Thursday, January 31, 2008

What can we Infer from a Condemned Proposition?


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Dear Professor,

I was hoping you could take some time out of your schedule and help me with a question.

1) How does one interpret those long lists propositions censured by Rome, usually in the form of a negative or affirmative proposition? Does one understand the contrary or the contradictory as the orthodox doctrine? Are there any dogmatic principles laid out in one of your manuals in dealing with the interpretation of these propositions?

2) For example, what would be the contrary and/or contradictory of the proposition?

Moreover, it is false that the civil liberty of every form of worship, and the full power, given to all, of overtly and publicly manifesting any opinions whatsoever and thoughts, conduce more easily to corrupt the morals and minds of the people, and to propagate the pest of indifferentism.

Or, what more specifically would be the contrary and/or contradictory of this [condemned] proposition of Quanta Cura:

The best constitution of public society and civil progress altogether require that human society be conducted and governed without regard being had to religion any more than if it did not exist; or, at least, without any distinction being made between the true religion and false ones.

What do you make of this supposed contradictory formulation?

The best constitution of public society and civil progress DO NOT require that human society be conducted and governed without regard being had to religion any more than if it did not exist, or at least without any distinction being made between the true religion and false ones. [...]

It seems that this actually makes the proposition state the very thing the Pope was condemning as an actual possibility. It seems borderline nonsensical even. Would not the contradictory be posited in replacing "without" with the word "with"?

3) Could you take some time to break down the above proposition into it's constituent parts i.e. the subjects, objects, predicates, and so on.

4) And finally, how would you respond to this supposed exposition of logic:

This is why the condemnation of a proposition as false necessarily implies that the contradictory is true, but does not necessarily imply that the contrary is true. For example, from the condemnation of the proposition that human arguments opposed to the Catholic faith should always be allowed free room for discussion, it follows that at least sometimes they shouldn't, but not that they never should, nor even that they shouldn't as a rule with limited exceptions. From the condemnation of the proposition that no offenders against the Catholic religion should be penalized to a greater extent than public peace may require, it follows that at least some of them should, but not that all of them should, nor that any of them must be punished to a far greater extent than public peace may require.

To claim that the condemnation of a proposition establishes that the contrary of the proposition is true, rather than merely that the contradictory is true--like this: "Rather the contrary of the condemned doctrine would state [...]" [emphasis added]--is to perpetrate a fraud that will deceive only those who are not accustomed to employ even the rudiments of logic in comparing the teachings of Vatican II to prior teachings.

I would greatly appreciate your thoughtful response in this matter. Please let me know if you are still accepting donations as I know your time is valuable.

Thanks,
M.S.


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Dear M.,

1) I checked my best manual on Fundamental Theology (the Spanish Jesuit manual published by BAC in the 50's) and, although it does give an impressive treatment of the different notae theologicae, it does not seem to address the issue of deriving or inferring true propositions from condemned propositions. I am assuming that there must be many, much-more extensive, traditional monographs on Fundamental Theology that do go into the issue (after all, manuals are just summaries for seminarians), but I am not familiar with any (yet).

2) However, traditional logic does provide (almost) all the the tools that we need to make these inferences. The principles of making these inferences are not properly theological (that's why they are not likely to be found in theological textbooks) but philosophical. They belong to the discipline of logic.

The only distinction we need to import from theology is the obvious fact that there are different levels of condemned propositions (cf. the notae theologiae). Sometimes propositions are condemned as false. When a proposition is condemned as false, then we can utilize traditional logic to infer the truth of its contradictory. Sometimes, however, they are condemned in a "weaker" form, as doctrines that must not be taught or that sound offensive, or rash, etc., but not as doctrines that are necessarily "false" (the Magisterium will actually term them as doctrines that are "offensive to pious ears," or "rash," or something of the sort). When a proposition is condemned in one of these weaker ways, one cannot logically infer that its contradictory (or its "contrary" or whatever) is true. So let us find out how to derive the truth of the contradictory of a proposition that is condemned in the "stronger" way (i.e., as false).

[If you are not familiar with the traditional Square of Opposition, you might want to read this page before proceeding. You may ignore the last parragraph, as it pertains to "non-existent entities" (such are the trivial concerns of modern logic) and does not matter for our issue.]

It is ALWAYS the case that, if a proposition is false, its contradictory (not the same thing as its "opposite" or its "contrary" or its "sub-contrary" or its "sub-alternate") must be true. The question is what exactly is the contradictory of a given proposition. It ultimately depends on how the proposition is formulated. For simple categorical propositions of universal and particular quantity, it's quite easy: just refer to the Square of Opposition. However, not all propositions are simple (some are compound) and not all are universal or particular (some are singular and others indefinite); in these cases, the Square of Opposition does not apply. In fact, neither of the condemned propositions you gave me are simple universal or particular propositions and, therefore, we cannot use the Square of Opposition to derive the truth of their contradictories.

The first condemned proposition you cited is an example of a compound proposition:

It is false that the civil liberty of every form of worship, and the full power, given to all, of overtly and publicly manifesting any opinions whatsoever and thoughts, conduce more easily to corrupt the morals and minds of the people, and to propagate the pest of indifferentism.

