# Formal structure of a logical argument

#### Speakpigeon

Valued Senior Member
For those interested, thank you to try to express the formal structure of the following argument as you understand it:
Premise 1 - For all we know, somebody's conscious mind may be the state of a group of neurons in this person's brain;
Premise 2 - What somebody does is determined by the state of a group of neurons in this person's brain;
Conclusion - Therefore, for all we know, what somebody does may be determined by the conscious mind of this person.
Everything is admissible as long as it's what you think is the best expression of the structure of the argument and that you are prepared to argue your view.
Still, I will myself keep away from this thread to let you all try to arrive at a consensus independently of my own view, hopefully through something like a rational debate.
EB

As to your request: you're trying to use deductive reasoning with uncertain premises, thus resulting in an uncertain conclusion. If you approach it with certain premises (i.e. remove the "as far as we know") and then apply that uncertainty as a measure of soundness, I think it would be easier to understand.

With certain premises, the formal structure is invalid. A syllogism is valid if and only if it is impossible for the premises to be true and the conclusion to be false. In this case, and I think this was either pointed out to you - or at least alluded to - in your other thread, you're suffering from a case of undistributed middle.

Your syllogism - removing the uncertainty of the premise to a matter of soundness - boils down to:
P1 - conscious mind is the state of a group of neurons
P2 - what we do is determined by the state of a group of neurons
C - what we do is determined by our conscious mind

This is invalid as the group of neurons in P1 and P2 might not be the same.

A similar example:
P1 - the weather is a group of atoms
P2 - what we do is determined by a group of atoms
C - what we do is determined by the weather

Introducing the uncertainty into the premise 1 rightly makes the conclusion uncertain, but in an otherwise valid form the level of uncertainty in the conclusion should match the uncertainty in the premise. Yet your syllogism has far more uncertainty in the conclusion than in the premise, due to the undistributed middle.

So it is invalid.

determined by the conscious mind of this person.

Questions:
Is the conscious mind involved in coughing, scratching an itch, breathing, kicking when a doctor taps your knee with a rubber mallet, sneezing, yawning, blinking, laughing, etc...etc...?

Why are you (OP) making the same crappy arguments when I have previously in another thread proved them false?

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Housekeeping items

1. Please, address the OP and refrain from derails (Beer w/Straw, sculptor).
2. Remember that you cannot address the OP if your start by rephrasing the argument (Sarkus). The OP is asking for the logical structure of the argument given in the OP, not any other argument you may want to concoct.
3. And for those who may be fuzzy about the notion of logical structure, here is the Wiki page explaining the notion of formal fallacy, which you may think applies here:
Formal fallacy
In philosophy, a formal fallacy, deductive fallacy, logical fallacy or non sequitur (Latin for "it does not follow") is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic system, for example propositional logic. It is defined as a deductive argument that is invalid. The argument itself could have true premises, but still have a false conclusion. Thus, a formal fallacy is a fallacy where deduction goes wrong, and is no longer a logical process. However, this may not affect the truth of the conclusion since validity and truth are separate in formal logic.
4. Reminder: I will myself keep away from this thread to let you all try to arrive at a consensus independently of my own view, hopefully through something like a rational debate.
Thanks
EB

If you post something and don't allow others to dissect it into its pertinent parts, requiring inconsequential rephrasing, then you are in effect just trolling.
If you can not see how their dissection retains the relevance to your OP then ask.

However, to summarise and build upon my previous post:
If the argument is intended to imply a consistency in uncertainty between premise and conclusion then it is invalid, for reasons given (undistributed middle).
If the level of uncertainty in the conclusion is independent of the uncertainty in the premise then you have produced a valid syllogism but it suffers from equivocation with regard "for all we know".

