Perhaps the most commonly used account of validity is modal; it is the idea that an argument is valid when, its premises being true, the conclusion cannot be false. This account of validity makes the following argument valid:
Socrates is human;
therefore Socrates is an animal.
However, it would often be said that this is not valid in terms of its form; it is not formally valid but materially valid. Since anything formally valid that does not equivocate would certainly have also to be materially valid, the question arises as to what the principle is identifying an argument as formally valid. The usual principle suggested is some variant of Buridan's idea that it has to hold for all terms, keeping the form common to all of them the same. Thus people would usually say that the above argument is not formally valid because it would not be invariant under a consistent but arbitrary substitution of terms:
New Orleans is a city;
therefore New Orleans is a river.
But I'm not sure we should let this pass so easily. For one thing, 'keeping the form the same' has to apply to the actual logical principles used in drawing the conclusion, and it seems clear enough that the New Orleans argument does not use the same logical principles to draw its conclusion that the Socrates argument does. The conclusion in the Socrates argument 'works' because it simply moves the predicate from specific to general; that's what pretty much anyone making the argument would be doing. But this is not involved at all in the New Orleans argument.
One could perhaps argue that this is somehow not part of the argument's form, but it's difficult to see how it wouldn't be. It certainly would be if I did something like this:
Socrates is an animal that is rational;
therefore Socrates is an animal.
But there's not any obvious way in which this is different from the other. Logical terms are not words but meanings, so if 'human' includes 'animal' as part of its definition, the movement from 'human' to 'animal' should be as formal as the movement from 'animal that is rational' to 'animal', if they both proceed on the same principles, which they appear to do.
One could perhaps argue that the original is an enthymeme:
Socrates is human;
(everything human is an animal);
therefore Socrates is an animal.
This is certainly formally valid. But it's unclear that the implicit premise actually adds anything that is not already in the first premise, for exactly the reason just noted.
If one took each logical term to be a 'slot', so to speak, in a classification system, then an argument's form relates these 'slots' to each other; but then one would expect species-to-genus inference to be as formal as subalternation, universal instantiation, or inference involving the dictum de omni et nullo.
It has been noted by others that, while we can fairly easily handle the notion of logical form in particular logical systems, we don't have any general account of logical form. This is a related issue, I think, since there appears to be no useful account, applicable to the full range of arguments people would want to consider formally valid, that also obviously rules out the possibility that the classification of the terms can be part of the formal structure of an argument.
Wednesday, May 27, 2015
Tuesday, May 26, 2015
Links and Linkabilia
Due to a busy term, some of these are quite late; but still possibly of interest.
* Yogi Berra turned 90.
* Communication between bird species (and even some other animals, like squirrels) seems more extensive than had previously been thought.
* A humorous look at fake degree programs by way of their use of stock photos.
* Teresa Blankmeyer Burke on doing philosophy in American sign language.
* Ed Feser on C. S. Lewis on Transposition
* Larry Hurtado on the question of how far Paul was influenced by Stoicism
* Rav Elchanan Samet on rabbinical interpretations of the command not to put a stumblingblock in front of the blind.
* I'm way late on this, but apparently the official English translation of the Ukrainian Catholic Catechism is supposed to come out this year. I put this here in part to remind myself to keep an eye out for it.
* Greg Sadler on Anselm on divine power and greatness
* John Farrell discusses the decline of the priest-scientist
* A Clerk of Oxford discusses a Pentecost sermon by the tenth-century Saxon Aelfric.
* A periodic table of firework colors
* John Norton on Einstein's Zurich notebook (and scientific creativity)
* Catholicism in space
* Marina Folescu on Thomas Reid's philosophy of mind at the IEP
* Charles C. Petersen on the great Byzantine military strategy handbook, the Strategikon.
* Yogi Berra turned 90.
* Communication between bird species (and even some other animals, like squirrels) seems more extensive than had previously been thought.
* A humorous look at fake degree programs by way of their use of stock photos.
* Teresa Blankmeyer Burke on doing philosophy in American sign language.
* Ed Feser on C. S. Lewis on Transposition
* Larry Hurtado on the question of how far Paul was influenced by Stoicism
* Rav Elchanan Samet on rabbinical interpretations of the command not to put a stumblingblock in front of the blind.
