Wednesday, December 12, 2012

The Difference between Traditional and Modern Logic and the Difference it Makes


This is the first two pages or so of a 20 page essay I wrote some years ago. I've gone back to it several times, realizing it needed more work. I am going to use the recent article by Peter Kreeft in Touchstone Magazine and the recent response at First Thoughts as an excuse to go ahead and start posting it in pieces here to give me an excuse to finish it. It is still in draft form and parts of it clearly need more work, but what I'll publish here is at least approaching some kind of finished form.

I am often asked why, as a logic teacher, I teach traditional logic rather than the modern system of logic, which is much more common today.  I would like to answer this question by explaining what traditional logic is and how it differs from modern logic.

In analyzing the differences between traditional and modern logic, we will discuss the assumptions behind the two systems, the structure of the systems and their competing purposes.  As we do this, we should be aware that, for the most part, the nature of these differences is not disputed by the chief proponents of either system.  In other words, both traditional and modern logicians agree that these are in fact the differences: their only disagreement has to do with the extent of the differences and the merit of the respective systems.

What is Traditional Logic?
Traditional logic is the system of logic originally formulated by Aristotle, the Greek philosopher, in the fourth century B. C.  It was taken up by the great Christian thinkers of the Middle Ages, who simplified its structure and formalized the methods of teaching it to students.

Traditional logic involves mostly the study of the classical syllogism.  Here is a classic example of a simple syllogism, which we will use shortly as a way to see how the two systems of traditional and modern logic are different:
All men are mortal
Socrates is a man
Therefore, Socrates is mortal
Traditional logic has also been called “term logic,” since it deals primarily (but not exclusively) with the relation of terms in an argument (in this case, the terms man, mortal, and Socrates). Whether the reasoning is valid depends on the proper arrangement of these terms in an argument.

It wasn’t until the 18th and 19th centuries that Aristotle’s system of traditional logic fell on hard times.  Beginning in the Enlightenment, the influence of scientific materialism grew tremendously.  Because of the incredible technological progress made possible by the sciences, the quantitative methods of science came eventually to be seen as an intellectual elixir, applicable to any and all intellectual disciplines.  The whole discipline of philosophy changed, beginning with William of Ockham, and continuing on into the radical rationalism of Descartes and the radical empiricism of Francis Bacon—the two intellectual traditions that still constitute the two basic impulses of the modern mind.

Traditional logic appealed to Medieval thinkers not only because it was based on Aristotelian metaphysical assumptions (not a big surprise since it was Aristotle who developed it in the first place), but also because of its uses in the determination of Christian truth. It was displaced by modern mathematical logic for two reasons: first, because of the rejection by modern philosophers of certain traditional assumptions about meaning and reality—assumptions that affect the entire system of logic; and second, because modern philosophers were looking for a way to make a science out of human reasoning—a way to completely capture the intricacies of human statements in a formal “scientific” system.

The chief actors in the drama that produced modern logic were Gottlob Frege, Bertrand Russell, Alfred North Whitehead, and Ludwig Wittgenstein. Frege, partly through his unsuccessful effort to show that mathematics was reducible to logic, developed a method of quantifying thoughts and inferences in a system of symbols. Russell and Whitehead took the basic conceptual framework of Frege’s symbolic system and used it to develop a full-fledged system of symbolic logic in their book, Principia Mathematica, the purpose of which, like Frege’s work, was to prove that mathematics was an extension of logic, but the most influential aspect of which was its system of logic. Wittgenstein both influenced and was influenced by Russell, and many of his ideas affected the Principia. Wittgenstein is reputed to have invented the truth tables that have become an essential fixture of modern logic.

