Aristotelian Logic Primer

[LegionOnomaMoi]

I don't think he is talking about the paradox.

It doesn't matter. A sorites "argument" is an instance of the paradox.

 

[Curious George]

It doesn't matter. A sorites "argument" is an instance of the paradox.

I think he is referring to the polysyllogism

See sorites as used here:

http://etc.usf.edu/lit2go/37/logic-deductive-and-inductive/466/chapter-11/

https://www3.nd.edu/~maritain/jmc/etext/logic-58.htm

https://en.m.wikipedia.org/wiki/Polysyllogism

 

[LegionOnomaMoi]

I think he is referring to the polysyllogism

Which would by definition require a non-Aristotelian many-valued logic.

See sorites as used here:

I don't need to. I saw "sorites" as defined in the text cited (and basically plagiarized). Also, the uses you refer to are examples of the sorites paradox.

 

[Curious George]

Which would by definition require a non-Aristotelian many-valued logic.


I don't need to. I saw "sorites" as defined in the text cited (and basically plagiarized). Also, the uses you refer to are examples of the sorites paradox.

This is my understanding:

Sorites arguments of the paradoxical form are to be distinguished from multi-premise syllogisms (polysyllogisms) which are sometimes also referred to as sorites arguments.

From: http://plato.stanford.edu/entries/sorites-paradox/

 

[Logikal]

1) The relationship you describe between language and logic (e.g., the copula or any similarly stative verb or verbal construction and predicates in Aristotelian/classical logic)
2) The nature of the Sorites paradox or sorites arguments (the two are identical; see your own text A Concise Introduction to Logic (11th Ed.) here: "A sorites is a chain of categorical syllogisms in which the intermediate conclusions have been left out. The name is derived from the Greek word soros, meaning “heap,” and is pronounced “sōrītëz,” with the accent on the second syllable. The plural form is also “sorites.”; the relevant example is that one might find in a textbook on many-valued and/or fuzzy logics- an argument that requires a reasoning chain in which the truth values of certain propositions are not binary but rather depend upon vague quantifications or degrees).
4) All your claims about Aristotle
5) The nature of syllogistic arguments
6) The nature of the word "philosopher" and all other references to any terms found in Aristotle or Greek literature more generally.
7) Elementary linguistic terms such as "noun phrase" and their relationship to logic.
7) QUANTIFICATION



You've ripped off Hurley's text from the Concise Introduction series, but don't understand it. The predicate is a VERB (and can be a copula). The predicate relates the subject to what you (following Hurley) call the "predicate term" and what most of us familiar with logic would call an "argument", "variable", etc., or just not refer to at all but rather rely on the multiplicity of the predicate itself and a subsequent appropriate designation (e.g., a "two-place" predicate will necessarily have two "terms" that are related to the "subject" by the predicate). The "middle term" Hurley refers to is simply the component shared by the (by definition) two-premise form of a syllogism. One cannot, from two premises, infer the validity of anything from these two unless they relate in some way, namely in that they refer to the same "object", concept, etc., or properties of one of these ("All crows are black" & X is not black " are related by the property "BLACK" as applied to crows, and therefore allow us to infer that X is not a crow).


That's because it does. It's a central reason for many-valued logics, all of which are non-Aristotelian


The etymology is simply the use of the Greek word in relation to a (sand) heap. If one removes a grain of sand from a sand heap, it is still a heap of sand. But remove enough grains, and you will eventually be left with a single grain. There is no point at which a heap goes from being a heap to not a heap given a single removal of a grain of sand, yet Aristotelian logic demands this.

I'm aware. I've not only written about this but served as a consult for others here. The problem is that you don't seem to be familiar with these sources except to the extent you don't understand them. That's why, when I ask for citations, I don't mean sources, but literally citing specific parts of sources (particularly Aristotle) that would support the things you state.


A paradox is a type of argument pattern. A "sorites argument" is an argument that is strictly invalid in Aristotelian logic but problematically so.
.

You regurgitated them from Hurley, and badly.

I will cite the information we are discussing that gives me REASON for what I have stated. To do so will take time. So here I want to specifically address what I think our disagreement is and it resolves around what a proposition is. I will prove to you later that multiple sources use the term SORITES without mentioning any paradox. You say they are identical and I will prove this claim: "a SORITES is identical to a paradox" is FALSE.
I never attempted to cite any author Hurley or Copi who I also mentioned who discusses SORITES again without any paradox. I will quote specific portions for you to see. What I am expressing is the concept and it seems you only desire word for word literally.
This comes again to what a proposition is. It seems there is a generation of philosophers in a philosophy department (and all math professors I see) that teach a proposition is A SENTENCE. I will point out several references that DID NOT teach this way. I for instance was taught a proposition is what is expressed by a declarative sentence and are not sense verifiable. There are a multitude of students taught in this way -- not propositions are literally declarative sentences. I will provide this information for you. The catch is what I quote will not be identical word for word with what I said. The vibe I get from you is that is what you care about. Propositions can express the same idea using different words literally. I will point this out to you. You seem to be strictly literal: I.e., you will say the sentence does not say . . . ! I speak of propositions sir, not sentences. No I did not learn this from any textbook but directly from a qualified Professor with a PhD in a college. More than one PhD qualified professor EXPRESSED the same idea: a proposition is NOT physical. You cannot see them, hear them , etc.
You mention further about the paradox and why modal logics began but you cannot keep the proper definition of PROPOSITION and go on the way you do. The proposition "there will be a sea battle in the reed sea" is a proposition and has a truth value that is either true or false. The context suggests a human might not be aware which truth value the proposition holds. You seem to be steering this direction and that has nothing to do with argument evaluation which classical logic is deemed for and you like many others state that position of science. Logic that I discussed above is not a science in this regard but an art. You are expressing "being practical" which is only covered by a type of SCIENCE. There is no such thing as an unpractical science by definition of the word science. What I am discussing is the art side of logic. You are trying to use a hammer to clean windows and they say show me where it says I can't use a hammer in this way. Normal communication is not what I expressed you are to use categorical form. If you want to use modern language then do so but you ought not do so if you express an argument and want the argument evaluated. You give a logical a lot of translating to do which is NOT practical for him. I have said over and over the rules I STATE about the NOUN or Noun phrases in the subject and predicate is to PREVENT deception 100%. Using modern language and not strictly using nouns will allow the possibility of equivocation or other language based fallacies. If anyone tries being slick in a argument strictly following categorical form The person will be immediately exposed. I am specifically telling you and all people it will be near impossible to deceive IF you follow the rules. Hence why people refuse to use categorical form. At some point the words used can have the context change: " well that is not what I really meant . . . " Line used all the time practically. Using specific nouns or noun phrases stops you from later on saying you meant something else.

 

[LegionOnomaMoi]

I think our disagreement is and it resolves around what a proposition is.

Wrong. Our disagreement is far more fundamental. I don't think you have any knowledge of logic or Aristotle beyond the kind demonstrated by your various inaccurate regurgitations of a book from the Concise Introduction series on modern Logic. Thus you speak about Aristotelian logic but have shown to be incapable of referring to Aristotle. You speak of propositions but fail even to deal with them as Aristotle does, let alone recognize the fundamental problems with Aristotelian "proposition" (see e.g., his discussion of ναυμαχία and its relation to modern possible world semantics and modal logic).

I will prove to you later that multiple sources use the term SORITES without mentioning any paradox.

Who cares? For someone so keen on leaping upon the falsely seeming etymological argument, you are sure caught up with irrelevant terminology here. Your own source doesn't use the term paradox, but describes exactly the same thing.

I never attempted to cite any author Hurley

No, you didn't. You just ripped him off. I own Hurley's book (I have taught this subject for years). I know how much you relied on the presentation in this source.

It seems there is a generation of philosophers in a philosophy department (and all math professors I see) that teach a proposition is A SENTENCE.