* I'm way late on this, but apparently the official English translation of the Ukrainian Catholic Catechism is supposed to come out this year. I put this here in part to remind myself to keep an eye out for it.
* Greg Sadler on Anselm on divine power and greatness
* John Farrell discusses the decline of the priest-scientist
* A Clerk of Oxford discusses a Pentecost sermon by the tenth-century Saxon Aelfric.
* A periodic table of firework colors
* John Norton on Einstein's Zurich notebook (and scientific creativity)
* Catholicism in space
* Marina Folescu on Thomas Reid's philosophy of mind at the IEP
* Charles C. Petersen on the great Byzantine military strategy handbook, the Strategikon.
Hanique, Part IV
A silence hung between us, and I narrowed my eyes. "What kind of game do you think you are playing here?" I asked.
"No games, Dr. Montgomery," he replied.
"Stop calling me Dr. Montgomery," I said; "that's not my name."
"As you wish," he said. "But it is important that you take all three pills -- not just the white, but also the red and yellow. Can we do that?" His arid face seemed sinister in the light from the window behind his desk, and I wondered what they would do to me if I refused.
"Yes," I said finally and cautiously.
"Good," he said with a brisk smile. He gestured at the professor of mathematics and the professor of biology. "Please take Dr. Montgomery back to his room."
They practically dragged me out of the chair and down the hell. At the door to my office there was some fumbling as the professor of mathematics had to try more than one key to open it. They pushed me inside and locked the door behind me, leaving me, no doubt, to think myself a patient in a madhouse.
But they made a mistake. As they dragged me from the chair in the Dean's office, I caught a good, clear glimpse of the quad outside the Dean's window, and the black helicopter in it. Clearly whoever it was that had stolen the copy of Vision of Two Souls by Catharine of Hanique had also suborned the Dean. The Dean, in turn, being a man of absolutely no imagination, had invented this nonsensical story of the pills.
Also, I had palmed the professor of biology's keys while the professor of mathematics was fumbling around with the door.
I sat down a moment, wondering how best to proceed. My head was aching a bit and I looked for an aspirin, but I could find none in the room and my pocket turned up nothing but some red and yellow buttons that had fallen off my shirt a few days before, which I had forgotten to sew back on. I just threw them in the trash; no time for them now.
Clearly the thing to do is to set out and find this mysterious Hanique and discover what happened to the missing book. It will be dangerous, no doubt; one can hardly expect people who fly around in black helicopters stealing books and bribing Deans to be safe. But that is a true academic life, to purse truth at all costs and regardless of the obstacles. And when I actually retrieve the book and lay bare the mystery! It will vindicate my life's research.
But it is, again, dangerous, so I realized that I needed to leave some record, so that the Dean and his goons in the biology and mathematics departments cannot have the last word. This, my dear reader, is the manuscript you have in hand; I had already started writing it, so it was suitable for leaving an exact and objective record of events as they have happened to me. I will hide it, I think, by the statue of St. Catharine of Bologna. If you read this, I hope that I will have already returned from Hanique with the fruits of my research! But if not, at least someone else knows of the adventure I have had, and perhaps can carry on the pursuit, so that one day the human race may know the mystery of St. Catherine of Boulagnon, which has come to be tied so strangely to the mystery of Hanique.
"No games, Dr. Montgomery," he replied.
"Stop calling me Dr. Montgomery," I said; "that's not my name."
"As you wish," he said. "But it is important that you take all three pills -- not just the white, but also the red and yellow. Can we do that?" His arid face seemed sinister in the light from the window behind his desk, and I wondered what they would do to me if I refused.
"Yes," I said finally and cautiously.
"Good," he said with a brisk smile. He gestured at the professor of mathematics and the professor of biology. "Please take Dr. Montgomery back to his room."
They practically dragged me out of the chair and down the hell. At the door to my office there was some fumbling as the professor of mathematics had to try more than one key to open it. They pushed me inside and locked the door behind me, leaving me, no doubt, to think myself a patient in a madhouse.
But they made a mistake. As they dragged me from the chair in the Dean's office, I caught a good, clear glimpse of the quad outside the Dean's window, and the black helicopter in it. Clearly whoever it was that had stolen the copy of Vision of Two Souls by Catharine of Hanique had also suborned the Dean. The Dean, in turn, being a man of absolutely no imagination, had invented this nonsensical story of the pills.
