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Philosophos
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 Posted: Sat Sep 01, 2007 11:17 am Post subject: Pop Quiz: Logic |
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The purpose of this quiz is to demonstrate how logic can be useful in revealing hidden assumptions in an argument. Almost none of what we say in daily life is necessarily "logical" because there are many hidden premises in everyday speech. These often go unnoticed. Here's a simple case study that exemplifies this.
Jean's been going to her psychotherapist for panic attacks. She often experiences them for no identifiable reason, and experiences them in a number of different ways. Jean feels many sensations during her panic attacks that feel like a heart attack to her, such as a rapid heartbeat. Her doctor told her the following to try and soothe her during a panic attack: "The heart is a muscle. It does not hurt a muscle to exercise it, so having a rapid heartbeat won't hurt your heart."
Is the doctor's advise logical?
If you are versed in logic, write out a form of the doctors argument that is valid in the logic of your choice. Be sure to make explicit any hidden presumptions needed to write a valid argument.
If you are not versed in logic, answer the following question: is the doctors advise logically valid as stated (i.e. using the doctor's own words, does the conclusion necessarily follow from the premises)? If not, can it be made valid by adding additional assumptions? If so, what are they? If not, why not?
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Chaoslord2004
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| Posted: Sun Sep 02, 2007 12:09 am Post subject: Re: Pop Quiz: Logic |
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| Philosophos wrote: | "The heart is a muscle. It does not hurt a muscle to exercise it, so having a rapid heartbeat won't hurt your heart."
Is the doctor's advise logical?
If you are versed in logic, write out a form of the doctors argument that is valid in the logic of your choice. Be sure to make explicit any hidden presumptions needed to write a valid argument.
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1. The heart is a muscle
2. If the heart is a muscle, then exercising a muscle won't hurt it.
3. exercising a muscle won't hurt it
4. If exercising a muscle won't hurt it, then a rapid heart beat won't hurt a heart
5. a rapid heart beat won't hurt a heart
This is simply 2 applications of modus ponens. For all you formal buffs, here is the argument presented formally:
1. P
2. P --> Q
3. Q
4. Q --> R
5. R
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rock
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| Posted: Sun Sep 02, 2007 6:18 am Post subject: |
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| Quote: |
If you are not versed in logic, answer the following question: is the doctors advise logically valid as stated (i.e. using the doctor's own words, does the conclusion necessarily follow from the premises)? If not, can it be made valid by adding additional assumptions? If so, what are they? If not, why not?
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No,
The assumption the doctor makes is that a rapid heart beat is exercise. Therefore it must be shown that her rapid heart beat is within the realm of being classified as exercise.
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Philosophos
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| Posted: Sun Sep 02, 2007 3:44 pm Post subject: |
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Thanks, guys. I hope this helped some lurkers in showing how putting an argument into a logically valid form (meaning the premises must lead to the conclusion if the premises are true) helps expose underlying presuppositions to attack. Here, chaos was charitable to the argument's validity. He came up with a valid set of premises that capture what the doctor was saying, and which led to the conclusion. Rock then attacked the soundness of the argument by questioning the truth of chaos' premise 4. This demonstrates how logic can lay the soft white underbelly of an argument to bare, allowing one to attack it at it's' weak points; weak points that would remain implicit and hidden had you not put the argument into its logical form.
Here's another argument that is theologically relevant, and may be a little more difficult to translate, as I'm going to include a rhetorical question in it. I got this example, as well as inspiration for this thread, from Jeff Lowder on his "Empty Tomb" show with Bob Price & Reggie.
"Matthew reports that the Jews claimed that Jesus' body must have been stolen from the tomb. This is in fact evidence that the tomb was empty - for why would the Jews make this claim if they knew that the tomb wasn't empty in the first place?"