I've never met any philosophers or mathematicians who equated sentences with propositions. This is so obviously wrong as to be a priori ludicrous (think of the imperative mood).

Propositions can express the same idea using different words literally.

They can't, except ideally and therefore formally (mathematically), abstracted away from any meaning. See e.g., Grayling's (An Introduction to Philosophical Logic) example of "Der Schnee ist weiß" and "The snow is white").

More than one PhD qualified professor EXPRESSED the same idea: a proposition is NOT physical.

And a sentence is?

The proposition "there will be a sea battle in the reed sea" is a proposition and has a truth value that is either true or false.

Not according to Aristotle. This would entail fatalism (as he states in detail), and therefore is not "truth-bearing" (is not a proposition).

Logic that I discussed above is not a science in this regard but an art.

Not according to Aristotle, and there is nothing about major and minor premises in a syllogism that is an "art" rather than something far more exact and precise than any of the sciences.

What I am discussing is the art side of logic.

Which is about as meaningful as discussing the musical side of logic, or the astrological side of logic.

Normal communication is not what I expressed you are to use categorical form.

Logic isn't normal. It isn't even intuitive. It was developed precious few times even in the non-formal way Aristotle did. Your misuses of terms from Hurley demonstrate this doubly, as 1) they are misuses and 2) the are not terms or concepts found in normal communication. Some 50 years of research in the cognitive sciences and elsewhere have shown that people do not, in general, think logically without training (even such basic logical inferences as "If A, then B THEN if not B, then not A" prove too challenging, as does the non-equivalence of "If A, then B" and "If B, then A").

If you want to use modern language then do so but you ought not do so if you express an argument and want the argument evaluated.

Coming from someone who uses terms like "noun phrase", "copula", "minor premise", "syllogism", etc., in a post explicitly related to a development by a Greek over 2 millennia ago, this particular statement is pretty comical.

 

[Logikal]

Wrong. Our disagreement is far more fundamental. I don't think you have any knowledge of logic or Aristotle beyond the kind demonstrated by your various inaccurate regurgitations of a book from the Concise Introduction series on modern Logic. Thus you speak about Aristotelian logic but have shown to be incapable of referring to Aristotle. You speak of propositions but fail even to deal with them as Aristotle does, let alone recognize the fundamental problems with Aristotelian "proposition" (see e.g., his discussion of ναυμαχία and its relation to modern possible world semantics and modal logic).


Who cares? For someone so keen on leaping upon the falsely seeming etymological argument, you are sure caught up with irrelevant terminology here. Your own source doesn't use the term paradox, but describes exactly the same thing.


No, you didn't. You just ripped him off. I own Hurley's book (I have taught this subject for years). I know how much you relied on the presentation in this source.

I've never met any philosophers or mathematicians who equated sentences with propositions. This is so obviously wrong as to be a priori ludicrous (think of the imperative mood).


They can't, except ideally and therefore formally (mathematically), abstracted away from any meaning. See e.g., Grayling's (An Introduction to Philosophical Logic) example of "Der Schnee ist weiß" and "The snow is white").


And a sentence is?

Not according to Aristotle. This would entail fatalism (as he states in detail), and therefore is not "truth-bearing" (is not a proposition).


Not according to Aristotle, and there is nothing about major and minor premises in a syllogism that is an "art" rather than something far more exact and precise than any of the sciences.


Which is about as meaningful as discussing the musical side of logic, or the astrological side of logic.


Logic isn't normal. It isn't even intuitive. It was developed precious few times even in the non-formal way Aristotle did. Your misuses of terms from Hurley demonstrate this doubly, as 1) they are misuses and 2) the are not terms or concepts found in normal communication. Some 50 years of research in the cognitive sciences and elsewhere have shown that people do not, in general, think logically without training (even such basic logical inferences as "If A, then B THEN if not B, then not A" prove too challenging, as does the non-equivalence of "If A, then B" and "If B, then A").


Coming from someone who uses terms like "noun phrase", "copula", "minor premise", "syllogism", etc., in a post explicitly related to a development by a Greek over 2 millennia ago, this particular statement is pretty comical.

You are making a lot of assumptions above. Again I did not rip off Hurley or any other author who express the same concepts as I do. Why you insist on saying or expressing a read Hurley and ran away with it in the wrong direction is quite comical to me. I own several books on Logic. Hurley happens to be ONLY ONE of the books. I will put this in proper perspective below and CITE the context you seem to misrepresent. I want to be clear that what I have stated has been taught for quite some time in Catholic education as some of my sources will show. I also want to make clear YOUR claim was a Sorites cannot be separated from a paradox. I claimed the two terms (Sorites and Paradox) have independent meanings in logic itself and you are talking about something outside of basic logic when you use the term "The Sorites Paradox". I am confident in my assertion that Sorites is about logical FORM and not always about a form of paradox. I am sure a logic 101 course need not go into "The Sorites Paradox". Here are some sources:


Cardinal Mercier. (1912). Elements of Logic. The Manhattanville Press:New York. [retrieved from https://www3.nd.edu/~maritain/jmc/etext/logic-58.htm]
"58. Varieties of the Categorical
Syllogism. -- The categorical syllogism has for its premises two categorical propositions. It will be useful to note
some of its possible structural modifications.
Such are the forms of reasoning called epicheireme, polysyllogism and sorites, enthymeme.
(1) The epicheireme (epi and cheirô to take in hand) now{1} designates a syllogism one or both premises of which
is immediately accompanied by the proof.
The polysyllogism is a series of syllogisms in which the conclusion of each serves as premise for the next. In
practice the polysyllogism is condensed, under the form of sorites (sôros, heap), into a series of propositions
where the predicate of the first becomes the subject of the second, and so on, in such a way that the predicate of the
last in the series may he coupled with the first subject.
Example: The human soul forms abstract thoughts; a being capable of abstract thoughts is spiritual; a spiritual being is by nature imperishable; a being naturally imperishable cannot be annihilated; a spiritual being that cannot be annihilated will live with an immortal life; therefore the human soul is immortal.{2}
[FootNote:{1} In Aristotle epicheireme means an attempt at demonstration as opposed to a demonstration properly so called.
{1} The enthymeme is commonly reckoned among the more or less disguised forms of the syllogism, as though it consisted
merely in leaving one of the premises to be understood, not expressed. This is too secondary a circumstance to justify
giving the enthymeme a place of its own among the forms of syllogism. As a matter of fact Aristotle understood by
enthymeme a syllogism the conclusion of which is only more or less. probable.]
The above bold emphasis is mine. You again sound like you knew the etymology of the word Sorites and made a connection that is not required to accompany PARADOX. It may accompany the word PARDOX accidentally but as the context above indicates Sorites refers to a FORM of an ARGUMENT and TYPE OF SYLLOGISM.

Fr. Manuel Pinon. (1979). Logic Primer. Rex Book Store: Manila, Phillipines.

"The Sorites is an abridged Polysyllogism, wherein the intermediate Conclusions are left out (Sorites i.e., heaped up syllogisms). It consiste of propositions connected in such a manner that the predicate of the preceding one becomes the subject of the following, and so on, until the Conclusion joins the Subject of the First Premise with the Predicate of the Last Premise. . . . It should be noted that the Sorites, like the Pollysylogism has inverted premises. The first premise is the true Minor premise, and the intermediate premises are the true Major premises of the component syllogisms" (p.p. 148-149).