Also, I had palmed the professor of biology's keys while the professor of mathematics was fumbling around with the door.
I sat down a moment, wondering how best to proceed. My head was aching a bit and I looked for an aspirin, but I could find none in the room and my pocket turned up nothing but some red and yellow buttons that had fallen off my shirt a few days before, which I had forgotten to sew back on. I just threw them in the trash; no time for them now.
Clearly the thing to do is to set out and find this mysterious Hanique and discover what happened to the missing book. It will be dangerous, no doubt; one can hardly expect people who fly around in black helicopters stealing books and bribing Deans to be safe. But that is a true academic life, to purse truth at all costs and regardless of the obstacles. And when I actually retrieve the book and lay bare the mystery! It will vindicate my life's research.
But it is, again, dangerous, so I realized that I needed to leave some record, so that the Dean and his goons in the biology and mathematics departments cannot have the last word. This, my dear reader, is the manuscript you have in hand; I had already started writing it, so it was suitable for leaving an exact and objective record of events as they have happened to me. I will hide it, I think, by the statue of St. Catharine of Bologna. If you read this, I hope that I will have already returned from Hanique with the fruits of my research! But if not, at least someone else knows of the adventure I have had, and perhaps can carry on the pursuit, so that one day the human race may know the mystery of St. Catherine of Boulagnon, which has come to be tied so strangely to the mystery of Hanique.
Sui Juris Churches XV: The Eritrean Catholic Church
(on sui juris churches in general)
Liturgical Family: Alexandrian
Primary Liturgical Language: Ge'ez
Juridical Status: Metropolitan
Approximate Population (to Nearest 10,000): 160,000
Brief History: The relationship of Eritrean Christianity to Ethiopian Christianity has always been complicated by the difficult relations between Eritrea and Ethiopia. Eritrea was converted to Christianity along with Ethiopia as part of the Kingdom of Aksum, but as Aksum's might waned, the kingdom of Medri Bahri rose; it was a Christian kingdom, and fought off the Adal Sultanate, but it was often in conflict with the Abyssinian Kingdom from which modern-day Ethiopia descends. In 1517 it temporarily became part of the Ottoman Empire; the Ottomans would eventually be driven out, but still remained a major influence until the coming of the Italians at the end of the nineteenth century. This Italian period, which lasted until the British threw the Italians out in 1941, saw the arrival of many Catholic missionaries. In 1930 an Ordinariate was established for Catholics in Eritrea, but it was a Latin Rite Ordinariate. In 1951, the British left, and the Ordinariate for Eritrea was abolished, replaced by an exarchate that was attached to the Ethiopian Catholic Church. In 1959 a separate Latin Rite Vicariate was established for Latin Rite Eritreans, and in 1961, Eritrea's status was raised from an exarchate to an eparchy.
Despite a strong desire for independence, the country was federated with Ethiopia under pressure from the United Nations; Emperor Haile Selassie would then forcibly annex the country in 1962. This led to a decades-long war until Eritrea finally established independence in 1993. In response to the independence, John Paul II reorganized the eparchial structure of the country and abolished the Latin Vicariate (which was, in any case, caring for a dwindling population), thus putting all Latin Rite Catholics under the authority of the Ethiopian Catholic bishops of Eritrea, making the nation the only nation in the world in which all Catholics regardless of rite are under the authority of Eastern Catholic bishops. In 2015, Francis detached the Eritrean eparchies from the Ethiopian Catholic Church and raised the eparchy of Asmara to a Metropolitan Archeparchy.
Notable Monuments: St. Joseph's Cathedral in Asmara.
Notable Saints: St. Justin de Jacobis (July 31); St. Frumentius (October 27); St. Kaleb Elesbaan of Axum (October 27).
Extent of Official Jurisdiction: The Archeparchy of Asmara and three suffragan eparchies, all in Eritrea. (Sphere of influence always extends beyond the official jurisdiction due to members of the church living outside of any official jurisdiction of the church.)