The Differences Between Traditional and Modern Logic
The first thing to note about the differences between traditional and modern logic is that they are indeed different.  Although most modern logicians see the differences as differences in degree, they still consider these differences significant.  Irving Copi, the author of one widely used college logic text, does not reject the traditional system, but he does see the two systems as being very different:

Although the difference in this respect between modern and classical logic is not one of kind but of degree the difference in degree is tremendous.” [Introduction to Logic, 3rd Ed., 1968, Irving Copi, p. 212]

To the traditional logician, the difference goes even deeper:

“Aristotelian logic and symbolic logic,” says Edward Simmons, “are radically distinct disciplines.” [The Scientific Art of Logic: An Introduction to the Principles of Formal and Material Logic, 1961, Edward D. Simmons, p. 322]

Jacques Maritain, a traditional logician who referred to modern symbolic logic as “logistics,” put it this way:
Logistics differs essentially from Logic … Logistics and logic remain separate disciplines, entirely foreign to one another. (emphasis in the original)
Many traditional logicians, in fact, reject much of modern logic as mistaken.  Maritain, in fact, goes so far as to argue that modern logic is not logic at all.  This favor is returned by some modern logicians.  Traditional logic, says Bertrand Russell, one of the founders of the modern system, “is as definitely antiquated as Ptolemaic astronomy.” [Bertrand Russell, A History of Western Philosophy (New York: Simon and Schuster, 1945), p. 195].  Anyone wanting to know Russell’s view of Aristotelian logic will find it at the end of his chapter on Aristotle in this book:
I conclude that the Aristotelian doctrines with which we have been concerned in this chapter are wholly false, with the exception of the formal theory of the syllogism, which is unimportant.  Any person in the present day who wishes to learn logic will be wasting his time if he reads Aristotle or any of his disciples. [Russell, p. 202]
So there.

In short, some of the most important traditional and modern logicians agree that the systems are different, and some advocates of the respective systems reject, in whole or in part, the opposing system.

As we mentioned above, the two systems differ in three respects:  First, the assumptions behind the two systems are different.  Second, the format or structure of the two systems is different.  Third, the respective purposes of the two systems are different.  In all three cases—in the assumptions, structure, and the purpose—the traditional system reflects traditional views, and the modern system reflects modern views about reality. Each system is based on a different metaphysic.

To be continued ...

UPDATE: Although I am still in the process of finishing the line of thought started in this post, I have posted another related article on the issue of why traditional logic does not employ truth tables that should be of interest to those interested in this article: here

24 comments:

Old Rebel said...

Martin,

A very approachable and concise introduction to a topic I find both fascinating and intimidating.

I'm looking forward to your future installments.

Lee Faber said...

So what is Ockham's relation to Aristotelian logic? He wrote several commentaries on Aristotle's logic, as well as the summa logicae. I've only read the first 100 pages or so of the latter, but apart from obvious nominalist positions on universals, the logic as such seemed similar to what one finds in Peter of Spain.

Also, nominalism didn't begin with Ockham. It was fairly common in the west in the 12th century; if one starts their study of scholasticism there, one finds that the nominalists by and large constitute the 'common opinion' of the middle ages, with the metaphysicians Aquinas and Scotus the outliers.

YT said...

I stumbled upon your fine post when I was looking up criticisms of symbolic logic. I am an avid reader of Veatch and I am glad there are others (like you) who have followed the schism of the two logics so closely. Keep up the good work, I look forward to the final product.

Anonymous said...

Hi, I am from Australia.
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1. www.beezone.com/whiteandorangeproject/index.html
2. www.beezone.com/AdiDa/ScientificProof/tableofcontents.html
3. http://spiralledlight.wordpress.com
4. www.dabase.org/aletheon.htm
5. http://global.adidam.org/books/ancient-teachings
6. www.aboutadidam.org/readings/asana_of_science/index.html

Anonymous said...

I always have trouble comprehending words such as "metaphysical", "epistemological", etc. I have been wishing for some time that this post would be finished. I would really like to see some examples as well.

j a higginbotham

Anonymous said...

