The sign said, 'Fine for parking here,' and since it was fine, I parked there.

J reports in "Who's afraid of the big big Equivocality?"

""The sign said "Fine for parking here", and since it was fine, I parked there.""

Apparently, the words are cognate.

'Fine' and 'fine' both come from Latin 'finis'.

If something is 'fine', it means it's near the end (Latin 'finis') and that is, in the highest level of excellence.

Similarly, an amount of money is related, surely, to some 'end' -- why are they collecting it.

J quotes:

"The sign said "Fine for parking here","

Surely the sign didn't 'say' -- but 'read':

The logical form seems to be:

There exists an x, such that x is a fine". This is the consequent. The antecedent being, binding the 'x': "If you park (your car, rather than yourself) here" -- where 'here' is deictic and applies to what is in front of the sign, not to the universe.

----

J continues to quote:

"and since it was fine, I parked there.""

This seems to involve a flout of modus ponendo ponens.

The sign notably didn't read, that it WAS fine. Only that if you PARKED there, it was (a) fine.

So, it seems that the conclusion does not really follow.

---

A way to interpret the 'saving' of the 'rational' face here is:

"if you park here, there is a fine"
--
"There is a fine (weather).
---


---

Here the logical form is

p ) q
q

But surely from the posing of the consequent we cannot draw ANY inference. This is a fallacy, but not of equivocation. It's the fallacy of affirming the consequent.

Affirming the consequent, sometimes called converse error, is, however, a formal, not an informal fallacy, committed by reasoning in the form:

1.If P, then Q.
2.Q.
3.Therefore, P.

As wiki notes, an argument of this form is invalid, i.e., the conclusion can be false even when statements 1 and 2 are true. Since P was never asserted ("you park the car"), as the only sufficient condition for Q ('it is (a) fine (day)'), other factors could account for Q (while P was false), surely.

Usually, plus, the weather has nothing to do with you parking the car here (or there).

The name affirming the consequent derives from the premise Q, which affirms the "apodosis" clause of the "if" premise.

One way to demonstrate the invalidity of this argument form is with a counterexample with true premises but an obviously false conclusion. For example:

If Bill Gates misparks his Rolls Royce, it is fine.
It is fine. (What?)
Therefore, Bill Gates misparks his Rolls Royce.

BUT: Misparking one's Rolls Royce is not the only way to be 'fine'. There are any number of other ways to be 'fine' (or 'fined').

Arguments of the same form can sometimes seem superficially convincing, as in the following example:

The sign read, "It is a fine, if you park your car here"
I park my car here.
Therefore, it is a fine.


But surely misparking your car is not the only (if one at all) cause of a fine (day), since many other factors -- metereological, etc. -- may intervene.

The following is a more subtle version of the fallacy embedded into conversation.

A: Fine if you DON'T park.

B: Fine?

B attempts to falsify A's conditional statement ("if you don't park") implicating: how can I NOT park? -- and providing evidence he believes would contradict the conversational implicature. However, B's question ("fine?") does not really contradict A's statement, which says nothing about questions. What would be needed to disprove A's assertion are examples of ways in which you cannot park.

However, if claims P and Q express the same proposition, then the argument would be trivially valid, as it would beg the question.

If P, then P.
P.
Therefore, P.
This is also the case for definitions. For example.

If a man is a bachelor, then he's an unmarried male
John is an unmarried male.
Therefore, John is a bachelor.

In everyday discourse, however, such cases are rare. Note the rewrite:

If you miskpark, you mispark
you mispark
--- Therefore you mispark.

Or:

If it's fine, there's a fine.
--- there's a fine
--- Therefore, it's a fine (day).


The validity of such definitions is due to the fact that definitions can be expressed as an if and only if (see below).

Clearly if the definition of "fine" is "an amount of money" (rather than, say, 'a fine day') then the propositional statement: "Fine for parking here" if and only if "it is a fine day", must be true. But in normal speech it is awkward to use the phrase "there is a fine", to mean, 'it is a fine day'. So we substitute the valid but less complete "if", giving the conventional form which is similar to the form of the formal fallacy.

The reason the conclusion of an argument that affirms the consequent does not follow is the lack of a unique cause for "you mispark". However, if it is explicitly stated that the consequent could only have one cause (known as an "if and only if" statement or biconditional), the argument becomes valid. For example:

If he's not inside, then he's outside.
He's outside.
Therefore, he's not inside.


Or:

You mispark
You mispark -- you'll get fined (or it is a fine day).
-- Therefore, you mispark (iff it's a fine day).

The above argument may be valid, to some, but only if the claim "it's NOT fine if you get fined" follows from the first premise. More to the point, the validity of the argument stems not from affirming the consequent, but affirming the antecedent.

Such if and only if statements often make their way into detective mysteries.

Only if the suspect came in through the window, would he leave no marks in the hall.
No marks were found in the hall.
The cigar ends show he was in the room.
Therefore, he used the window.
Here, P is "entering through the window" and Q is "leaving no marks in the hall".

No such subtlety in "The sign said, 'Fine if you park here'". Surely if a potential criminal is going to produce a 'crime', he will not be reading 'signs' -- let alone respecting what they say or read.

Use of the fallacy in science, especially quantum physics (as NOT practiced by quantum physicists).

Although affirming the consequent is an invalid inference, it is defended in some contexts as a type of abductive reasoning, sometimes under the name "inference to the best explanation".

E.g.

It is not fine (to park here).
I park
---- I AM, however, fined.


That is, in some cases, reasoners argue that the antecedent is the best explanation, given the truth of the consequent -- that the reasoner gets fined.

For example, someone considering the results of a different scientific experiment may reason in the following way:

Theory P predicts that we will observe Q.
Experimental observation shows Q.
Therefore theory P is true.
For example,

Some computer models show CO2 from automobile exhaust will warm the planet,
Data shows warming has occurred,
Therefore, the warming was caused by automobile exhaust.

Or, more to the point:

Only if you mispark, it is 'fine' (i.e. there is a fine for that).
It is NOT fine.
--- Therefore, you parked well.

However, such reasoning is still affirming the consequent and logically invalid (e.g., Let P = you mispark your car and Q = you get a fine (day)). The strength of such reasoning as an inductive inference depends on the likelihood of alternative hypotheses, which shows that such reasoning is based on additional premises, not merely on affirming the consequent.

The complete conversational implicature treatment is best seen if we consider, 'Post hoc ergo propter hoc', taking into account any implicature that may arise from 'fine'. Some Griceans call this the "ELIZA effect" (after a famous logician).