Sister Miriam Joseph. (1937). THE TRIVIUM: The Liberal Arts of Logic, Grammar, and Rhetoric. Ed by Marguerite McGlinn. retrieved from
http://media.evolveconsciousness.org/books/consciousness/The Trivium - The Liberal Arts of Logic, Grammar, and Rhetoric - Sister Mirriam Joseph.pdf

"A sorites is a chain of enthymemes or abridged syllogisms, in which the conclusion of one syllogism becomes a premise of the next; one premise of every syllogism but the first and the conclusion of all but the last are unexpressed, that is, merely
implicit. There are two types of sorites: (1) that in which the conclusion of one syllogism becomes the major premise of the next; (2) that in which it becomes the minor premise of the next. Although it is possible to construct valid sorites in each of the four figures and to combine syllogisms of different figures in one sorites, we shall consider only the two traditional types in Figure I, the Aristotelian sorites and the Goclenian sorites, both of formally unlimited length. They are the only forms likely
to be actually used in our reasoning. The formal unity of each of these sorites is emphasized by regarding it as a syllogism in Figure I with many middle terms." (p.p.135-138).
You can download and read in PDF form:

Patrick Hurley. (2008). A Concise Introduction to Logic. 12thEd. Cengage Learning: Stamford, CT.

"A sorites is a chain argument of categorical syllogisms in which the intermediate conclusions have been left out. The name is derived from the Greek word soros, meaning "heap," and is pronounced "soritez," with the accent on the second syllable. The plural form is also "sorites". Here is an example:
All bloodhounds are dogs.
All dogs are mammals.
No fish are mammals.
Therefore, no fish are bloodhounds.

The first two premises validly imply the intermediate conclusion "All bloodhounds are mammals." If this intermediate conclusion is then treated as a premise and put together with the third premise, the final conclusion follows validly. The sorites is composed of two valid categorical syllogisms and is therefore valid." (p. 307)

Bold emphasis is added to indicate WHY I say sorites is a FORM of SYLLOGISM. Please show me where a paradox is relevant to this discussion of a form of categorical syllogism! He mentions the root of the word aka the etymology in a historical context of the word Sorites. Notice in the example Hurley gives he does not mention anything about a paradox. hurley's example has nothing to do with any sort of paradox. If you still think it does then please use Hurley's example and show wherein the paradox lies. The Sorites Paradox is a different thing altogether. Perhaps the original sorites example was in the FORM of a Paradox, but again this focus is on the origin or history of the word (aka part of the etymology). This does not mean all chain arguments are paradoxes. You show that SOME sorites are paradoxes. Show me that ALL SORITES are PARADOXES.

Notice I have provided at least three sources --not just one source being Hurley as you think. There are numerous books that teach in a similar method. What I hoped to show is that this indicates a teaching style that was TAUGHT by qualified instructors BACK IN THE DAY and the teaching style today is different. Today the teaching style I would say lacks details and lowers the quality because some of the concepts have been watered down. I can't find too many online mathematical sources that say a proposition is NOT a sentence. They all say a proposition is a declarative sentence and is a linguistic entity which is what you also hinted at with your push of a type of grammar reference. You are using a hammer to clean windows still.

Now perhaps you are correct in the sense that I may have used a term differently than Aristotle's context but again I did not invent it. I was TAUGHT it. The Catholic church has tried to keep Aristotelian logic alive for a long time and perhaps along the way they expanded on some of the concepts Aristotle expressed but did not go into many specifics about. This is likely do to Saint Thomas Aquinas and many others who followed in Aquinas' foot steps. Note that all of the catholic sources seem to express the SAME IDEAS and that is how it was taught. Catholic sources that teach logic is quite different from non-Catholic sources. The Catholic sources seem to go into more depth with terminology in prose way before they even get to Symbolic logic, Mathematical logic, Modal logic and so on. For instance the only sources on "Material Logic" --which many students are never exposed to -- are usually going to be Catholic sources. Today Material Logic goes by the name Epistemology but a new student to logic would not make that connection from non-Catholic education. So in this light some of the SAME concepts are taught but may go by different TERMINOLOGY. So your correction in the sense that what I have said Aristotle expressed may be technically correct. Aristotle made mistakes in most of his writings and all scholars know Aristotle made many objective and technical errors in writings. Saint Thomas Aquinas (and those who followed and adored Aquinas) seemed to be the person (and people) who tried to keep the Aristotle system alive by making modifications where necessary. Sure Aristotle never used the term Material Logic literally. This addition was made by John of saint Thomas to indicate the portion of logic Aristotle mentioned about knowing truth of the content of the premises versus knowing the truth of a valid syllogism by form alone (aka what we refer to as FORMAL LOGIC). So I will take the correction that Aristotle might have not meant exactly what I stated in his time period and in his writings. The improvements still should be considered as objective. They are either true or false propositions. The method as I have shown comes from Catholic sources and not non-Catholic sources. So I can accept correction. I can accept Aristotle specifically meant a form of paradox originally. The concept does apply elsewhere as well; this may be why other people may have modified the concept away from the paradox.
So it is a bit nit picking to say Aristotle literally meant Sorites Paradox and Logikal said something at odds literally. You are expressing the literal sentences on a page and expressing it is wrong to go into how other scholars say he must really be expressing a type of formal argument in general and refer sorites as a formal pattern for arguments. Clearly the latter is proven above. You express the literal verbatim version whereas I express the conceptual version without the pit falls as corrected by educated members of the Catholic church.

 

[LegionOnomaMoi]

You are making a lot of assumptions above. Again I did not rip off Hurley or any other author who express the same concepts as I do. Why you insist on saying or expressing a read Hurley and ran away with it in the wrong direction is quite comical to me.

Perhaps it is because you duplicate exactly his terminology which, to one familiar with texts on logic more generally, is idiomatic.

I will put this in proper perspective below and CITE the context you seem to misrepresent. I want to be clear that what I have stated has been taught for quite some time in Catholic education as some of my sources will show.

You don't cite catholic sources (and you can't here; even catholic Priests or friars can't define "Cathologic" logic and certainly can't define anything as Catholic Aristotelian logic, as Aristotle predates the Catholic church).

I also want to make clear YOUR claim was a Sorites cannot be separated from a paradox.

Correct. Now, what you have to demonstrate is that any of your ad hoc citations shows differently. You don't. You quote a bunch of random sources which one could easily discover via google, but don't demonstrate how these indicate a difference between a sorites "argument" and the paradox.

In Aristotle epicheireme means an attempt at demonstration as opposed to a demonstration properly so called.
{1} The enthymeme is commonly reckoned among the more or less disguised forms of the syllogism, as though it consisted
merely in leaving one of the premises to be understood, not expressed. This is too secondary a circumstance to justify
giving the enthymeme a place of its own among the forms of syllogism. As a matter of fact Aristotle understood by
enthymeme a syllogism the conclusion of which is only more or less. probable.

FINALLY! A citation (if indirect) from Aristotle! Alas, it simply gives evidence against your use of sorites and your understanding of Aristotelian logic, for it is mere evidence that the sorites paradox (or "argument" or whatever you wish) was foreign to Aristotle, as indeed it was (at least insofar as our sources tell).

The Sorites is an abridged Polysyllogism

Something COMPLETELY absent from your posts, and therefore irrelevant to any of your claims about them. You can't claim to have addressed anything related to polysyllogisms when you didn't address these, and you haven't related these to the sorites paradox, making the above another pointless claim.

Sister Miriam Joseph. (1937)

I was TAUGHT it. The Catholic church has tried to keep Aristotelian logic

My sister attended CUA. My brother attended CUA and two other more "hardcore" catholic universities. Other than I, my whole family is catholic. I've read Catholic writings from the pre-Scholastics past the early Modern era. I've also read Aristotle and the Patristics. As "Aristotelian" logic doesn't accord with your misrepresentation of Hurley, neither does the Catholic church's

This is likely do to Saint Thomas Aquinas and many others who followed in Aquinas' foot steps. Note that all of the catholic sources seem to express the SAME IDEAS and that is how it was taught. Catholic sources that teach logic is quite different from non-Catholic sources.

It predated Aquinas by many centuries.

 

[Logikal]

Perhaps it is because you duplicate exactly his terminology which, to one familiar with texts on logic more generally, is idiomatic.


