existential import

[Roger Bissell]

6 minutes ago, merjet said:

Fred Sommers' Term Logic handles relations.

The Logic of Natural Language (Sommers), page 185:

+ a₁ +R¹²³ + a₂ - a₃

_{An example proposition on page 187 is: "Some sailor read some (particular) poem to every girl."}

_{The minus sign here means “every” and “not some”. At other times it means "not".}

Something to Reckon With, by George Englebretsen inspired by Fred Sommers' work, page 116: “a complex term of the form +A+A is equivalent to +A.”

So I will apply this to your horse-tail-animal example. That's hopefully correctly; I'm not steeped in this stuff and read the books years ago.

    - H + T      Every horse has a tail.

   + A + T      Some animals have tails.    

Therefore:

-       - H + A + T + T     and 

-        - H + A + T     Every horse is an animal with a tail. 

Take another proposition:

Some animals have no tail.  + A – T    

Combining this with - H + T yields – H + A.  Every horse is an animal. 

2

Thanks for posting this, Merlin. I have put off reading Engelbretsen for too long. He has moved onto my short list, thanks to this.

REB

[merjet]

4 minutes ago, Roger Bissell said:

Thanks for posting this, Merlin. I have put off reading Engelbretsen for too long. He has moved onto my short list, thanks to this.

REB

Glad to help. Maybe it's time for me to reread both books.

[BaalChatzaf]

1 minute ago, Roger Bissell said:

Thanks for posting this, Merlin. I have put off reading Engelbretsen for too long. He has moved onto my short list, thanks to this.

REB

The Sommers-Englebertson extension of term logic is significant.  Yet is is limited. It cannot formulate its own metalogic and we cannot use it to get results such as incompleteness and undecidability.  It will not extend  to handling computability questions  as does first and second order logic. 

The Sommers-Englebertson scheme might be useful for parsing legal documents as it is more closely related to natural language than is First and Second order quantifier logic.  

You will notice that this scheme was inspired by the success of the Boole-Frege line of development.  For over 2000 years from the time of Aristotle it was not seen.  The Aristotelian approach could not have produced this extension.

[merjet]

24 minutes ago, BaalChatzaf said:

 The Aristotelian approach could not have produced this extension.

Well, of course not. So let's blame him for not having Merlin's (the other one) crystal ball.   After all, he died before Euclid and Archimedes were born, let alone Newton, Euler, Gauss, and so on. 

[BaalChatzaf]

26 minutes ago, Roger Bissell said:

Thanks for posting this, Merlin. I have put off reading Engelbretsen for too long. He has moved onto my short list, thanks to this.

REB

Read Fred Sommers first.  He came up with the idea of beefing up term logic in the first place.  He and Engelbretsen have published both together and separately on the extension of term logic. 

[BaalChatzaf]

2 minutes ago, merjet said:

Well, of course not. So let's blame him for his severe lack of clairvoyance.   After all, he died before Euclid and Archimedes were born, let alone Newton, Euler, Gauss, and so on. 

And you will notice that for 2000 years no one picked up the deficit.  It was not until  Boole and Frege took a completely different approach to logic (creating a mathematical form of logic)  that any further progress was made.  Fred Sommers who was well versed in modern mathematical logic took up the task to see if term logic could be beefed up properly.  It can be so extended to a degree but it does not lend itself well to meta-logical and meta-mathematical results such as were gotten by Post, Turing and Godel.  

[BaalChatzaf]

Quote

2 hours ago, Roger Bissell said:

Of course, they are. "Considered as" is just another way of saying "viewed from the perspective of." All identity ("is") statements - except instances of A is A - are assertions that a given thing viewed from two different perspectives is the same thing, i.e., is itself. That's why propositions work, and that's why syllogistic works. This is affirmed by various realist schools of thought, from Thomists like Aquinas and, more recently, Henry Veatch, to Ontological Atomists like Butchvarov (whose Being Qua Being has an extremely valuable and clarifying discussion of formal "a is a" identity and material identity, which is involved in non-tautological propositions).

When I put things in parenthesis, they are just for clarification, so that no shyster can come along and run with ambiguity and claim the argument is invalid. In other words, I'm making sure the reader knows what I am and am not trying to argue.

