# IF, THEN and exceptions

I'm trying to figure out if (2) necessarily follows from (1). Or can (1) and (2) be true together?

1) whoever does X, except for the reason of Y, commits Z

2) whoever does X, for the reason of Y, does not commit Z

It kinda makes sense to me that (2) would follow but I'd appreciate any feedback, as the middle use of an exception throws me off.

The two sentences are different and neither entails the other. The first says that doing X has the consequence Z except for reason Y, which means that Y is a necessary condition for escaping from the charge of Z: it is the only allowable excuse. The second says that X does not have the consequence Z where reason Y applies, which means that Y is a sufficient condition for escaping from the charge of Z. That Y is necessary does not entail that it is sufficient or vice versa. The first sentence is consistent with there being cases where even a claim of reason Y does not suffice to escape from Z. The second sentence is consistent with there being cases where a claim of reason Y is not needed: other excuses would work too.

• Wondering how is this different from my answer... Sep 17, 2018 at 17:11
• I think we agree; I'm just giving an answer without the symbolism. If I was being fussy though, I would not symbolise it using material implication, since real world legal reasoning always allows for exceptions. Sep 17, 2018 at 18:51

1) whoever does X, except for the reason of Y, commits Z

This specifies the necessary and sufficient condition for having committed Z. There is only one possible "excuse" for X, namely Y.

2) whoever does X, for the reason of Y, does not commit Z

This specifies only a sufficient condition for not having committed Z. Y is an "excuse" for X, possibly one of several.

(2) follows from (1)

EXAMPLE

Suppose...

X = kills someone

Y = self-defense

Z = the crime of murdering that person

(1) Whoever kills someone, except for the reason of self-defense commits the crime of murdering that person.

This specifies the necessary and sufficient conditions for having committed the crime of murdering someone. There is only one possible excuse, namely self-defense.

Murder <=> Killing & ~Self-Defense

EDIT: This seems to work based on the truth table. Check out each line where the definition (col. 4) is true.

It's interesting, however, to see what doesn't work. Killing => (Murder <=> ~Self-Defense) would seem not to work. See line 5 of this truth table. The definition (col. 4) is true, Killing (col. 1) is false, but Murder (col. 2) is true. The general rule is that if the antecedent ("Killing" in this case) is false, then anything goes for the consequent ("Murder <=> ~Self-Defense"). It may or may not be true.

(2) Whoever kills someone for the reason self-defense does not commit the crime of murdering of that person.

This specifies only a sufficient condition for not having committed the crime of murder. Self-defense is one of possibly several excuses. Self-defense is an excuse for killing someone, possibly one of several.

Killing & Self-Defense => ~Murder

(2) would, however, follow from (1).

EDIT: See truth table

• You have tricked yourself in the first part, because we do not need to put murder and killing example. We can create such an example where Z can be commited when X is not commited. E.g. anyone who is late except for the reason of very bad weather violates rules. Sep 17, 2018 at 19:59
• @rus9384 Your example has X = arrives late, Y = bad weather, Z = a violation of the lateness rule, which may or may be the only rule. From (1), we have Z <=> X & ~Y. From (2), X & Y => ~Z. The logic is the same. I don't understand your objection. Sep 17, 2018 at 21:07
• No, we mustn't say Z is violation of this particular rule. OP includes nothing about this. You may assume fallacies. Whoever argues that all swans are white, except when he means all swans in given area is commiting faulty generalizaton fallacy. Sep 17, 2018 at 21:56
• @rus9384 Of course, it is a violation of a particular rule -- a rule about being late in your example. You are talking nonsense! Sep 17, 2018 at 22:13
• So, I provided you a new example even if the old was bad. This time it does not make sense that only those who are saying all swans globally are white commit faulty generalization fallacy. Its definition does not involve swans. Sep 17, 2018 at 22:19

It kinda makes sense to me that (2) would follow but I'd appreciate any feedback, as the middle use of an exception throws me off.

I think both the statements are in a way saying the same thing. as one does not follow from the other. however if some subset would do x and linked z together even if the reason y would be there- then it can be said to link to the reason y in opposition.

1) whoever does X, except for the reason of Y, commits Z

2) whoever does X, for the reason of Y, does not commit Z

Let's formalize it (if X is not done, no reason to investigate Y):

1) X ∧ ¬Y → Z

2) X ∧ Y → ¬Z

We have third option ¬X in case of which either Z or ¬Z can be the case.

Now lets inverse the propositions.

¬1) ¬Z → (¬X ∨ (X ∧ Y))

¬2) Z → (¬X ∨ (X ∧ ¬Y))

We can see that ¬1) does not necessarily imply 2), nor ¬2) implies 1).

Now let's deformalize it.

What follows from 1) is:

Whoever does X, for reason of Y, either commits Z or does not commit Z.

What follows from 2) is :

Whoever does X, except for the reason of Y, either commits Z or does not commit Z.

Therefore they are independent, but can be true at once. In that case we can formalize it as:

(¬X ∨ (X ∧ Y)) ↔ ¬Z

Of course, in informal language, except can have another meaning, but everyday speech is too vague to do such investigations.

I do not think the second follows from the first. However, the two could be true together.

=================

(1) If X and not-Y, then Z. Premise.

Not-(X and not-Y) or Z. Equivalence.

Not-X or Y or Z. De Morgan's.

==================

(2) If X and Y, then not-Z. Premise.

Not-(X and Y) or not-Z. Equivalence.

Not-X or not-Y or not-Z. De Morgan's.

==================

The two statements share only one premise (not-X), and the other two are different. The two are saying different things, and so could be true at the same time.

• Well, another derivation of my result. "The two are saying different things, and so could be true at the same time." This is meaningless. If they said the same things they could be true at the same time as well. What is meaningful is that they can have different truth values at the same time. Sep 23, 2018 at 2:10
• @rus9384 I responded to the question as written. Sep 23, 2018 at 16:54