You don't cite catholic sources (and you can't here; even catholic Priests or friars can't define "Cathologic" logic and certainly can't define anything as Catholic Aristotelian logic, as Aristotle predates the Catholic church).


Correct. Now, what you have to demonstrate is that any of your ad hoc citations shows differently. You don't. You quote a bunch of random sources which one could easily discover via google, but don't demonstrate how these indicate a difference between a sorites "argument" and the paradox.

FINALLY! A citation (if indirect) from Aristotle! Alas, it simply gives evidence against your use of sorites and your understanding of Aristotelian logic, for it is mere evidence that the sorites paradox (or "argument" or whatever you wish) was foreign to Aristotle, as indeed it was (at least insofar as our sources tell).


Something COMPLETELY absent from your posts, and therefore irrelevant to any of your claims about them. You can't claim to have addressed anything related to polysyllogisms when you didn't address these, and you haven't related these to the sorites paradox, making the above another pointless claim.




My sister attended CUA. My brother attended CUA and two other more "hardcore" catholic universities. Other than I, my whole family is catholic. I've read Catholic writings from the pre-Scholastics past the early Modern era. I've also read Aristotle and the Patristics. As "Aristotelian" logic doesn't accord with your misrepresentation of Hurley, neither does the Catholic church's


It predated Aquinas by many centuries.

I have been for the last few days. I would like to point out I have shown without question that the sorties is a type of syllogism. You are obsessed with the sorties paradox and can't seem to let it go. You are specifically addressing something other than a categorical form which I mentioned. I am talking apples and you are bringing up oranges. Still I have made several quotes from district sources and you neverer addressed my claim that the term sprites can be used outside of mentioning any paradox. I quoted Hurley directly and you did not show me how Hurley's own example is a PARADOX. You have the burden of proof there because you made the claim all sorites involve a paradox. You ignored my request of showing there is a paradox in the example given.

Again I point out that I have over 20 years in logic. I did not recently read Hurley and post it here. I have had qualified PhD instructors but you make up what you like about me and say I plagiarized Hurley. I don't get it.

I pointed out that the recent sources I gave you came from PhD authors who were PRODUCTS of a Catholic education system and studied logic there. Show me a Catholic source that uses DIFFERENT terminology please. You are missing the point. Obviously Aristotle predates the Catholic Church. I stated to you that the Catholic Church tried to stay true to the classical system and not jump on the modern mathematical bandwagon. I would say now most student in logic will learn mathematical logic. Would you agree? The intent as I stated in my first post is not the same. Mathematical logic is symbol manipulation. It does not look for deceptive techniques which classical logic does. You did not address any of those claims in my early post in the thread. You went on your own tangent about history and sentence structure. I have stated there were adjustments made to classical logic by the Catholic Church as well as some Islamic scholars. You did not address any of those claims. The relevance is those additions expand on topics begun by Aristotle but developed them further AND added some terminology to the classical.

You are not understanding concepts well. If poly syllogism is defined as it is I do not need to mention them. Sorites IS STILL a sub class to polly syllogisms regardless. You mentioning that I failed to mention them seems pointless. There are types of Polly syllogisms and sorites is one; epichriema is another.

I think you are taking Aristotle so literally you have missed the additional information added to classical logic. I have stated Aristotle is not my only source and it is not the only reputable source. Corrections and improvements have been made BEFORE mathematical logic came about. Catholic university materials will demonstrate that fact. You can't sit back and expect all humans to prove stuff to YOU as if you are royalty. You have to make AN EFFORT as well to see if there is other material that says what I am saying. You seem to make no effort. I made effort to show the existence of such materials and you doubt the sources I gave as a Google search. You make an effort a REAL effort and you will see many concepts were improved upon from the original. You are stuck with literal reading books and missing the concepts and contexts I have brought up in the posts earlier. You keep harping on Aristotle did not literally wrote that or know what that was. That was not my point ever. The concepts were my point.

 

[LegionOnomaMoi]

I would like to point out I have shown without question that the sorties is a type of syllogism. You are obsessed with the sorties paradox

You realize that the entire point of the paradox (or a central point) is the formulation of syllogisms which result in paradoxes, right? You seem rather obsessed with distinguishing the sorites paradox with a sorites argument when in reality they are equivalent: a series of statements following what should be a series of truth-preserving inferences but can yield a paradoxical conclusion because of the nature of sorties arguments.

And, actually, I don't really care about the Sorites gaffes you've made. It's more the basic misunderstanding of logic, Aristotle, and plagiarism (combined with an attempt to support your view by searching desperately for sources that yielded rather laughable results that all happen to be available for free online: a 1912 translation of 1902 Désiré Mercier's Logique: Cours de Philosophie, an out of print obscure logic primer, and a 1937 book by Sister Mariam Joseph that isn't actually even a logic text per se.

I quoted Hurley directly and you did not show me how Hurley's own example is a PARADOX.

You quoted Hurley's description, and plagiarized Hurley for your original posts.

Again I point out that I have over 20 years in logic.

20 years in logic and you have to rely on out of print books and those available for free online to cover for ripping off of Hurley? And after explicit claims about what Aristotle said, you can't even point to places in a translation where he does.

I have had qualified PhD instructors but you make up what you like about me and say I plagiarized Hurley. I don't get it.

The point of the Brief Introduction series is to provide an elementary familiarity for those who have no background knowledge of the topic as simply as possible. So these texts usually don't conform to typical texts intended to actually be used to teach the topic or be used as a textbook. As such they use different strategies, terms, etc., than one finds in more typical sources used to learn these topics. I've taught and tutored the philosophy of logic, symbolic logic, mathematical logic, set theory, and related topics long enough to know standard presentations. Your presentation wasn't just non-standard, but includes verbatim quotes and nearly verbatim quotes from the non-standard text you then cited.

I pointed out that the recent sources

RECENT? One was practically published in the 19th century, another from the 30s, and none were recent.

Show me a Catholic source that uses DIFFERENT terminology please.

That's easy. Yours. One of your sources uses the term "enthymemes". Another favors epicheireme (although lists enthymeme), and the third uses neither.

I stated to you that the Catholic Church tried to stay true to the classical system and not jump on the modern mathematical bandwagon.

Tarski not only taught at a major Catholic college but received an honorary degree from there. Bolzano wasn't just Catholic and a logician who embraced mathematics but was a mathematician. Professor of Logic Peter Geach was awarded the papal cross. A center of development of mathematical logic, the Warsaw Logical school, contained no few devout Catholics. And the "mathematical bandwagon" only goes back to Frege.

I would say now most student in logic will learn mathematical logic. Would you agree?

No, they don't. Few do. And most students majoring in mathematics have a woefully inadequate knowledge of mathematical logic. This is partly because formal logic remains philosophical despite its mathematical nature, partly because of the use of set theory as a common language for logicians and mathematicians that make it unnecessary for logicians or mathematicians to study mathematical logic, and partly because non-mathematical logic is already mathematical enough even as covered in philosophy of logic. Hence its designation as a formal system or language.

Mathematical logic is symbol manipulation.

So is writing. Logic, mathematical or no, relies on formally defined mathematical rules that license or justify the inference of premises, statements, etc., from others based on formal frameworks. It is impossible to determine the validity of an argument using logic without a mathematical framework of axioms, schemata, or similar set of "rules" sanctioning inferences that are truth-preserving.

It does not look for deceptive techniques which classical logic does.

Aristotelian logic IS classical logic.

I think you are taking Aristotle so literally you have missed the additional information added to classical logic.

Aristotelian logic is also called classical logic. Both terms are used to distinguish the logical tradition Aristotle founded from e.g., modal logic, tense logic, quantum logic, and other logics not equivalent with Aristotelian logic. Mathematical logic/symbolic logic IS equivalent, and IS called Aristotelian logic.[/QUOTE]

 

[Logikal]

I do not know why you think the way you do. Your choice of beliefs are way off. All of the logic sources I have use the same terminology. You seem unfamiliar with the terms I quoted. I gave you reference that clearly use the terminology to demonstrate the use of the terms since you doubted me.

