regarded as dishonest.

So, even in a modal logic scheme, I would continue to argue that the flesh of (1)(b) should be atomic.

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  • What about necessarily ( c -> probably b )? I think it gets closest to the intended meaning of the law as you are trying to explain in your second to last paragraph.
    – user21820
    Commented May 14, 2015 at 15:11
  • Well, more like believes (necessary ( c -> b). Or, maybe more like... reasonably believes ( probably (necessary (c -> b) ) ). The "necessary" part is needed because the law doesn't let you off the hook if the other does not know of the appropriation.
    – Daniel
    Commented Jun 13, 2015 at 22:59
  • Yes something like that.. I can't be bothered to think carefully about what the exact modal representation could be though..
    – user21820
    Commented Jun 14, 2015 at 6:56
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You can normally see nested IFs with an And operator (sorry, I work with computers -0 it's how this stuff presents itself to me) So it would be :

Honest appropriation of property = 
(he appropriates the property in the belief that he would have the other’s consent) AND (the other knew of the appropriation and the circumstances of it)

or as an if clause ..

if  (he appropriates the property in the belief that he would have the other’s consent) AND (the other knew of the appropriation and the circumstances of it) then (Honest appropriation of property) =true

You can use the AND operator because with any nested 'if':

  • the first 'if' must be true in order for the second (nested) 'if' to be evaluated
  • the second (nested) 'if' must be true for the whole statement to be true

Therefore both IFs must be satisfied. So it acts like an AND.

hope this helps

EDIT: Note that sometimes the order of the conditions is important - for example:

If the cat has a caught mouse and the mouse is alive, then the mouse must be rescued.

If this were swapped around (check for mouse health first then see if there is a caught mouse) it would be difficult to evaluate because the cat may not have caught a mouse - there is no mouse to check on.

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  • ps. It seems strrange to word a law like this - but in computing terms, there's an advantage to nested IFs : if the first IF isn't true, then you don't spend any cpu time evaluating the second IF. Commented Dec 4, 2014 at 12:13
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    I would recommend all philosophy students to learn a programming language. Mathematicians, also. It is one of the few ways to get practical working experience dealing with abstract conceptual logic. Commented Dec 5, 2014 at 16:45
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    In many common programming languages using boolean conjunction would be no different from using nested if-statements due to lazy evaluation. Also, you should point out that it is not commutative because the second condition/conjunct might only be well-defined when the first one holds.
    – user21820
    Commented May 13, 2015 at 13:39
  • So there is no speed advantage to using nested if-statements instead of direct conjunction, and it is essentially just a matter of style.
    – user21820
    Commented May 13, 2015 at 13:41
  • @user21820 "In many common programming languages" .. yes, but not all langauges. In the languages that do implement lazy evaluation, there would be no speed advantage. No disadvantage either. I completely take your point about it not being commutative though. Commented May 14, 2015 at 9:40
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The analysis in terms of AND does not convey the same force, so you should not understand the requirement as a conjunction of two conditionals.

The original requires: A is not dishonest in appropriating B's property if A appropriates B's property believing that B would consent if B knew of the appropriation and its circumstances.

This can be understood as follows: IF {(A approps B's prop) AND [A believes that (IF (B knew circs) THEN (B would consent))]} THEN (A approps not dishonestly)

What the setup tells you, then, is a sufficient condition for "not dishonest appropriation". The sufficient condition is all that resides inside the {} brackets--i.e., A appropriates B's property and A believes that if B knew the circumstances B would consent. Since the {} brackets enclose a conjunction, both of the conjuncts must be satisfied in order for the sufficient condition to be met. If either conjunct fails, then the consequent (not dishonest appropriation) fails also.

I hope that this helps!

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    Your innermost implication, "(IF (B knew circs) THEN (B would consent))," is actually not made by the statute. That implication is always true if B does not know the circumstances, but we know that the intent behind this statute is to cover cases where B does not know the circumstances. The if there is not conditional or biconditional, but hypothetical.
    – Daniel
    Commented Dec 6, 2014 at 6:11

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