For instance, expanding the copula "is" to read "is (the same thing as)" is not a violation of logic but a clarification of it. It is highlighting the fact that the function of a categorical proposition is not to attribute the predicate to the subject, nor to assign the subject membership in the predicate class, but to assert that what is referred to by the subject is the same thing as what is referred to by the predicate.

And that is also why I, and all standard logic texts, and Aquinas, insist that propositions be put in "standard form," where you are literally saying that a thing (viewed from one perspective) is the same thing as that thing (viewed from another perspective). Again, that is how propositions and syllogisms work. Without the Law of Identity (and its corollaries) standing at least in the background, as the court of last resort, none of our utterances are intelligible.   

Here is an example: Venus considered as the morning star is (the same thing, viewed from a different perspective, as) Venus considered as the evening star.

Two syllogisms, identity throughout:

Syllogism 1. Phosphorus is (the same thing as) Venus considered as the morning star.

Venus considered as the morning star is (the same thing, viewed from a different perspective, as) Venus considered as the evening star.

Therefore, Phosphorus is (the same thing, viewed from a different perspective, as) Venus considered as the evening star.

Syllogism 2. (from conclusion of 1.) Phosphorus is (the same thing, viewed from a different perspective, as) Venus considered as the evening star.

Venus considered as the evening star is (the same thing as) Hesperus.

Therefore, Phosphorus is (the same thing, viewed from a different perspective, as) Hesperus.

Really? Hmmmm...

A tail of a lion, considered as a species (lion), is also a tail of the same lion, considered as a genus (animal).

A tail of a lion, considered as an individual, is a tail of the same lion, considered as a species (lion).

Therefore, a tail of a lion, considered as an individual, is a tail of the same lion, considered as a genus (animal).

Seems like all you're complaining about is that I didn't use X and Y in my argument.

X, a tail of a lion, Y, considered as a species (lion), is also X, a tail of the same lion, Y, considered as a genus (animal).

X, a tail of a lion, Y, considered as an individual, is X, a tail of the same lion, Y, considered as a species (lion).

Therefore, X, a tail of a lion, Y, considered as an individual, is X, a tail of the same lion, Y, considered as a genus (animal).

To me, that's just needless alphabet-soup, when the original version makes the case clearly and in depth. The original lays out the relations between parts and wholes and between individuals, species, and genera - and incorporates them into a categorical syllogism composed of three categorical propositions. By spelling out the relational complexities in ordinary language, it avoids paradox and fallacy that often results from excessive symbolization (e.g., the Goedel Slingshot argument). It doesn't get more Aristotelian than that.

Supposedly such "gotcha" cases as this reveal the weak underbelly of Aristotelian logic, but it seems to me that they instead reveal its power and adaptability. Ironically, your rehashing of the modernist sophistries is making me more confident in the power of perspicuously applied Aristotelian logic than before.

We've already been through this twice in the past. I met your challenge both times, and you refused to accept it both times. That's enough for the book I'm doing. (I won't quote you unless you want me to.) 

If they are NOT the primary argument forms in mathematics and the physical sciences, why are YOU championing them? 

REB

My error.  Conditional logic is the major mode logic used in mathematics and physics.  Categorical-Syllogistic is not the form of mathematical proofs these days.  Actually conditional reasoning was used  first by Euclid.  That is why you don't see syllogisms used in Euclid.   Constructing syllogistic ethymemes is just too clumsy to deal with geometric (and other mathematical) proofs.  It was the if-then logic of the stoic schools that prevailed in mathematics,  not the Aristotelian syllogistic.  Aristotle's approach could not deal properly with multi-term predicates (i.e. relations). 

For a quick introduction to Sommers-Englebretsen term logic  do see 

https://www.ontology.co/biblio/englebretseng.htm

http://www.oocities.org/genericAI/GI-SommersTFL.htm

 

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[BaalChatzaf]

1 hour ago, Roger Bissell said:

Thanks for posting this, Merlin. I have put off reading Engelbretsen for too long. He has moved onto my short list, thanks to this.

REB

see here for a summary of term logic compared to first order logic.

http://www.oocities.org/genericAI/GI-SommersTFL.htm

[BaalChatzaf]

Here is an excellent paper by Fred Sommers on Term Logic from the Notre Dame Journal of Logic.

Fred Sommers is the logician who brought term logic back from the dead.

 

Please see:  http://projecteuclid.org/download/pdf_1/euclid.ndjfl/1093635336