You have failed to demonstrate the HURLEY sorites example and show the alleged paradox. Show me the Paradox specifically using the example Hurley gave and I quoted earlier. Your definition of the terminology seems to be quite different from what I learned and what I read all the time in logical texts. You still refer to history and etymology and you claim you do not. You say all sorites arguments are paradoxes and you are wrong. Show what the paradox is in Hurley, please in the quote I used specifically that is in his text.

The terms enthymemes, sorites are found in typical logic texts and works. Epicheirema is not a typical logic term and I found only catholic source use that term as well as Polly syllogism, simple apprehension, and other terms not found standard non catholic works. You are under the thinking enthymemes and epicheirema are identical and its your mistake. Understand the concepts and you will see the distinction-- they are not identical. The fact that some authors do not use some logical terms means nothing. The terms still exist if they can be found in earlier works. William t. parry and Edward Hacker also have a text called Aritotelian Logic which you will find uses the same terminology as the other sources I mentioned and you think are laughable. I have demonstrated the terms in the correct usage in multiple texts. I did my part. The fact you dislike some sources is besides the point. All I had to show was the terms existed and were used in the same context I used the same terms. Because you were not familiar with the terms doesn't stop the world from spinning.

Set theory directly belongs to math. None of the logic texts --written by PHILOSOPHERS -- I mentioned including HURLEY, COPI and COHEN, etc have set theory anywhere in the text. I even looked in other logic texts written by Philosophers and not many of those texts include set theory. Are you specifically saying SET TEHORY is not a component of MATH? Philosophers prior to the 19th century had no need for set theory and was not taught in PHILOSOPHY. Mathematial logic came into existence around 1845-1850-- not any sooner than that. Math and logic have not been connected in a serious way until then. So my point of logic being about preventing deceptive reasoning holds true prior to mathematical approaches to logic. If students are learning SET THEORY then they are for sure learning MATHEMATICAL LOGIC. Set theory is MATH and only MATH. So you misunderstood the context of my question. Is mathematical logic which includes set theory the main focus for students learning logic today?
Set theory is a sub set of math just to be clear. You cannot have set theory without math. You seemed to think the other way around.

I have demonstrated that classical logic aka Aristotelian logic is distinct from symbol manipulation. Using the concepts I described in the first thread YOU CAN DETERMINE validity and truth value without knowing anything about set theory. IF one puts effort in logic one can move from one step of logic to the symbol manipulation. That is I can translate the predicate logic to classical provided the relationships are correct. Predicate logic hides the middle term from view. Once I know the middle term I can go from classical to predicate logic and vice versa. I believe the logical concepts are universal regardless of which system you use. Objectively the rules of inference are universal in any deductive logical setting. Humans will try to limit which inference rules another person can use. Deductive logic sets no such rules.

 

[LegionOnomaMoi]

You seem unfamiliar with the terms I quoted.

I can read ancient Greek. The terms are not a problem. The fact that you back your claim about "Catholic logic" or "Catholic logicians" by citing a "recent" text written a over a century ago, a text that wasn't even a logic text but more general, and an out-of-print book that just so happens to have the pages you quoted from online is the problem.

Show me the Paradox specifically using the example Hurley gave and I quoted earlier.

Finally. The paradox is how the logical chain can involve only valid statements and thus fulfill Hurley's criterion ("The rule in evaluating a sorites is based on the idea that a chain is only as strong as its weakest link. If any of the component syllogisms in a sorites is invalid, the entire sorites is invalid"), yet still be invalid. The paradox isn't that all sorites arguments are paradoxical, but that sorites lead to paradoxes:
"The epithet 'sorites' is in fact a pun; in Greek it means 'heap'. It names not only one of the most famous applications of the form of argument, concluding that either (by addition) 10,000 stones no not make a heap, or (by substraction) that 1 stone does make a heap, but also the method of argument itself."
Read, S. (1995). Thinking About Logic: An Introduction to the Philosophy of Logic. Oxford University Press.

And for an example with a structure like Huxley's:

Hyde, D. (2011). The sorites paradox. In Vagueness: A Guide (Logic, Epistemology, and the Unity of Science Vol. 19) (pp. 1-17). Springer.

The paradox and the argument are the same thing. This doesn't mean that any argument of this form is a paradox, it means that the argument structure itself is seemingly truth-preserving (provided valid premises) but leads to clearly, paradoxically false conclusions.


Your definition of the terminology seems to be quite different from what I learned and what I read all the time in logical texts. You still refer to history and etymology and you claim you do not. You say all sorites arguments are paradoxes and you are wrong. Show what the paradox is in Hurley, please in the quote I used specifically that is in his text.

The terms enthymemes, sorites are found in typical logic texts and works.

Not frequently, at least not for those of us who don't go looking for century-old texts to quote-mine from:
"There is a classical category of arguments, discussions of which enjoyed a certain vogue toward the end of (what Bochenski has called) the Dark ages in logic (i.e., from the Renaissance up until near the turn of the present century), namely, enthymemes" (italics in original; emphases added).
Anderson, A. R., & Belnap, N. D. (1961). Enthymemes. The journal of philosophy, 713-723.

However, they do occur. Why? Because enthymemes is Greek (ἐνθύμημα) and found in Aristotle, although the original senses are obsolete and the "logic" definition is not only a mistake ("This sense is due to a misapprehension (already in Boethius a524), the description of the enthymeme (sense 1) as ‘an imperfect syllogism’ (ἀτελὴς συλλογισμός) having been interpreted as referring to its form instead of its matter"), but also fundamentally problematic (see e.g.,
Hitchcock, D. (1998). Does the traditional treatment of enthymemes rest on a mistake?. Argumentation, 12(1), 15-37.).

Epicheirema is not a typical logic term and I found only catholic source use that term as well as Polly syllogism

Then you didn't really look very hard. Kennedy defines it as follows:
"a kind of amplification of the Aristotelian syllogism and enthymeme in which a proposition (part 1) is supported by a variety of reasons (part 2), then a second proposition (what would be the minor premise in a syllogism) is stated (part 3), and that is followed by a variety of reasons for believing it (part 4). The fifth part then states the conclusion. Such an argument in Greek is sometimes called an epicheirema, literally ‘a handful’."
Kennedy, G. A. (1994). A New History of Classical Rhetoric. Princeton University Press.

Like your other Greek term, this one was also taken from Aristotle and used in Renaissance and pot-Renaissance texts:
"A syllogism is now vulgarly called an Epicheirema..when to either of the two premises, or to both, there is annexed a reason for its support."
Hamilton, W. S. (1856). Lectures on Metaphysics Physics and Logic. W. Blackwood and Sons.

"The peculiar name Epicheirema is given to a syllogism when either premise is proved or supported by a reason implying the existence of an imperfectly expressed prosyllogism."
Jevons, W.S. (1870). Elementary lessons in logic. Macmillan.

and other terms not found standard non catholic works.

Out of curiosity, what are the "standard" Catholic works? Century old obscure texts you found online aren't standard, but obscure. "Standard" texts aren't out-of-print, for example.

You are under the thinking enthymemes and epicheirema are identical and its your mistake.

I'm not, actually. The terms aren't used in all of your sources, they aren't used quite the same if they are shared, and therefore fulfill your request.

William t. parry and Edward Hacker also have a text called Aritotelian Logic which you will find uses the same terminology as the other sources I mentioned and you think are laughable.

I find it laughable that you claim to have the experience you do but rely on obscure texts available on line and one Concise Introduction series book on logic which you plagiarize from. I have lots of books with both those words (the LSJ, all the LOEB volumes with Aristotle's works, Cicero's De Inventione, several logic texts and even more on argumentation and rhetoric or the history of these, etc.). True, some are in other language like German, but not all (e.g., "a specific type of complex argument...the epicheirema, also called the five-part argument" in Henkemans, A. F. S. (2001). Argumentation Structures. Crucial Concepts in Aargumentation Theory (pp. 101-134). Amsterdam University Press.