Confusing use of "quantify" with no explanation.
Both this post and the Kreeft article seem to use "quantity" in specialized or inconsistent ways. Here we have "the quantitative methods of science" (which to me in the common usage of quantity means to assign numbers to things) but also "method of quantifying thoughts and inferences in a system of symbols" (i don't see any numbers involved here).
Indeed, Wikipedia gives two definitions:
express or measure the quantity of.
"it's very hard to quantify the cost"
2.
LOGIC
define the application of (a term or proposition) by the use of all, some, etc., e.g., “for all x if x is A then x is B.”

It would be nice if this distinction were made clear. Just as with "theory" in science or common usage, the meaning is quite different and can be confusing.

j a higginbotham



Martin Cothran said...

UPDATE: Although I am still in the process of finishing the line of thought started in this post, I have posted another related article on the issue of why traditional logic does not employ truth tables that should be of interest to those interested in this article: http://vereloqui.blogspot.com/2015/11/why-traditional-logic-doesnt-employ.html

Greg H. said...

Would Jacques Lacan's reworking of Aristotle's square of opposition

http://www.swingtradesystems.com/lacan/lacan-and-aristotle.html

qualify as modern (or even post-modern) logic?

Greg

radha said...

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We have provided over $30 Billion in business loans to over 50,000 business owners just like you. We use our own designated risk technology to provide you with the right business loan so you can grow your business. Our services are fast and reliable, loans are approved within 24 hours of successful application. Do you find yourself in a bit of trouble with unpaid bills and don't know which way to go or where to turn? What about finding a reputable Debt Consolidation firm that can assist you in reducing monthly installment so that you will have affordable repayment options as well as room to breathe when it comes to the end of the month and bills need to get paid? LoansNow international financial company is the answer. Reduce your payments to ease the strain on your monthly expenses. We offer loans from a minimum range of $10,000 to a maximum of $700 million Dollars. Intermediaries/Consultants/Brokers are welcome to bring their clients and are 100% protected. Give us a try and be free from financial problems by Phone Contact: ++1 (860)866-4085 Email: goodnewsloancompany7@gmail.com In complete confidence, we will work together for the benefits of all parties involved. Do not keep your financial problems to yourself in order for you not to be debt master or financial stress up, which is why you must contact us quickly for a solution to your financial problems. It will be a great joy to us when you are financially stable Email us via: goodnewsloancompany7@gmail.com
Our services include the following below
______________________________________________________
*Personal loans *Truck & Car Loans *Debt consolidation loans
*Student Loans *Home & Hotel Loans *Marriage & Celebration Loans
*Agricultural & Farm Loans *Real Estate & Construction Loans
*Business Start-up Loans or Business Expansion Loans. We offer all types of loans
We are a financial consultants that handles international finances for any amount of banking instruments. We have the access/contacts to raise from $10 thousand to $700 Million Dollars. We have brought ailing industries back to life and we back good business ideas by providing funds for their up start. We have network of Investors that are willing to provide funds of whatever amount to individuals and organizations to start business and operations. Our company has recorded a lot of breakthroughs in the provision of first class financial services to our clients, especially in the area of Loan syndication and capital provision for individuals and companies. We offer loan to individual and public sector that are in need of financial Assistance in a low interest rate of 2%. Bad credit acceptable,The Terms and Conditions are very simple and considerate, We are a group of energetic and experienced loan professionals with thorough knowledge of financial markets, we are committed in providing our customers and suppliers with simple and competitive forms of finance solutions for all business users. I believe you might be interested in starting up a new business in need of funding or expanding the scope of your already existing businesses, our investors are also interested in funding / partnering and ready to invest large sum on traders who are ready to proof their expertise in the new industry with our reliable loan company and other TOP PRIME AAA BANKS like Bank of America, HSBC, Lloyds, Wells Fargo, The Best Banks for SBA Loans and many more. You will never regret anything in this loan transaction because i will make you happy via email {goodnewsloancompany7@gmail.com} getting a loan from this company is 100% assured and guaranteed contact by email goodnewsloancompany7@gmail.com
Regards
Goodnewsloancompany
Phone Contact: +1 (860)866-4085
Email: goodnewsloancompany7@gmail.com

LOAN said...

