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Author Topic: Is there a formal logical term for this? (w/ expl of what the H I was talking about)
Dagonee
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A rule states the following:

"If fact X is necessary for result Y then X is a Z."

From this rule, it is possible to derive this new rule:

"If Y could result whether fact X is true or not, then fact X is not a Z."

Is there a formal word for this kind of transpositioning? (I'm not even sure if transpositioning an accurate way to describe this.)

If anyone does better with words, then here are the two statements in full:

"Any fact which increases the sentence beyond the statutory maximum is an element of the crime."

"If a sentence could be given whether or not a particular fact has been found, then that fact is not an element of the crime.

[ May 19, 2006, 10:14 AM: Message edited by: Dagonee ]

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Destineer
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Let's unpack what you're trying to say.

Probably this should be re-formulated in first-order logic. Right now you've written it in predicate logic, but statements like "X is a Z" aren't well defined in predicate logic, since the variables always stand for sentences.

quote:

"If fact X is necessary for result Y then X is a Z."

"Any fact which increases the sentence beyond the statutory maximum is an element of the crime."

A very simple way of translating this would be

Sx->Ex

"if x is necessary for the sentencing then x is an element of the crime."

quote:
"If a sentence could be given whether or not a particular fact has been found, then that fact is not an element of the crime.
The inference here sounds like
Sx -> Ex
not-Sx
:not-Ex

But this is actually invalid! It could be that Sx->Ex, not-Sx and Ex.

One valid inference in the ballpark is

Sx <-> Ex
not-Sx
:not-Ex

But this would require that you strengthen your claim:
quote:

"If and only if fact X is necessary for result Y, X is a Z."

"Any fact which increases the sentence beyond the statutory maximum is an element of the crime, and any element of the crime increases the sentence..."


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Destineer
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See, what your first statement establishes is that being necessary for the sentencing entails being an element of the crime, but it doesn't establish that being an element of the crime entails being necessary for the sentencing.
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dkw
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I suspect any formal term would be obscure enough that you'd have to explain what you meant anyway, so you might as well just explain what you mean in the first place.
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MrSquicky
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I may be missing something, but it sounds to me like you're just talking about a necessary condition.

The transposition you're talking about sounds to me to be the contrapositive (or possibily obverse, but probably not) inference.

I hope those help.

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Destineer
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It does sound like the contrapositive of a necessary condition is clost to what he's going for, but that's not quite it.

Sounds like the intended inference is

All A's are B.
If x is not an A, x is not a B.

That's not valid. The actual contrapositive would be

All A's are B.
If X is not a B, x is not an A.

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Dagonee
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quote:
But this would require that you strengthen your claim:
Ah, your right. Some context:

The rule as it existed was "Any fact which increases the sentence beyond the statutory maximum is an element of the crime."

The case I'm analyzing dealt with the question "Is a which increases the minimum sentence an element?"

Clearly, the first rule neither compels nor precludes a "yes" answer.

The ultimate decision was that the answer is no, and in doing so, it changed the rule from a statement about classifying facts to a statement about the sentence: "If a sentence could be given whether or not a particular fact has been found, then that fact is not an element of the crime."

In doing so, it implictly added a new proposition, that a fact which does not affect the maximum sentence is not an element of the crime (adding the "only if" clause).

All this I have parsed out, but I was trying to come up with a word to explain the transition - especially the change in the subject of the "if" clause from the fact to the sentence.

I was looking for a word I could use to refer back to the entire transformation after I explained it. I was using "restatement" but thought something else might work better. I was trying to come up with "contrapositive" (I only got 4 hours sleep last night, but I remembered the "contra" part), and I think that's accurate for one of the steps involved in the transformation, but not as an adequate summary of the whole thing.

Thanks for the help.

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MrSquicky
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Looking at it, I agree that the contraposition (or obversion) works only if you are really saying A <-> B in the first sentence. Otherwise, the second sentence isn't an inference; it's just another proposition.
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SoaPiNuReYe
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This reminds me too much of Algebra class.
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Tatiana
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Oh, hmmm, I read it again. I don't know any word for that transposition.

If X then Y ---> If NotY then NotX

Is that the thing you're looking for a word for?

Could it be a contrapositive?

Oh wait, here we go! Do you mean the rule of transposition?

(Select the (logic) one from the list that comes up when you click on that link. Hatrack wouldn't let me use a url that included parentheses.)

I think that's what you're asking, but I'm not totally sure I understand your question. I hope it's helpful, anyway. [Smile]

[ May 14, 2006, 05:15 PM: Message edited by: Tatiana ]

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Peter Howell
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This thread has served to show me how much I've forgotten over the last few years. I've taken more courses on formal logic than I care to count, and the vast majority of this stuff is just giving me a headache... it's late, maybe I should just forget all of this and go to bed.
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BlueWizard
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Dagonee

"Any fact which increases the sentence beyond the statutory maximum is an element of the crime."

"If a sentence could be given whether or not a particular fact has been found, then that fact is not an element of the crime."


That seems a poorly worded sentence, or pair of sentences, if you ask me. And while I took Logic in college, I can't imagine what the correct term for this is. No offense, but since it was probably written by lawyers, the lack of clear wording and clear intent isn't that unexpected.