The fact you dislike some sources is besides the point.

I don't dislike them. It's not the texts, it's why you relied on them.

Set theory directly belongs to math.

So does logic. So does probability, arithmetic, geometry, etc., but unlike these and other areas which were once solely in the domain of philosophy, set theory remains deeply ingrained in philosophy and intricately and inexorably bound with logic. Mathematical logic was invented by a philosopher (Frege) and then developed by philosophers (Russell, Whitehead, Lewis, Łukasiewicz, Tarski, Kripke, etc.) and continues to be developed, taught, and contributed to by philosophers (e.g., my intro to mathematical logic professor). The founder of the Journal of Symbolic Logic and a founder of computability theory (also intricately tied to logic) was not only a philosopher but deeply religious

None of the logic texts --written by PHILOSOPHERS -- I mentioned including HURLEY, COPI and COHEN, etc have set theory anywhere in the text.

None of them had many-valued logic either. Some texts by philosophers combine set theory and logic, and I have several textbooks I've taught with that are definitely mathematical but contain entire chapters on logic. You should probably read Logic And Theism.

Are you specifically saying SET TEHORY is not a component of MATH?

Not at all. It is clearly a subject of mathematics (as is logic), and much of mathematics are subjects of philosophy.

Philosophers prior to the 19th century had no need for set theory and was not taught in PHILOSOPHY.

Set theory didn't exist until the 19th century. It was invented by Cantor. Also, the distinction between and philosophy is recent.

Math and logic have not been connected in a serious way until then.

There wasn't any serious distinction, partly because mathematicians were all philosophers and partly because of colloquial vs. scholarly senses of the term.

If students are learning SET THEORY then they are for sure learning MATHEMATICAL LOGIC.

Not really (at least no more than those learning logic are learning set theory).

Set theory is MATH and only MATH.

Wrong. Not only does it appear in many a logic text including those that aren't mathematical, but in philosophy of logic texts.

You cannot have set theory without math. You seemed to think the other way around.

Or I know something about the history and practice of both subjects. Aristotle connected logic with geometry and both were forms of mathematics (also a Greek word).

Predicate logic hides the middle term from view.

Predicate logic began with Aristotle.

Once I know the middle term I can go from classical to predicate logic and vice versa.

No, you can't. You can't even evaluate most derivations/arguments from classical propositional logic if you with such limitations. For example, "either it is raining or it isn't" must be true but is one proposition and "it is raining and not raining" is false but is again one proposition.

 

[Logikal]

The fact that you back your claim about "Catholic logic" or "Catholic logicians" by citing a "recent" text written a over a century ago, a text that wasn't even a logic text but more general, and an out-of-print book that just so happens to have the pages you quoted from online is the problem.

You have misunderstood what I stated. I stated the terms such as epicheirema, and Material Logic were recent in relation to the logic time line: classical logic, medieval logic, modern logic (symbolic logic which includes Predicate logic) and the most recent MATHEMATICAL LOGIC.
Like I said earlier, many logic concepts were expanded from the original Aristotle texts namely from Islamic scholars and Catholic scholars in the medieval time period. A lot of time went by were logic was stagnant. Mathematical Logic became what it is (i.e., took off as popular) because of George Boole the mathematician. Boole's challenge to the traditional Square of Opposition was famous and other developments made Boole an elite source for MATHEMATICAL LOGIC. His first formal writings were labled Algebraic logic. To be clear MATHEMATICAL LOGIC came about from developments AFTER BOOLE. You mention Frege who first put logic in a form LIKE mathematics but this was not full blown MATHEMATICAL LOGIC and neither was Boole's. Historically, DeMorgan was the first person to likely USE the term MATHEMATICAL LOGIC but in his context it was not a field by itself but a distinguishing factor from language based logic "philosophic logic". My source for this is The Development of Modern Logic edited by Leila Haaparanta (2009). This source is BIG into the history of logic. Many of the articles by different authors point out the intents and purposes of the logic developments. I also have the Kneale and Kneale classic The Development of Logic (1962) which discussed periods of logic developments. Boole gets his own section of "algebra of logic" in both historic texts just mentioned. It is not that Boole did contributed to Mathematical Logic alone but much came about BECAUSE of HIM. I am not saying no one else had the ideas to put math and logic into one subject. Boole's work was more influential than even FREGE. Boole put the concepts into practical use like a science. Like a science Boole redefines PROPOSITION to be a physical reference (aka a sentence of grammar) and not a concept as in Philosophy. Boole and other redefine "contraposition" and other terms that had different contexts in classical logic because the intent WAS DIFFERENT. Mathematical logic is not primarily meant for argument evaluation like classical logic. Classical logic was used to used for purposes like to inform and gain knowledge; the symbolic manipulations of Mathematical logic is not interested in detecting deceptive reasoning but only interested in VALID REASONING. This means all of the premises can be false with the conclusion being false and no one really cares as long as the argument no matter how ridiculous is VALID.
My instructors did not care about VALIDITY, but SOUNDNESS. That is a sound argument must be formally valid and the argument has to make sense and inform. Mathematical logic on the other hand creates arguments just for the sake of writing symbols: "Look at what I can do; I could write this argument in predicate logic if I wanted to . . . " So basically the mathematical logic is more of an exercise than a method of knowledge where the goal is informing people or gaining new knowledge. I would not get away with writing false premises. Mathematical logic has no qualms about false premises. Classical logic cared about the truth of the premises and ARGUMENTS rested on the TRUTH of the premises. If all of my premises are true and RELEVANT then something could be worthy of an argument. To randomly put premises down and a conclusion is an exercise with little purpose. There is a difference between arguments with PURPOSE and arguing stuff just because. . . .

Finally. The paradox is how the logical chain can involve only valid statements and thus fulfill Hurley's criterion ("The rule in evaluating a sorites is based on the idea that a chain is only as strong as its weakest link. If any of the component syllogisms in a sorites is invalid, the entire sorites is invalid"), yet still be invalid. The paradox isn't that all sorites arguments are paradoxical, but that sorites lead to paradoxes:

You did not address what I asked but gave YOUR example. I specifically stated use Hurley's example. I guess you saw that ALL SORITES do not necessarily lead to paradoxes! Let me fix part of your quote for you: "The paradox isn't that all sorites arguments are paradoxical, but that [SOME] sorites [CAN] lead to paradoxes . . . "
Your expressed proposition PRIOR to this was that "the Sorites was Identical to the paradox". With this you are changing the tune. I want you to SHOW the PARADOX specifically in Hurley not SOME OTHER source! I stated SOME sorites ARE NOT paradoxes and you expressed ALL sorites are paradoxes. This is a classic square of opposition disagreement. I express an O proposition and you express an A proposition. Both of us can't be correct! You will not find a paradox in Hurley. I also used Copi and Cohen but you ignored that one. I do not know why you cannot see the sorites as more than one categorical form in conjunction which is what the concept of sorites expresses. I can break the sorites down into separate syllogisms all the time.
I gave examples for Copi & Cohen as well as Hurley. I do not know why you refer to Hurley so much with ME when I gave multiple sources. If you think I PLAGARIZED Hurley, I hope you also think HURLEY plagiarized Irving Copi & Carl Cohen! I do believe Hurley's text is AFTER the famous COPI & Cohen textbook series. Hurley began in 1985 if I am not mistaken. If you hold the texts side by side Hurley basically copied the entire format from Copi & Cohen. Look at the Contents and you will see the same concepts, same layout and in the same order presented by Copi & Cohen. So if you think I plagiarized Hurley, Hurley plagiarized Copi & Cohen! I have OTHER BOOKS besides these on logic.
There is so much that describes the label MATHEMATICAL LOGIC found in The Development of Modern Logic edited by Leila Haaparanta (2009) I would have to quote half the book. I emphasis the obscure texts I quoted and you found laughable were not meant to be authorities or anything to write home about. You miss the purpose for the grammar I suppose. My purpose was to show that people WERE EDUCATED that way. The authors held PhD's in Philosophy. The writings were DIFFERENT time PERIODS. The terminology was used and expressed identical meanings (not identical sentences) from all the sources. I never said I used recent catholic works. The context is key. My intention was to suggest that Catholic texts from any period will match the obsure texts terminology I used. A lecturer in classic logic today --not modern logic-- would STILL used the same terms and define them like I did and those obscure and laughable sources I used.
Poly syllogism is the general category. Epicherema, Enthymemes and Sorites are sub categories of a Poly syllogism. What your sources in your quote are doing is NOT distinguishing the sub categories; as a result one may confuse one with the other like you seem to indicate. You miss the specifics and miss the point of using the terms. You may think the differences are trivial which seem to me why you respond the way you do.
This claim is false or perhaps out of context:
"No, you can't. You can't even evaluate most derivations/arguments from classical propositional logic if you with such limitations. For example, "either it is raining or it isn't" must be true but is one proposition and "it is raining and not raining" is false but is again one proposition"