ATTENTION ARE YOU IN NEED OF PERSONAL LOAN/INVESTMENT LOAN/BUSINESS FUNDING???Email: goodnewsloancompany7@gmail.com
We have provided over $30 Billion in business loans to over 50,000 business owners just like you. We use our own designated risk technology to provide you with the right business loan so you can grow your business. Our services are fast and reliable, loans are approved within 24 hours of successful application. Do you find yourself in a bit of trouble with unpaid bills and don't know which way to go or where to turn? What about finding a reputable Debt Consolidation firm that can assist you in reducing monthly installment so that you will have affordable repayment options as well as room to breathe when it comes to the end of the month and bills need to get paid? LoansNow international financial company is the answer. Reduce your payments to ease the strain on your monthly expenses. We offer loans from a minimum range of $10,000 to a maximum of $700 million Dollars. Intermediaries/Consultants/Brokers are welcome to bring their clients and are 100% protected. Give us a try and be free from financial problems by Phone Contact: ++1 (860)866-4085 Email: goodnewsloancompany7@gmail.com In complete confidence, we will work together for the benefits of all parties involved. Do not keep your financial problems to yourself in order for you not to be debt master or financial stress up, which is why you must contact us quickly for a solution to your financial problems. It will be a great joy to us when you are financially stable Email us via: goodnewsloancompany7@gmail.com
Our services include the following below
______________________________________________________
*Personal loans *Truck & Car Loans *Debt consolidation loans
*Student Loans *Home & Hotel Loans *Marriage & Celebration Loans
*Agricultural & Farm Loans *Real Estate & Construction Loans
*Business Start-up Loans or Business Expansion Loans. We offer all types of loans
We are a financial consultants that handles international finances for any amount of banking instruments. We have the access/contacts to raise from $10 thousand to $700 Million Dollars. We have brought ailing industries back to life and we back good business ideas by providing funds for their up start. We have network of Investors that are willing to provide funds of whatever amount to individuals and organizations to start business and operations. Our company has recorded a lot of breakthroughs in the provision of first class financial services to our clients, especially in the area of Loan syndication and capital provision for individuals and companies. We offer loan to individual and public sector that are in need of financial Assistance in a low interest rate of 2%. Bad credit acceptable,The Terms and Conditions are very simple and considerate, We are a group of energetic and experienced loan professionals with thorough knowledge of financial markets, we are committed in providing our customers and suppliers with simple and competitive forms of finance solutions for all business users. I believe you might be interested in starting up a new business in need of funding or expanding the scope of your already existing businesses, our investors are also interested in funding / partnering and ready to invest large sum on traders who are ready to proof their expertise in the new industry with our reliable loan company and other TOP PRIME AAA BANKS like Bank of America, HSBC, Lloyds, Wells Fargo, The Best Banks for SBA Loans and many more. You will never regret anything in this loan transaction because i will make you happy via email {goodnewsloancompany7@gmail.com} getting a loan from this company is 100% assured and guaranteed contact by email goodnewsloancompany7@gmail.com
Regards
Goodnewsloancompany
Phone Contact: +1 (860)866-4085
Email: goodnewsloancompany7@gmail.com

LOAN said...

