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Chaoslord2004
Philosopher & Logician
Joined: 29 Aug 2004
Posts: 8438
Local time: 12:15 AM
Location: Minnesota
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 Posted: Thu Aug 07, 2008 10:11 am Post subject: Ask a Logician |
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Every once an a while I get a PM asking me a logic question. I have decided to make a thread devoted to answering all your pressing questions on logic, philosophy of logic and philosophy of mathematics.
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An artist sees beauty in a painting. I see beauty in a logical proof.
"All error is due to extraneous factors, reason itself does not err"
~Kurt Gödel |
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romans120
Resident Theist
Joined: 14 Aug 2007
Posts: 2123
Local time: 11:15 PM
Location: The God Shaped Hole in Your Heart
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| Posted: Thu Aug 07, 2008 10:43 am Post subject: Re: Ask a Logician |
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| Chaoslord2004 wrote: | | Every once an a while I get a PM asking me a logic question. I have decided to make a thread devoted to answering all your pressing questions on logic, philosophy of logic and philosophy of mathematics. |
I'm honestly not being snoooty. (thought you might think I was cuz of the other discussion). but it might be helpful to list your credentials so we know how seriously to take your opinion
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For what can be known about God is plain to them, because God has shown it to them. 20 For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse. Romans 1:19-20
Check out my weblog at http://romans120.wordpress.com/ |
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Chaoslord2004
Philosopher & Logician
Joined: 29 Aug 2004
Posts: 8438
Local time: 12:15 AM
Location: Minnesota
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| Posted: Thu Aug 07, 2008 10:56 am Post subject: Re: Ask a Logician |
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| romans120 wrote: | | Chaoslord2004 wrote: | | Every once an a while I get a PM asking me a logic question. I have decided to make a thread devoted to answering all your pressing questions on logic, philosophy of logic and philosophy of mathematics. |
I'm honestly not being snoooty. (thought you might think I was cuz of the other discussion). but it might be helpful to list your credentials so we know how seriously to take your opinion |
let me know when you have a serious question.
_________________
An artist sees beauty in a painting. I see beauty in a logical proof.
"All error is due to extraneous factors, reason itself does not err"
~Kurt Gödel |
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Mr_C
Reckoner
Joined: 26 Jun 2006
Posts: 6752
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Location: Pale Blue Dot
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| Posted: Thu Aug 07, 2008 11:50 am Post subject: |
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He's a master debator and a cunning linguist...
/despises leykis |
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romans120
Resident Theist
Joined: 14 Aug 2007
Posts: 2123
Local time: 11:15 PM
Location: The God Shaped Hole in Your Heart
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| Posted: Thu Aug 07, 2008 11:53 am Post subject: Re: Ask a Logician |
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| Chaoslord2004 wrote: | | romans120 wrote: | | Chaoslord2004 wrote: | | Every once an a while I get a PM asking me a logic question. I have decided to make a thread devoted to answering all your pressing questions on logic, philosophy of logic and philosophy of mathematics. |
I'm honestly not being snoooty. (thought you might think I was cuz of the other discussion). but it might be helpful to list your credentials so we know how seriously to take your opinion |
let me know when you have a serious question. |
it is a serious question. Do you have a degree is it your career? I
_________________
For what can be known about God is plain to them, because God has shown it to them. 20 For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse. Romans 1:19-20
Check out my weblog at http://romans120.wordpress.com/ |
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gnosis
Forum Master
Joined: 27 Feb 2008
Posts: 2490
Local time: 12:15 AM
Location: California
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| Posted: Thu Aug 07, 2008 11:55 am Post subject: |
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OK here's a serious question. How do you feel about Nietzsche's statement:
| Quote: | | Nietzsche: "Logic, too, also rests on assumptions that do not correspond to anything in the real world" |
What do you feel are the limitations of logic?