Your notion of argument is certainly not TWO PREMISES with a CONCLUSION. Your example is incomplete or you don't even present an ARGUMENT. What you have is a single proposition; that is fine with predicate logic (doing stuff just because you can) because you are not trying to be informative but trivial. Classical logic does not allow this. You should not be putting premises and conclusions out there just for the sake of it! I hope you see the difference there: one is doing something to (at least attempt to) INFORM while the other is doing something because he has free time. In Mathematical logic you can even have something from nothing! That is a conclusion with NO PREMISES! Well it ought to be clear the context of the term ARGUMENT where there are NO PREMISES is not what Aristotle had in mind is it? To prove a tautology for the sake of it does not enhance knowledge. The purpose is clearly different.

 

[Thief]

I think therefore ...I am
I like it simple

 

[Willamena]

I think therefore ...I am
I like it simple

Wrong thread.

 

[Skwim]

Reminds me of the blond guy in Good Will Hunting.

 

[LegionOnomaMoi]

You have misunderstood what I stated. I stated the terms such as epicheirema, and Material Logic were recent in relation to the logic time line: classical logic, medieval logic, modern logic (symbolic logic which includes Predicate logic) and the most recent MATHEMATICAL LOGIC.

Propositional logic was developed by "mathematicians" (in so far as you wish to differentiate the philosophers from Leibniz onward, who founded symbolic logic before Boole was born, and philosophers). Predicate logic wasn't developed until after Boole was dead. As for Medieval logic, one of the primary methods used to advance it was splitting apart Aristotelian logic into two:

"Medieval logic is often divided into two parts: the old and the new logic. The demarcation is based on which Aristotelian texts were available. The old logic is primarily based on Aristotle’s Categories and De interpretatione (this includes discussions on propositions and the square of opposition, but importantly lacks the prior analytics, which deals with the syllogism) while the new logic had the benefit of the rest of Aristotle’s Organon (in the second half of the 12th century). Many medieval logicians refined Aristotle’s theory of the syllogism, with particular attention to his theory of modal logic. The medieval period, however, was not confined to reworking ancient theories. In particular, the terminist tradition produced novel and interesting directions of research. In the later medieval period, great logicians such as Abelard, Walter Burley, William of Ockham, the Pseudo-Scotus, John Buridan, John Bradwardine and Albert of Saxony made significant conceptual advances to a range of logical subjects." (emphases added)
Asmus, C & Restall, G. (2012). A History of the Concept of the Consequence. In D. M. Gabbay, F. J. Pelletier, & J. Woods (Eds.) Logic: A History of its Central Concepts (Handbook of the History of Logic Vol. 11) (pp. 11-61). Elsevier.

Also, propositional logic doesn't allow for quantifiers. This is because in order to show logical relations hold for quantification one must introduce variables, because propositions can't be quantified over (e.g., "All crows are black" asserts that there is a predicate P="is black" such that for anything x, if x is a crow then Px ("x is black") must be true). Given the classic "All men are mortal" and "Socrates is a man", and treating both as a propositions, we find that in order to conclude anything we must recognize (as Aristotle did) that these are predicates over which the first has been quantified such that anything of the form "X is a man" can be said to imply "X is mortal". This is predicate logic (hence the predication). It was developed from Aristotle onwards (see e.g., Bonevac's "History of Quantification" in the volume cited above).

Like I said earlier, many logic concepts were expanded from the original Aristotle texts namely from Islamic scholars and Catholic scholars in the medieval time period.

Islamic scholars developed algebra. The scholastics didn't do that much to expand upon Aristotle (and what they did do can't exactly be seen as an expansion of Aristotle as they weren't presented with a consistent, singular Aristotelian logic thanks to the lack of access to Aristotle's texts), and in fact it was Galileo's challenging of Aristotle more than Catholicism that got him in trouble. Once post-scholastic philosophy and therefore mathematics really got going, we find (voila!) an entire system of mathematical logic present in the 1600s thanks to Leibniz. On p. 591 of my edition of Russell's A History of Western Philosophy, we find that Leibniz "did work on mathematical logic which would have been enormously important if he had published it; he would, in that case, have been the founder of mathematical logic, which would have become known a century and a half sooner than it did in fact."
Instead, it wasn't until Gottlob Frege that
1) Symbolic (predicate) logic was formalized
2) An attempt was made to equate logic and mathematics by the creation of an axiomatic arithmetic using formal logic.

Frege's attempt to turn mathematical/symbolic logic into "math" failed (it was Russell who proved this in a letter written to Frege shortly before the publication of his next major work, in which he subsequently described the crushing blow he had been dealt by Russell's letter). Some decades later, it was believed that the task to make logic mathematical and allow the entirety of mathematics to rest upon logic (or, at that stage, at least arithmetic, but most of the rest followed upon the development of an axiomatic arithmetic) thanks to the monumental 3-volume work by Russell and Whitehead (the PM). This collapsed utterly when Kurt Gödel not only proved that Russell and Whitehead failed, but that no system of mathematical logic could exist (that is, the goal of mathematical logic had been to enable the rendering of any mathematical statement into logic, allowing any mathematical statement to be proved logically; Gödel showed this was impossible, and mathematical logic became nothing more than a formalization of rules developed by logicians since Aristotle all the way to philosophers today).

Mathematical Logic became what it is (i.e., took off as popular) because of George Boole the mathematician.

Boole was also a philosopher, and predicate logic didn't exist until after his death. Also, his work falls more under set theory than logic.

Boole's challenge to the traditional Square of Opposition was famous and other developments made Boole an elite source for MATHEMATICAL LOGIC.

The opposition to the "Square of Opposition" (which isn't actually in Aristotle) began over a millennia before Boole. Lucius Apuleius produced a different schematic in his treatise on logic written in the 2nd century (even if it was misattributed to him, the work is nonetheless that old). It was re-worked and challenged by the scholastics and early modern philosophers/mathematicians.

His first formal writings were labled Algebraic logic.

Actually, modern algebra allowed us to realized that Boole's work primarily on set theory (which is why even today Boolean logic/algebra uses set-theoretic notation) could be considered in terms of an algebra, but modern algebra (abstract algebra) wasn't yet sufficiently well developed to make the connections between logic, set theory, and algebra. Also, the binary nature of truth-bearing propositions means any formulation of classical (Aristotelian) logic is an algebra.

To be clear MATHEMATICAL LOGIC came about from developments AFTER BOOLE.