If you post something and don't allow others to dissect it into its pertinent parts, requiring inconsequential rephrasing, then you are in effect just trolling. If you can not see how their dissection retains the relevance to your OP then ask.
For the moment, I can certainly see that you are unable to get yourself to post a formal expression of the argument. Other people already have, and I agree with their resolution, so it's clearly possible, and once it is formalised, I guess you'll be able to explain yourself.
However, to summarise and build upon my previous post:
If the argument is intended to imply a consistency in uncertainty between premise and conclusion then it is invalid, for reasons given (undistributed middle).
If the level of uncertainty in the conclusion is independent of the uncertainty in the premise then you have produced a valid syllogism but it suffers from equivocation with regard "for all we know".
"For all we know" is no equivocation. If you don't know what that means, sure, end of conversation.
As for your "undistributed middle" suggestion, here is the Wiki page on that: https://en.wikipedia.org/wiki/Fallacy_of_the_undistributed_middle
Look in there and tell me which one looks remotely like my argument.
Here is one example, just to goad you:
All Z is B
Some Y is Z
Therefore, all Y is B​
By the way, I'm blissfully ignorant of what "trolling" may mean apart from "I disagree with you but I bloody can't prove I'm right".
Well, at least this is what I was able to surmise from the various people who have accused me of trolling.
I asked for the logical structure. If you can't get yourself to address this, then I'm not interested since I already tried the informal route, to no avail.
EB

I don't know how to formalize 'for all we know...', certainly not without introducing modal operators.

Introducing 'know' introduces an epistemic operator, but Speakpigeon doesn't seem to want to acknowledge epistemic modal logic. I'm not sure what to make of the 'For all we...' prefixed to it. Does it suggest an assessment of probability, which in turn would suggest many-valued logic and a violation of Aristotle's law of the excluded middle? Or is it just another way of expressing the hypothetical nature of the 'if' in a standard conditional ('if A, then...'), such that A might be either T or F?

If we retain the 'For all we know...' and try to represent it in formal logic, we seem to have moved beyond classical logic. If we don't, then Sarkus is justified in removing it from the argument.

For the moment, I can certainly see that you are unable to get yourself to post a formal expression of the argument. Other people already have, and I agree with their resolution, so it's clearly possible, and once it is formalised, I guess you'll be able to explain yourself.
You asked people to express the formal structure of the syllogism as they understood it. That you don't like the way some people have expressed it goes counter to you having claimed in the OP that anything was admissible as long as they think it the best expression they could.

"For all we know" is no equivocation. If you don't know what that means, sure, end of conversation.
It is equivocation for the simple reason that you are relying on words that express a continuum as if they are being used consistently. That is equivocation.
As for your "undistributed middle" suggestion, here is the Wiki page on that: https://en.wikipedia.org/wiki/Fallacy_of_the_undistributed_middle
Look in there and tell me which one looks remotely like my argument.
Here is one example, just to goad you:
All Z is B
Some Y is Z
Therefore, all Y is B​
Look at the first example.
The form of this is identical to your syllogism:
All students carry back packs
My grandfather carries a backpack
Therefore my father grandfather is a student.

Form:
All S = P
G = P
Therefore G = S

Your argument, stripped of uncertainty in the premise:
P1 - conscious mind is the state of a group of neurons
P2 - what we do is determined by the state of a group of neurons
C - what we do is determined by our conscious mind

Form:
C = N
All D = N
Therefore C = D

Other than the two premises being in a different order, the form is the same, and you are suffering from a bout of undistributed middle. QED.
By the way, I'm blissfully ignorant of what "trolling" may mean apart from "I disagree with you but I bloody can't prove I'm right".
Well, at least this is what I was able to surmise from the various people who have accused me of trolling.
It is often, and as used in this case, a term for those who are wrong, won't listen to those who are trying to correct them, and do so in a manner unconducive to further discussion.
I asked for the logical structure. If you can't get yourself to address this, then I'm not interested since I already tried the informal route, to no avail.
You asked for the responder to express the formal structure. They could do it in interpretive dance if they thought that it was the best way. If you only want them to post a formal structure then you should be more explicit than effectively asking them to express something in their own words.