Breaking the first sentence down, it seems to say -

The extreme facts related to the crime can serve as justifications for a sentence longer that the standard maximum. Facts that can influence sentencing in this way must be elements of the crime by virtue of their ability to influence sentencing.

If justification already exists for a longer than maximum sentence independent of the facts, then any particular facts are not elements of the crime. Since those particular fact don't influence sentencing, they are not elements of the crime.


If seems as if they are trying to define what is and what isn't an Element of the Crime.

Facts that are substantial and significant enough to influence sentencing beyong the Maximum would be considered 'Elements of the Crime'.

Fact that do not carry enough weight to justify greater than maximum sentence, are not considered 'Elements of the Crime'.

I know that doesn't actually answer your question, but it's my take on what is intended.

Steve/BlueWizard

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BlueWizard
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Sorry to post again so soon, but I think I have found a very condensed way of stating the problem and that might help those knowledgable in Applied Logic to determine that proper term for what we are seeing.


Condensed version-

It is because it does.

It isn't because it doesn't.


Expanded-

It is an 'element of the crime' because it does effect sentencing beyond the maximum.

It isn't an 'element of the crime' because it doesn't effect sentencing beyond the maxium.


Though I leave it to the experts, it seems like flawed logic to me. It doesn't help you determine whether a specific Fact is or isn't an Element of the Crime, so that that Fact can be applied to or disregarded when it come to determining sentencing.

Steve/BlueWizard

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Dagonee
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Steve, I think part of the seeming uselessness stems from my not making something clear: this is definitional. We're not trying to decide whether a fact can be used to raise the maximum sentence, but rather whether the fact is an element or not. The input into the process is "effect on sentencing." The output is "element or not."

For constitutional reasons, we must determine what is an element of the crime. For example, elements serve an important role in protecting us from double jeopardy, and they also determine what issues must be submitted to a jury.

Most people don't consider it too much, but a jury right wouldn't mean much if we couldn't define what it is a jury must decide.

The easy part: anything the legislature says is an element is definitely an element.

However, imagine the following scenario. The legislature defines a crime called battery:
quote:
Whoever touches someone in an offensive manner without consent shall be guilty of battery. (Ignore the squishyness in "offensive" and several terms below - assume for now that we know exactly what they mean.)

The punishment for battery shall be no more than 30 days in jail except that:
1.) if the offensive touching amounts to physical violence, the maximum punishment shall be 1 year in jail.
2.) if the offensive touching causes any bodily injury, the maximum punishment shall be 5 years in jail.
3.) if the offensive touching causes serious bodily injury, or involves the use of a firearm, the maximum punishment shall be 20 years.
4.) if the offensive touching is intended to cause serious bodily injury and does cause such injury, or the touching causes the death of another, the maximum punishment shall be 40 years.
5.) if the offensive touching is intended to cause the death of another and does, the maximum punishment shall be life in prison.

6.) If a firearm is used in the commission of a battery, the minimum sentence shall be 5 years, no part of which may be suspended.

The items 1-6 are called "sentencing factors" by the legislature, the other part contains the "elements."

Elements must be submitted to the jury. Under the legislature's definition, the jury must decide whether the prosecutor proved the following beyond a reasonable doubt:

a.) Defendant touched victim.
b.) The touching was offensive.
c.) Victim did not consent to the touching.

If the jury returns a verdict of guilty (meaning it found all three facts beyond a reasonable doubt), the judge makes findings of fact that result in a maximum sentence of anywhere from 30 days to life in prison, and might have a minimum sentence of 5 years. For example, if the judge finds it more likely than not that the defendant used a gun and caused serious bodily injury, he must give the defendant 5 years and can give as many as 20.

Note that no jury will have decided whether a gun was involved, and the standard of proof that a gun was involved is more likely than not instead of beyond a reasonable doubt.

My paper was about Justice Scalia's vote in a line of cases that stated that a jury MUST find any fact that increases the maximum sentence, but that a judge may find facts that increase the minimum (as long as that minimum is below the maximum). In other words, that number 6 is not an element unless the legislature says so, but 1-5 are whether they say so or not.

The court lineup was very strange. Justices Ginsburg, Souter, Stevens, and Thomas found that the jury must decide any fact that changes the maximum or minimum is an element and therefore must be proven to the jury's satisfaction beyond a reasonable doubt. Justices Rehnquist, Kennedy, O'Connor, and Breyer found that judge-found facts can increase the maximum and minimum sentences, subject to some form of due process review for rationality. They specifically allowed a sentence to double based on a judge-found fact that racial bias motivated the crime.

Justice Scalia was the swing vote. Note the strange lineup - the most conservative justice (Thomas) siding with three of the four liberals, Justice Breyer (one of the staunch liberals) siding with Rehnquist, Kennedy, and O'Connor - three of the most conservative on criminal procedure rules (O'Connor was seldom a swing vote on such issues).

The paper's task was to resolve the apparent contradiction in Scalia's votes on the minimum and maximum.

Anyway, the point of all this is that determining what is an element of the crime is both important and depends on how that element affects sentencing.

It's a nitpicking, gritty legalism with profound effects on many criminal procedure rights - some say the most significant line of criminal procedure decisions in two decades.

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