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"Agnostics: Atheists without balls." -Stephen Colbert |
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Chaoslord2004
Philosopher & Logician
Joined: 29 Aug 2004
Posts: 8438
Local time: 12:15 AM
Location: Minnesota
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| Posted: Thu Aug 07, 2008 12:18 pm Post subject: |
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| gnosis wrote: | OK here's a serious question. How do you feel about Nietzsche's statement:
| Quote: | | Nietzsche: "Logic, too, also rests on assumptions that do not correspond to anything in the real world" |
What do you feel are the limitations of logic? |
Well, in general, logic, like any tool, will be limited in its scope. One limitation was demonstrated by Godel and Paul Cohen: in an formal system in which basic truths of arithmetic are probable, there will be propositions which if the system is consistent, will be true, but unprovable. As it turns out, there are infinitely many such propositions.
In other words, our rigorous methods of proof, will never be able to prove every truth of mathematics. This is a severe limitation. Or take the continuum hypothesis which states there are not sizes of infinity between the set of integers and the set of real numbers. In the strongest theory of sets, zermelo-fraenkle set theory, this proposition is undecidable. Indeed, there are many undecidable propositions in ZFC.
Lets not forget the paradoxes which plague mathematics...
But on to Nietzsche. He is correct, pure mathematics and pure logic do not correspond to the real world. I mean, take the transfinite numbers. I mean, there is no such transfinite number in the universe.
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An artist sees beauty in a painting. I see beauty in a logical proof.
"All error is due to extraneous factors, reason itself does not err"
~Kurt Gödel |
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Moloth
Fateless
Joined: 27 Aug 2003
Posts: 23105
Local time: 12:15 AM
Location: Warner Robins, GA
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| Posted: Thu Aug 07, 2008 12:53 pm Post subject: |
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what is your level of formal education in logic and/or philosophy, Chaos?
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-=The Believer is Happy; the Skeptic is Wise=-
www.Moloth.com
Last edited by Moloth on Tue Feb 30, 2026 13:61 am; edited 426 times in total |
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Wickedtruth
Forum Master
Joined: 09 May 2008
Posts: 2214
Local time: 12:15 AM
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| Posted: Thu Aug 07, 2008 12:56 pm Post subject: |
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| Moloth wrote: | | what is your level of formal education in logic and/or philosophy, Chaos? |
I dropped out of college...can I still criticize people? :/ |
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Chaoslord2004
Philosopher & Logician
Joined: 29 Aug 2004
Posts: 8438
Local time: 12:15 AM
Location: Minnesota
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| Posted: Thu Aug 07, 2008 1:03 pm Post subject: |
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| Moloth wrote: | | what is your level of formal education in logic and/or philosophy, Chaos? |
Let me post part of my CV...
Undergraduate Emphasis
Logic
Logic Courses Taken
Introduction to Logic (Critical Reasoning)
Symbolic Logic
Modal Logic
Topics in Mathematics: Mathematical Logic & Gödel’s Incompleteness Theorems
Probability Theory
Advanced Symbolic Logic (currently taking)
Introduction to Set Theory (currently taking)
Conference Presentations
Presented a paper titled “Prior and The Liar” at the 2006 Minnesota Philosophical Student Meeting, Hosted by St. Thomas University
Presented a paper titled “A Critique of Nicholas Rescher’s Theory of Paradox Resolution” at the 2007 Minnesota Philosophical Student Meeting. Hosted by St. Cloud State University.
Presented a paper titled “Practical Rationality within The Prisoner’s Dilemma” at the 2008 Minnesota Philosophical Society Meeting. Hosted by Gustavious Adulphos University.
Presented a paper titled “Practical Rationality within The Prisoner’s Dilemma” at the 2008 St. Cloud State University Student Research Colloquium.
Presented a paper titled “Why the Language Faculty Evolved by Natural Selection: A Critique of Chomsky” at the 2008 St. Cloud State University Student Research Colloquium.
Commentary Given at Conferences
Gave a commentary on a paper titled “Correspondence and Knowledge: An Inquiry into Whether Correspondence Applies to All Objective Knowledge” at the 2007 Minnesota Philosophical Student Meeting.