Look at the first example.
The form of this is identical to your syllogism:
All students carry back packs
My grandfather carries a backpack
Therefore my father grandfather is a student.
Ah, excellent. Something reasonable.
So, this is given by the Wiki page as an instance of the formal structure:
All Z is B
Y is B
Therefore, Y is Z
See https://en.wikipedia.org/wiki/Fallacy_of_the_undistributed_middle for more details.
Form:
All S = P
G = P
Therefore G = S
Er, no. Let me repeat: the backpack example is given by the Wiki page as an instance of the formal structure:
All Z is B
Y is B
Therefore, Y is Z
See https://en.wikipedia.org/wiki/Fallacy_of_the_undistributed_middle for more details.
And, clearly, my argument doesn't has this structure.
So, I guess, you are definitely of the very large tribe of unreliable witnesses lurking around here.
Your argument, stripped of uncertainty in the premise:
P1 - conscious mind is the state of a group of neurons
P2 - what we do is determined by the state of a group of neurons
C - what we do is determined by our conscious mind
Stripped of the uncertainty of the premise and of the conclusion it's no longer my argument.
End of conversation.
Thanks for not even trying.
EB

Form:
C = N
All D = N
Therefore C = D

Other than the two premises being in a different order, the form is the same, and you are suffering from a bout of undistributed middle. QED.
It is often, and as used in this case, a term for those who are wrong, won't listen to those who are trying to correct them, and do so in a manner unconducive to further discussion.
You asked for the responder to express the formal structure. They could do it in interpretive dance if they thought that it was the best way. If you only want them to post a formal structure then you should be more explicit than effectively asking them to express something in their own words.

I don't know how to formalize 'for all we know...', certainly not without introducing modal operators.

Introducing 'know' introduces an epistemic operator, but Speakpigeon doesn't seem to want to acknowledge epistemic modal logic. I'm not sure what to make of the 'For all we...' prefixed to it. Does it suggest an assessment of probability, which in turn would suggest many-valued logic and a violation of Aristotle's law of the excluded middle? Or is it just another way of expressing the hypothetical nature of the 'if' in a standard conditional ('if A, then...'), such that A might be either T or F?

If we retain the 'For all we know...' and try to represent it in formal logic, we seem to have moved beyond classical logic. If we don't, then Sarkus is justified in removing it from the argument.
I wonder how you guys go around making sense of what happens just right in front of you in the real world.
Good, I guess I now have a better notion of the limits of the human mind.
Thanks all the same.
EB

Er, no. Let me repeat: the backpack example is given by the Wiki page as an instance of the formal structure:

See https://en.wikipedia.org/wiki/Fallacy_of_the_undistributed_middle for more details.
And, clearly, my argument doesn't has this structure.
As demonstrated it clearly does have that structure.
All Z is B
Y is B
Therefore, Y is Z

This is the same as the form of the example given, replacing "is" for "=":
All S = P
G = P
Therefore G = S

Do you agree thus far?

Your argument actually follows this form even with the uncertainty left in.
The only difference is the change of order of the premises.
C = N
All D = N
Therefore C = D

With the uncertainty left in your premise, C simply becomes "For all we know, somebody's conscious mind..." or words to that effect.
That same uncertainty is then within the conclusion.
And as such it remains invalid.
Stripped of the uncertainty of the premise and of the conclusion it's no longer my argument.
End of conversation.
Thanks for not even trying.
For someone who claims not to know what trolling is you do a very good impersonation of it.

As demonstrated it clearly does have that structure.
All Z is B
Y is B
Therefore, Y is Z
This is the same as the form of the example given, replacing "is" for "=":
All S = P
G = P
Therefore G = S
Do you agree thus far?
No.
Yours has the first premise of the form "All s are such that P(s)", i.e. All students carry backpacks.
Not mine.
Check again. I put the argument here again for your convenience:
Premise 1 - For all we know, somebody's conscious mind may be the state of a group of neurons in this person's brain;
Premise 2 - What somebody does is determined by the state of a group of neurons in this person's brain;
Conclusion - Therefore, for all we know, what somebody does may be determined by the conscious mind of this person.
EB

Your argument actually follows this form even with the uncertainty left in.
The only difference is the change of order of the premises.
C = N
All D = N
Therefore C = D
With the uncertainty left in your premise, C simply becomes "For all we know, somebody's conscious mind..." or words to that effect.
That same uncertainty is then within the conclusion.
And as such it remains invalid.
For someone who claims not to know what trolling is you do a very good impersonation of it.