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Chaoslord2004
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| Posted: Sun Sep 02, 2007 6:42 pm Post subject: |
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Its good to come up with ridiculous arguments in order to show that soundness and validity are two distinct concepts within logic. Its also good at showing that a valid argument doesn't entail a true conclusion. Everyone can see this is a valid argument:
P1: If Ron is a bachelor, then he is unmarried
P2: Ron is a bachelor
C1: Therefore, he is unmarried.
It is a bit harder to see that this is a valid argument:
P1: If chickens sing, the moon will explode
P2: Chickens sing
C1: Therefore, the moon will explode.
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Philosophos
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| Posted: Sun Sep 02, 2007 7:21 pm Post subject: |
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Have you studied relevance logic yet, chaos?
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Chaoslord2004
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| Posted: Sun Sep 02, 2007 8:53 pm Post subject: |
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| Philosophos wrote: | | Have you studied relevance logic yet, chaos? |
Yes, but not in depth. The basic thesis of relevance logic is that only propositions relevant to the arguments conclusion can included into an arguments premises, correct? Hence, it restricts the unrestricted usage of disjunctive addition, subsequently eliminating the counter-intuitive idea that the argument for explosion is a valid argument. If I remember correctly, it also restricts both material and strict implication so as to do away with Curry's paradox.
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Philosophos
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| Posted: Sun Sep 02, 2007 9:14 pm Post subject: |
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| Chaoslord2004 wrote: | | Yes, but not in depth. The basic thesis of relevance logic is that only propositions relevant to the arguments conclusion can included into an arguments premises, correct? |
Right. In particular, it's a critique of the material conditional as well as disjunctive addition.
| Quote: | | Hence, it restricts the unrestricted usage of disjunctive addition, subsequently eliminating the counter-intuitive idea that the argument for explosion is a valid argument. If I remember correctly, it also restricts both material and strict implication so as to do away with Curry's paradox. |
Right. And as such, it can be paraconsistent.
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Mr_C
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| Posted: Sun Sep 02, 2007 10:31 pm Post subject: |
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This is fun, man. Thanks for starting this thread. I'll attack this from the layman's point of view.
| Philosophos wrote: |
"Matthew reports that the Jews claimed that Jesus' body must have been stolen from the tomb. This is in fact evidence that the tomb was empty - for why would the Jews make this claim if they knew that the tomb wasn't empty in the first place?" |
I think it's laid out sort of like this:
1. The Jews wouldn't claim that the body was stolen if the tomb wasn't empty
2. Matthew reports that the Jews claimed that Jesus' body must have been stolen from the tomb.
3. Therefore, the tomb was empty
The first place my mind went was (2). Matthew isn't an eye-witness account. We don't know who wrote the gospel according to Matthew, but chances are, it wasn't Matthew. The gospel itself was most likely based on a document or a series of documents referred to as "Q".
From Wiki:
| Quote: | | Critical biblical scholars, like Herman N. Ridderbos in his book Matthew, do not consider the apostle Matthew to be the author of this Gospel. He cites a number of reasons such as the text being in Greek, not Aramaic, the Gospel's heavy reliance on Mark, and the lack of characteristics usually attributed to an eyewitness account.[8] Francis Write Beare goes on to say "there are clear indications that it is a product of the second or third Christian generation. The traditional name of Matthew is retained in modern discussion only for convenience."[9] |
So that takes care of (2), but I can't help but want to examine (1) as well. Assuming for the sake of argument that Matthew was an eye witness and he did report that the Jews did in fact claim that "the body must have been stolen", there could be a variety of reasons for this. The most obvious of which being that they could have said it in response to claims of an empty tomb. Slightly less obvious is that Matthew could have lied in order to further his cause.
So, Mr. Nice...How did I do? |
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rock
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| Posted: Mon Sep 03, 2007 3:37 am Post subject: |
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1. The Jews wouldn't claim that the body was stolen if the tomb wasn't empty
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They would if they thought they could get away with it. Or the body could be in the tomb but say, buried, or for that matter the body was never in the tomb and it was all a big elaborate story.
( I hope I'm doing ok, I've never taken a logic class, just two philosophies classes and an ethics class. But um quite frankly I've learned more form these forums then I have school...)