Online Sources and Resources:
http://www.catholicgheez.org/
http://www.eparchyofkeren.com/
http://www.katolsk.no/
http://www.cnewa.org/
Liturgical Family: Alexandrian
Primary Liturgical Language: Ge'ez
Juridical Status: Metropolitan
Approximate Population (to Nearest 10,000): 160,000
Brief History: The relationship of Eritrean Christianity to Ethiopian Christianity has always been complicated by the difficult relations between Eritrea and Ethiopia. Eritrea was converted to Christianity along with Ethiopia as part of the Kingdom of Aksum, but as Aksum's might waned, the kingdom of Medri Bahri rose; it was a Christian kingdom, and fought off the Adal Sultanate, but it was often in conflict with the Abyssinian Kingdom from which modern-day Ethiopia descends. In 1517 it temporarily became part of the Ottoman Empire; the Ottomans would eventually be driven out, but still remained a major influence until the coming of the Italians at the end of the nineteenth century. This Italian period, which lasted until the British threw the Italians out in 1941, saw the arrival of many Catholic missionaries. In 1930 an Ordinariate was established for Catholics in Eritrea, but it was a Latin Rite Ordinariate. In 1951, the British left, and the Ordinariate for Eritrea was abolished, replaced by an exarchate that was attached to the Ethiopian Catholic Church. In 1959 a separate Latin Rite Vicariate was established for Latin Rite Eritreans, and in 1961, Eritrea's status was raised from an exarchate to an eparchy.
Despite a strong desire for independence, the country was federated with Ethiopia under pressure from the United Nations; Emperor Haile Selassie would then forcibly annex the country in 1962. This led to a decades-long war until Eritrea finally established independence in 1993. In response to the independence, John Paul II reorganized the eparchial structure of the country and abolished the Latin Vicariate (which was, in any case, caring for a dwindling population), thus putting all Latin Rite Catholics under the authority of the Ethiopian Catholic bishops of Eritrea, making the nation the only nation in the world in which all Catholics regardless of rite are under the authority of Eastern Catholic bishops. In 2015, Francis detached the Eritrean eparchies from the Ethiopian Catholic Church and raised the eparchy of Asmara to a Metropolitan Archeparchy.
Notable Monuments: St. Joseph's Cathedral in Asmara.
Notable Saints: St. Justin de Jacobis (July 31); St. Frumentius (October 27); St. Kaleb Elesbaan of Axum (October 27).
Extent of Official Jurisdiction: The Archeparchy of Asmara and three suffragan eparchies, all in Eritrea. (Sphere of influence always extends beyond the official jurisdiction due to members of the church living outside of any official jurisdiction of the church.)
Online Sources and Resources:
http://www.catholicgheez.org/
http://www.eparchyofkeren.com/
http://www.katolsk.no/
http://www.cnewa.org/
Monday, May 25, 2015
Three Wombs
The Syriac fathers view Christ's redemptive work as resulting from his entry into three wombs: the womb of Mary, the waters of the Jordan, and the depths of sheol. (This very concept is affirmed in the Maronite Anaphora for the consecration of baptismal water when the celebrant states, "By your will, Father, Son, and Holy Spirit, he abided in three places: in a womb of flesh, in the womb of baptism, and in the dark mansions of sheol.")
Seely Joseph Beggiani, Early Syriac Theology, Revised edition, CUA Press (Washington, D.C.: 2014) p. 41.
Hanique, Part III
I stared at him in bewilderment.
"Please sit down," the Dean said. "I always look forward to these talks, Dr. Montgomery." The smile on his face seemed permanently frozen.
I sat down, feeling nervous and edgy.
"I'm glad to have a chance to talk to you," I said. "I have made some recent discoveries that I need to talk to you about. The research may require travel funds."
"Discoveries?" The frozen smile somehow seemed slightly more frozen.
I began with the events of the conference and told him of my research since then.
"And you have drawn conclusions from this?"
"Conclusions?" I said angrily. "Conclusions? Getting conclusions from this evidential mess is impossible. Even to begin to get a hold on this problem, I'll need to go to Hanique myself and...."
"Where is this 'Hanique'?"
I was at a complete loss, suddenly realizing for the first time that I hadn't the faintest notion of where Hanique was located. The only evidence I had that it actually existed at all, and was not a corruption like 'Boulagnon' was usually assumed to be, as the obscure statement of the man at the conference. A man I could not contact, as I did not even know his name.
I was still caught up in the puzzle this presented when the voice of the Dean broke in.
"Dr. Montgomery," he asked, "have you been taking your medications?"
Startled by the odd, and rather insulting, question, I replied indignantly, "I don't take medications; I haven't had anything recently except a few aspirin."