No.
Yours has the first premise of the form "All s are such that P(s)", i.e. All students carry backpacks.
Not mine.
Check again. I put the argument here again for your convenience:
As said, the only difference is the change of order of the premises.
Do you expect to be taken seriously if you raise objection over the order of premises, and deem the analysis wrong or irrelevant as a result???

As said, the only difference is the change of order of the premises.
None of my premises is of the form All x are such that F(x).
Nothing further to be discussed with you. Ever.
Thanks.
EB

None of my premises is of the form All x are such that F(x).
Yes they are. If you say, as you did: "What somebody does is determined by..." then you are, quite explicitly, stating that all x are such that F(x) where x is "what someone does", and F(x) is "is determined by".... I.e. it is an explicit assertion that everything (i.e. all) somebody does is determined by... all x are such that they are determined by... all x are such that F(x).
QED.
Nothing further to be discussed with you. Ever.
Thanks.
So first you think the premises being in a different order somehow invalidates the analysis of the form of a syllogism, and now you think that none of your premises is in a certain form, even though your second premise quite clearly takes that exact form.
And you wonder why people take you for a troll. Ah, well. One day you might even grow up.

Yes they are. If you say, as you did: "What somebody does is determined by..." then you are, quite explicitly, stating that all x are such that F(x) where x is "what someone does", and F(x) is "is determined by".... I.e. it is an explicit assertion that everything (i.e. all) somebody does is determined by... all x are such that they are determined by... all x are such that F(x).
Then post the whole argument fully formalised as you seem to suggest here.
EB

Nothing further to be discussed with you. Ever.

What is it that you want from everyone else that posts here?

You seem to have read some philosophy (a good thing), you ask difficult questions that are often topics of controversy in the literature (a good thing) and you ask that other Sciforums participants post their views (a good thing). But then you attack and dismiss everything that they say (not a good thing).

You present the appearance of somebody who is trying to establish himself as the board's professor, creating a hierarchical relationship with everyone else. I don't know if that's the impression that you intend to create, but you seem to be alienating people who might otherwise have been your friends. (Sarkus is a nice guy and very smart.)

It might help to remember that a good teacher encourages his students to think for themselves, even when the teacher is convinced that he knows more than they do. Incessantly putting them down for venturing an idea isn't good teaching. You need to praise and encourage them, then very gently point out what you believe are weaknesses in their idea.

But in order to have anyone acknowledge you as their professor, you need to demonstrate that you really do have a superior grasp of the subject. So perhaps it's time for you to provide your own answers to the questions that you raise. Given that many of these questions are topics of active discussion in the literature, questions about which multiple views exist, that might be hard to do.

Then post the whole argument fully formalised as you seem to suggest here.

Why don't you post the "whole argument" formalized whatever way you prefer? I don't believe that you can. (I can't. I question whether it can be done in terms of classical propositional or predicate logic.) Sarkus already took his shot in post #9, but you simply dismissed his efforts in post #10. If you think that you can do better than Sarkus did, take your best shot.

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thank you
Premise 1 - For all we know, somebody's conscious mind may be the state of a group of neurons in this person's brain;
Premise 2 - What somebody does is determined by the state of a group of neurons in this person's brain;
Conclusion - Therefore, for all we know, what somebody does may be determined by the conscious mind of this person.

you are most welcome.
Premise 1
the tense seems to be a potential differentiation for the subjective ends to the nature of the premise.
Premise 2
again, tense seems to be running the debate.
Conclusion "for all we know"
= subjective disassociation from the nature of the topic

i think you need to restructure your sentences to apply the correct meaning to the implied meaning.
Scientifically you can not have a debate by discussing something that has not been defined to come to a term of factual finding on the nature of that specificity.
otherwise it is philosophical abstract discussion, rather than debate.