That's not clarity, just inaccuracy:
"The grammatical analysis of judgments was challenged in the late nineteenth century by logicians who took the model of analysis from mathematics. The words “function” and “argument” became part of the vocabulary of logic, and predicates that expressed relations as well as quantifiers were included in that vocabulary. In the new logic, which was mostly developed by Gottlob Frege (1848–1925) and Charles Peirce (1939–1914) and which was codified in Principia Mathematica (1910, 1912, 1913), written by A. N. Whitehead (1861–1947) and Bertrand Russell (1872–1970), the rules of logical inference received a new treatment, as the pioneers of modern logic tried to give an exact formulation of those rules in an artificial language."
from the introductory paper to Haaparanta, L. (Ed.). The Development of Modern Logic. Oxford University Press.

We can see clear, explicit use of mathematical abstractions in the development of logic at least as far back as Boethius.[/QUOTE]

 

[LegionOnomaMoi]

cont. from above:

Historically, DeMorgan was the first person to likely USE the term MATHEMATICAL LOGIC

Wrong. It first appears in Mines' (1853) Presbyterian Clergyman, years before De Morgan's use. Also, the term "mathematical induction" goes back at least two decades before Mines' 1853 use of "mathematical logic". The term "mathematical philosophy" is attested to even earlier.

My source for this is The Development of Modern Logic

You mean this? Ivor Grattan-Guinness states in his contribution to the volume on Peirce that the phrase “mathematical logic” was introduced by De Morgan in 1858 but that it served to distinguish logic using mathematics from “philosophical logic,” which was also a term used by De Morgan"
The author (in this case the editor) is wrong. Here's proof (thanks to Google Books' scan of the actual 1853 work by Mines): A Presbyterian Clergyman Looking for the Church.

This source is BIG into the history of logic.

No, it isn't. I own it. It's specific to modern logic, compared to e.g., the numerous volumes in the set Handbook to the History of Logic among many others and isn't actually as comprehensive as many a monograph or volume on the history of linguistics when it comes to the mathematization of logic. See e.g.,

Bańczerowski, J. (2006).”The Axiomatic Method in 20th-century European Linguistics.” In S. Aurour, E. F. K. Koerner, H-J Niederehe, & K. Versteegh (Eds.), Geschichte der Sprachwissenschaft: Ein internationales Handbuch zer Entwicklung der Sprachforschung von den Anfängen bis zur Gegenwart (2. Teilband). (pp. 2007-2026). Berlin: Walter de Gruyter.

Boë, L0J. (2006). “Tendances majeures du développement des sciences phonétiques au Xxe siècle: filiations, émergences et réarticulations.” In S. Aurour, E. F. K. Koerner, H-J Niederehe, & K. Versteegh (Eds.), Geschichte der Sprachwissenschaft: Ein internationales Handbuch zer Entwicklung der Sprachforschung von den Anfängen bis zur Gegenwart (3. Teilband). (pp. 2729-2751). Berlin: Walter de Gruyter.

Harris, R., & Taylor, T. J. (1997). Landmarks in Linguistic Thought I: The Western Tradition from Socrates to Sussure. (2nd ed.). London: Routledge.

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Seuren, P. (2006). “Early formalization tendencies in 20th-century American linguistics.” In S. Auroux, E. F. K. Koerner, H-J Niederehe, & K. Versteegh (Ed.) Geschichte der Sprachwissenschaft: Ein internationales Handbuch zer Entwicklung der Sprachforschung von den Anfängen bis zur Gegenwart (3. Teilband) (pp. 2026-2034). Berlin: Walter de Gruyter.

Tomalin, M. (2006). Linguistics and the Formal Sciences : The Origins of Generative Grammar. Cambridge: Cambridge University Press.

Mathematical logic on the other hand creates arguments just for the sake of writing symbols

You need to read your source again.

You did not address what I asked but gave YOUR example.

Because my example illustrates how sorites' arguments are all examples of the paradox even if they don't appear paradoxical. In other words, the logical chain of sorites arguments paradoxically allows the proof of invalid conclusions using only valid premises and logical inference. That's the whole point: the nature of sorites arguments generally, not a particular paradox using the template. It's the fact that this polysyllogistic-type argument structure is not truth-preserving that is the paradox.

I would have to quote half the book.

No you wouldn't:
"Following Bocheński’s view, Carl B. Boyer presented for instance the following periodization of the development of logic (Boyer 1968, 633): “The history of logic may be divided, with some slight degree of oversimplification, into three stages: (1) Greek logic, (2) scholastic logic, and (3) mathematical logic.” Note Boyer’s “slight degree of oversimplification” which enabled him to skip 400 years of logical development and ignore the fact that Kant’s transcendental logic, Hegel’s metaphysics, and Mill’s inductive logic were called “logic,” as well...
In recent research on the history of logic, this intimate relation between logic and mathematics, especially its connection to foundational studies in mathematics, has been taken into consideration. One may mention the present author’s Logik, Mathesis universalis und allgemeine Wissenschaft (Peckhaus 1997) dealing with the philosophical and mathematical contexts of the development of nineteenth-century algebra of logic as at least partially unconscious realizations of the Leibnizian program of a universal mathematics, José Ferreirós’s history of set theory in which the deep relations between the history of abstract mathematics and that of modern logic (Ferreirós 1999) are unfolded, and the masterpiece of this new direction, The Search for Mathematical Roots, 1870–1940 (2000a) by Ivor Grattan-Guinness, who imbedded the whole bunch of different directions in logic into the development of foundational interests within mathematics." (pp. 160-162 from the volume)
I also own the book cited by in this quote from your source, The Search for Mathematical Roots, 1870–1940, in which we find the opening:
"The story told here from §3 onwards is regarded as well known. It begins with the emergence of set theory in the 1870s under the inspiration of Georg Cantor, and the contemporary development of mathematical logic by Gottlob Frege and (especially) Giuseppe Peano. A culmination of these and some related movements was achieved in the 1900s with the philosophy of mathematics proposed by Alfred North Whitehead and Bertrand Russell." The author counter Russell and the others (and even Kurt Gödel) as philosophers.

My purpose was to show that people WERE EDUCATED that way.

Then you shouldn't have made claims about "cathologic logic" and ignored e.g., Lewis Carroll's Symbolic Logic, the PM, Frege's two great works, or other work contemporary to or written prior to the works you cited, which are merely obscure and not representative of the ways in which anybody was educated (and weren't all logic texts).

The writings were DIFFERENT time PERIODS

My intention was to suggest that Catholic texts from any period will match the obsure texts terminology I used.

The Catholic priests that taught logic at Thomas Moore and CUA both used texts from Springer's UTM series (my brother's was actually Naïve Set Theory, not even mathematical logic). There is no "Catholic logic" and hasn't been since almost the beginnings of the reformation. When I lectured (and tutored) at the Jesuit university BC the texts used mathematical logic texts and modern philosophy of logic texts as well as e.g., The Logic of Theism (filled with not only mathematical logic but non-Aristotelian logics).

A lecturer in classic logic today --not modern logic-- would STILL used the same terms and define them like I did and those obscure and laughable sources I used.
Poly syllogism is the general category. Epicherema, Enthymemes and Sorites are sub categories of a Poly syllogism. What your sources in your quote are doing is NOT distinguishing the sub categories; as a result one may confuse one with the other like you seem to indicate. You miss the specifics and miss the point of using the terms. You may think the differences are trivial which seem to me why you respond the way you do.
This claim is false or perhaps out of context:
"No, you can't. You can't even evaluate most derivations/arguments from classical propositional logic if you with such limitations. For example, "either it is raining or it isn't" must be true but is one proposition and "it is raining and not raining" is false but is again one proposition"

Your notion of argument is certainly not TWO PREMISES with a CONCLUSION.

The point was to show how much propositional logic can't even represent. I suppose the inability for propositional logic to deal with quantifiers would have more clearly demonstrated how little of Aristotle propositional logic can deal with.