"Aspirin," he said, the frozen smile turning suddenly into a frown. "Do you mean the white pills? You are only taking the white pills?"
"Aspirin are usually white," I replied sarcastically. "But I don't see what business it is of yours what I'm taking or not."
"And the others?"
"What others?"
"The red and the yellow pills," he replied. "What have you been doing with the red and yellow pills?"
"Look," I said. "You're just a Dean. You're not my doctor, so I don't understand why you keep talking about medications."
The frozen smile returned to the his face.
"Dr. Montgomery," the Dean said, "we both know that I am not the Dean."
I stared at him in bewilderment.
to be continued
"Please sit down," the Dean said. "I always look forward to these talks, Dr. Montgomery." The smile on his face seemed permanently frozen.
I sat down, feeling nervous and edgy.
"I'm glad to have a chance to talk to you," I said. "I have made some recent discoveries that I need to talk to you about. The research may require travel funds."
"Discoveries?" The frozen smile somehow seemed slightly more frozen.
I began with the events of the conference and told him of my research since then.
"And you have drawn conclusions from this?"
"Conclusions?" I said angrily. "Conclusions? Getting conclusions from this evidential mess is impossible. Even to begin to get a hold on this problem, I'll need to go to Hanique myself and...."
"Where is this 'Hanique'?"
I was at a complete loss, suddenly realizing for the first time that I hadn't the faintest notion of where Hanique was located. The only evidence I had that it actually existed at all, and was not a corruption like 'Boulagnon' was usually assumed to be, as the obscure statement of the man at the conference. A man I could not contact, as I did not even know his name.
I was still caught up in the puzzle this presented when the voice of the Dean broke in.
"Dr. Montgomery," he asked, "have you been taking your medications?"
Startled by the odd, and rather insulting, question, I replied indignantly, "I don't take medications; I haven't had anything recently except a few aspirin."
"Aspirin," he said, the frozen smile turning suddenly into a frown. "Do you mean the white pills? You are only taking the white pills?"
"Aspirin are usually white," I replied sarcastically. "But I don't see what business it is of yours what I'm taking or not."
"And the others?"
"What others?"
"The red and the yellow pills," he replied. "What have you been doing with the red and yellow pills?"
"Look," I said. "You're just a Dean. You're not my doctor, so I don't understand why you keep talking about medications."
The frozen smile returned to the his face.
"Dr. Montgomery," the Dean said, "we both know that I am not the Dean."
I stared at him in bewilderment.
to be continued
Sunday, May 24, 2015
Fortnightly Book, May 24
The fortnightly book this time around will be Umberto Eco's third novel, The Island of the Day Before. It's unlikely to top The Name of the Rose or Foucault's Pendulum, the only fiction works by Eco that I've read (I've read a large portion of his nonfiction), and a look at critical reviews shows that most people think it hasn't come close, but as it's Eco one can be sure that there will be plenty in the book to like, whatever its shortcomings.
In the 1640s, Roberto della Griva finds himself shipwrecked and cast up, not on a deserted island but on a deserted ship. He's stuck there because although he can see land, he cannot swim. It is thus a Robinsonade with a twist. (Telegraphed by the name of the main character, who is doubly Robin-ish: Robin is a diminutive for Robert and 'Griva' is Catalan for a thrush, of which a robin is one kind; and the robin references are increased by other names, like Wanderdrossel, also a name for a thrush.) It, of course, would not be an Eco novel without also being a treatise on epistemology, and one can see just by glancing through that we have Eco's full toolbox of semiotic quirks and curiosities -- doppelgangers and lists and anachronistic allusions and endlessly many other things.
In the 1640s, Roberto della Griva finds himself shipwrecked and cast up, not on a deserted island but on a deserted ship. He's stuck there because although he can see land, he cannot swim. It is thus a Robinsonade with a twist. (Telegraphed by the name of the main character, who is doubly Robin-ish: Robin is a diminutive for Robert and 'Griva' is Catalan for a thrush, of which a robin is one kind; and the robin references are increased by other names, like Wanderdrossel, also a name for a thrush.) It, of course, would not be an Eco novel without also being a treatise on epistemology, and one can see just by glancing through that we have Eco's full toolbox of semiotic quirks and curiosities -- doppelgangers and lists and anachronistic allusions and endlessly many other things.
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