ATTENTION ARE YOU IN NEED OF PERSONAL LOAN/INVESTMENT LOAN/BUSINESS FUNDING???Email: goodnewsloancompany7@gmail.com
We have provided over $30 Billion in business loans to over 50,000 business owners just like you. We use our own designated risk technology to provide you with the right business loan so you can grow your business. Our services are fast and reliable, loans are approved within 24 hours of successful application. Do you find yourself in a bit of trouble with unpaid bills and don't know which way to go or where to turn? What about finding a reputable Debt Consolidation firm that can assist you in reducing monthly installment so that you will have affordable repayment options as well as room to breathe when it comes to the end of the month and bills need to get paid? LoansNow international financial company is the answer. Reduce your payments to ease the strain on your monthly expenses. We offer loans from a minimum range of $10,000 to a maximum of $700 million Dollars. Intermediaries/Consultants/Brokers are welcome to bring their clients and are 100% protected. Give us a try and be free from financial problems by Phone Contact: ++1 (860)866-4085 Email: goodnewsloancompany7@gmail.com In complete confidence, we will work together for the benefits of all parties involved. Do not keep your financial problems to yourself in order for you not to be debt master or financial stress up, which is why you must contact us quickly for a solution to your financial problems. It will be a great joy to us when you are financially stable Email us via: goodnewsloancompany7@gmail.com
Our services include the following below
______________________________________________________
*Personal loans *Truck & Car Loans *Debt consolidation loans
*Student Loans *Home & Hotel Loans *Marriage & Celebration Loans
*Agricultural & Farm Loans *Real Estate & Construction Loans
*Business Start-up Loans or Business Expansion Loans. We offer all types of loans
We are a financial consultants that handles international finances for any amount of banking instruments. We have the access/contacts to raise from $10 thousand to $700 Million Dollars. We have brought ailing industries back to life and we back good business ideas by providing funds for their up start. We have network of Investors that are willing to provide funds of whatever amount to individuals and organizations to start business and operations. Our company has recorded a lot of breakthroughs in the provision of first class financial services to our clients, especially in the area of Loan syndication and capital provision for individuals and companies. We offer loan to individual and public sector that are in need of financial Assistance in a low interest rate of 2%. Bad credit acceptable,The Terms and Conditions are very simple and considerate, We are a group of energetic and experienced loan professionals with thorough knowledge of financial markets, we are committed in providing our customers and suppliers with simple and competitive forms of finance solutions for all business users. I believe you might be interested in starting up a new business in need of funding or expanding the scope of your already existing businesses, our investors are also interested in funding / partnering and ready to invest large sum on traders who are ready to proof their expertise in the new industry with our reliable loan company and other TOP PRIME AAA BANKS like Bank of America, HSBC, Lloyds, Wells Fargo, The Best Banks for SBA Loans and many more. You will never regret anything in this loan transaction because i will make you happy via email {goodnewsloancompany7@gmail.com} getting a loan from this company is 100% assured and guaranteed contact by email goodnewsloancompany7@gmail.com
Regards
Goodnewsloancompany
Phone Contact: +1 (860)866-4085
Email: goodnewsloancompany7@gmail.com

linda said...

HOW I GOT MY LOAN FROM THIS GREAT COMPANY

Hello my dear people, I am Linda McDonald, currently living in Austin Texas, USA. I am a widow at the moment with three kids and i was stuck in a financial situation in April 2018 and i needed to refinance and pay my bills. I tried seeking loans from various loan firms both private and corporate but never with success, and most banks declined my credit ,do not full prey to those hoodlums at there that call them self-money lender they are all scam , all they want is your money and you well not hear from them again they have done it to me twice before I met Mr. David Wilson the most interesting part of it is that my loan was transfer to me within 74hours so I will advise you to contact Mr. David if you are interested in getting loan and you are sure you can pay him back on time you can contact him via email……… (davidwilsonloancompany4@gmail.com) No credit check, no cosigner with just 2% interest rate and better repayment plans and schedule if you must contact any firm with reference to securing a loan without collateral then contact Mr. David Wilson today for your loan

They offer all kind of categories of loan they

Short term loan (5_10years)
Long term loan (20_40)
Media term loan (10_20)
They offer loan like
Home loan............., Business loan........ Debt loan.......
Student loan.........., Business startup loan
Business loan......., Company loan.............. etc
Email..........( davidwilsonloancompany4@gmail.com)
When it comes to financial crisis and loan then David Wilson loan financial is the place to go please just tell him I Mrs. Linda McDonald direct you Good Luck.......................