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Philosophos
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| Posted: Mon Sep 03, 2007 10:51 am Post subject: |
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| Mr_C wrote: | 1. The Jews wouldn't claim that the body was stolen if the tomb wasn't empty
2. Matthew reports that the Jews claimed that Jesus' body must have been stolen from the tomb.
3. Therefore, the tomb was empty |
Since I'm Mr. Nice, I won't tell you that this is an example of a pet peeve of mine that I like to call "proof by numbers" (kinda like paint by numbers). By labelling sentences with numbers, the argument takes on an air of formality which doesn't really exist within the argument itself. But since I'm nice, I'd never say such a thing.
| Quote: | | Matthew isn't an eye-witness account. We don't know who wrote the gospel according to Matthew, but chances are, it wasn't Matthew. The gospel itself was most likely based on a document or a series of documents referred to as "Q". |
You're starting to uncover underlying assumptions of the argument, but not completely. For what if the author of Matthew actually was contemporaneous with the supposed time Jesus lived? Does that then make his account true?
However, your thought belies another underlying assumption of the argument, but the way you've stated it doesn't quite come to the conclusion needed. Hint: if you're a gold member, Bob Price actually completed the thought you were having here on the "Empty Tomb show". Okay, so Matthew wasn't an eyewitness. Does that make what he recorded necessarily untrue?
| Quote: | | Assuming for the sake of argument that Matthew was an eye witness and he did report that the Jews did in fact claim that "the body must have been stolen", there could be a variety of reasons for this. |
Good. So what is the person who is arguing for the empty tomb here have to assume to make his argument valid?
| Quote: | | So, Mr. Nice...How did I do? |
Good, but try and complete the questions I brought up above. Also, do you think the argument as presented is valid? In other words, does the conclusion that the tomb was empty follow from the apologist's premises assuming that his premises were true? Or do you only think the argument to be unsound (i.e. that the premises are actually false, even though the argument is valid)?
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Philosophos
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| Posted: Mon Sep 03, 2007 10:54 am Post subject: |
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| rock wrote: | | Quote: |
1. The Jews wouldn't claim that the body was stolen if the tomb wasn't empty
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They would if they thought they could get away with it. Or the body could be in the tomb but say, buried, or for that matter the body was never in the tomb and it was all a big elaborate story.
( I hope I'm doing ok, I've never taken a logic class, just two philosophies classes and an ethics class. But um quite frankly I've learned more form these forums then I have school...) |
You're doing fine. But it may help if you look at my responses to Mr. C above. What are the specific assumptions the apologist needs to make the argument valid, if it isn't valid already? Once you explicitly lay out these assumptions, then you can attack their truth.
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Philosophos
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| Posted: Mon Sep 03, 2007 11:01 am Post subject: |
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Also, is anybody who's versed in formal logic up for trying to translate the empty-tomb argument?
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Daggett
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| Posted: Mon Sep 03, 2007 11:15 am Post subject: |
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| Quote: | | "The heart is a muscle. It does not hurt a muscle to exercise it, so having a rapid heartbeat won't hurt your heart." |
Others have already dealt with this, since it's such a simplistic argument, but I'll take my turn just the same.
Major premise: Excercise does not hurt muscles.
Minor premise: The heart is a muscle.
Conclusion: A rapid heartbeat does not hurt the heart.
Analysis: This is not a correct syllogism, because there exists an element of the conclusion which is not explicit in the premises.
Major premise: The conclusion of a correct syllogism mentions nothing that was not explicit in the premises.
Minor premise: The conclusion of the above syllogism mentions something that is not explicit in the premises.
Conclusion: The above syllogism is not a correct syllogism.
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Philosophos
When we look at you, we see an asshole
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| Posted: Mon Sep 03, 2007 11:20 am Post subject: |
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It's true that the categorical syllogism youwrote above is fallacious. But can every logical argument be translated into series of categorical syllogisms?
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