Gave a commentary on a paper titled “A Response to the Gettier Problem” at the 2007 Minnesota Philosophical Student Meeting.
Awards and Recognition
1st prize for my paper titled “Prior and The Liar” in the 2006 SCSU Philosophical Essay contest
2nd prize for my paper titled “A Critique of Nicholas Rescher’s Theory of Paradox Resolution” in the 2007 SCSU Philosophical Essay contest.
2nd prize for my paper titled “Pragmatic Rationality within The Prisoner’s Dilemma” in the 2008 SCSU Philosophical Essay contest.
Mentioned in the preface of How to Think Logically (Penguin Academics) by Gary Seay and Susana Nuccetelli for my clerical work.
Mentioned in the preface of Philosophy of Language: The Central Topics by Gary Seay and Susana Nuccetelli, for my clerical work.
Mentioned in the preface of A Companion to Epistemology (Blackwell Companions to Philosophy) edited by Matthias Steup, for my editorial work.
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My CV is longer, but this ought to suffice.
_________________
An artist sees beauty in a painting. I see beauty in a logical proof.
"All error is due to extraneous factors, reason itself does not err"
~Kurt Gödel |
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LakeGeorgeMan
Forum Sheriff
Joined: 22 Mar 2006
Posts: 413
Local time: 12:15 AM
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| Posted: Thu Aug 07, 2008 1:34 pm Post subject: |
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How's the job market for philosophers and 'logicians'?
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...Oozing my brain chemicals in your general direction... |
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LakeGeorgeMan
Forum Sheriff
Joined: 22 Mar 2006
Posts: 413
Local time: 12:15 AM
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| Posted: Thu Aug 07, 2008 1:37 pm Post subject: |
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| Chaoslord2004 wrote: |
1st prize for my paper titled “Prior and The Liar” in the 2006 SCSU Philosophical Essay contest
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I bet your mom is still braggin' to all the relatives and neighbors about that one...
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...Oozing my brain chemicals in your general direction... |
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Chaoslord2004
Philosopher & Logician
Joined: 29 Aug 2004
Posts: 8438
Local time: 12:15 AM
Location: Minnesota
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| Posted: Thu Aug 07, 2008 1:46 pm Post subject: |
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| LakeGeorgeMan wrote: | | How's the job market for philosophers and 'logicians'? |
Its a field of pure reasoning, the job market is never good.
_________________
An artist sees beauty in a painting. I see beauty in a logical proof.
"All error is due to extraneous factors, reason itself does not err"
~Kurt Gödel |
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LakeGeorgeMan
Forum Sheriff
Joined: 22 Mar 2006
Posts: 413
Local time: 12:15 AM
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| Posted: Thu Aug 07, 2008 1:50 pm Post subject: |
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Would you care to comment on the application and limitations of natural deduction Lambek calculus for object level derivations in our grammar, and how this is being pragmatically applied in specific commercial software solutions?
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...Oozing my brain chemicals in your general direction... |
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Chaoslord2004
Philosopher & Logician
Joined: 29 Aug 2004
Posts: 8438
Local time: 12:15 AM
Location: Minnesota
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| Posted: Thu Aug 07, 2008 2:02 pm Post subject: |
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| LakeGeorgeMan wrote: | | Would you care to comment on the application and limitations of natural deduction Lambek calculus for object level derivations in our grammar, and how this is being pragmatically applied in specific commercial software solutions? |
Well, the lambda calculus suffers from undecidability. So, for example, for any given algorithm A, if feed into the system it might be undecidability. In other words, there are correlates in this system as within number theory. Hence, we have a halting problem and Godel's Incompleteness theorems for the system:
(1) some lambda expressions, while true, will be undecidable.
(2) given any lambda expression A, it is impossible to know if the program will given an output of TRUE or FALSE, or if it will go one forever.
This is a severe limitation, in my view.
_________________
An artist sees beauty in a painting. I see beauty in a logical proof.
"All error is due to extraneous factors, reason itself does not err"
~Kurt Gödel |
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