This proposition starts with the words "It is false that..." For this reason, it is not a simple proposition, but a compound one. It is one proposition inside another. For the sake of clarity and economy of words, we'll abbreviate it as "~P." ("~" = "it is false that"; "P" = "the civil liberty... indifferentism." I hope you don't mind my using symbols to demonstrate the principle.) Now, this whole, complex proposition "~P" is condemned as false; therefore, we can say that ~P is false. Remember that if a proposition is false, then its contradictory is true. The contradictory of ~P is ~(~P), or simply P. So, if ~P is false, then its contradictory, P, is true.
(You can look at it this way: "~P is false" is itself a compound proposition. "~P is false" can be written in the following way: ~(~P). Now, if ~(~P), then P. Therefore, P is true. Put in words, if it is false that P is false, then it must be true that P is true. Therefore, P must be true. The principle that is operative here is the Principle of the Excluded Middle: there is no middle ground between truth and falsity.)

How does this translate into? How do you formulate the truth (the contradictory of the condemned proposition) in English?
The civil liberty of every form of worship, and the full power, given to all, of overtly and publicly manifesting any opinions whatsoever and thoughts, conduce more easily to corrupt the morals and minds of the people, and to propagate the pest of indifferentism.
Essentially, this means that civil liberty of worship and of opinion are conducive to the corruption of the people. This proposition (which is the contradictory of the condemned proposition) is true; we can safely derive this truth from the condemned proposition.


3) The second condemned proposition you cite is a simple proposition (not compound), but it is singular in quantity, not universal or particular, and, therefore, the Square of Opposition does not work either. It can be phrased this way (without loosing its essential meaning) so that it is clear that it is singular:

THE best constitution of public society [...] IS something that requires that human society be conducted and governed without regard being had to religion any more than if it did not exist; or, at least, without any distinction being made between the true religion and false ones.

It essentially says that a certain S is P. (S = "the best constitution of public society and civil progress"; P = "things that require that human society be conducted... false ones.") So we could formulate it logically as:
The best constitution of public society and civil progress" are "things that require that human society be conducted... false ones.
This is an affirmative singular proposition (if we interpret "the best constitution of publich society and civil progress" as forming a single, individual subject). Singular propositions follow what can be called "secondary opposition" (not primary opposition, which is what is expressed in the square of opposition). This means that they only have a contradictory, not a contrary. The contradictory of "a certain S is P" is "a certain S is not P." So, given that if a proposition is false, its contradictory must necessarily be true, this means that, since "a certain S is P" is false, "a certain S is not P" must be true.
What does this mean? It means that, because the condemned proposition,
The best constitution of public society and civil progress ARE things that require that human society be conducted... false ones
is false, its contradictory,
The best constitution of public society and civil progress ARE NOT things that require that human society be conducted... false ones
must be true.

If it does not make much sense it is simply because it remains in "logical form." Let us translate it to normal English:
The best constitution of public society and civil progress DOES NOT altogether require that human society be conducted and governed without regard being had to religion any more than if it did not exist; or [...] without any distinction being made between the true religion and false ones.
In other words, the best constitution of society does not require indifferentism. This is the truth that we can logically infer from the condemned proposition.

4) The author you cite is right in saying:
The condemnation of a proposition as false necessarily implies that the contradictory is true, but does not necessarily imply that the contrary is true.
He seems to be presuptiously asserting a principle of theological interpretation, but in fact it is simply applying a fundamental truth of the logic of categorical propositions to the particular instance of condemned propositions. The fact that one can infer, from the falsity of a proposition, the truth of its contradictory (and nothing at all of its contrary) is a basic principle of Aristotelian logic. But however basic, it is an important one to remember when interpreting the condemnations. This is perhaps best illustrated by means of an example of a condemned proposition that does follow the rules of the square of opposition, for it is in the square of opposition that the relationship between the contradictory and the contrary of a proposition is most clearly seen. Take this condemned proposition, for example (taken from Pope St. Pius X's Lamentabili):
In all the evangelical texts the name 'Son of God'' is equivalent only to that of 'Messias'. It does not in the least way signify that Christ is the true and natural Son of God.
This is a simple proposition; a universal affirmative. In terms of the square of opposition, we say it is an A-proposition. It says that all S's are P's. (S = "evangelical texts that use the name 'Son of God'"; P = "texts that do not signify that Christ is God") In logical form:

ALL evangelical texts that use the name 'Son of God' ARE texts that do not signify that Christ is God.

Now, the contradictory of an A-proposition (universal affirmative) is the O-proposition (particular negative). In logical form, this would be:

SOME evangelical texts that use the name 'Son of God' ARE NOT texts that do not signify that Christ is God."

Therefore, since the condemned A-proposition is false, the corresponding O-proposition is necessarily true. What is extremely important here is that we must not confuse the contradictory of a proposition with its contrary. The contrary of an A-proposition is its corresponding E-proposition. So the contrary of "All S's are P's" is "No S's are P's." Whereas the principle governing the relationship betwen contradictories states that if one of two contradictories is true, then the other must be false; the principle governing the relationship betwen contraries states that they cannot both be true, but they can both be false. Therefore, if we know that one is false, we cannot conclude that the other is true; in fact, we will not be able to conclude anything from that fact. For instance, "All extraterrestrial life forms are rational" and "No extraterrestrial life forms are rational" cannot both be true, but they can both be false. Hence, if we were to find out that one of these is false, we won't be able to infer that the other is true.

Therefore, from the fact that the condemned proposition,

SOME evangelical texts that use the name 'Son of God' ARE NOT texts that do not signify that Christ is God.

is false, I cannot infer that:

NO evangelical texts that use the name 'Son of God' ARE texts that do not signify that Christ is God." (= "All evangelical texts that use the name 'Son of God' signify that Christ is God.")

I do not mean to say that this last proposition is false (I would think it's true, though I'm no biblical scholar). All I'm saying is that its truth cannot be inferred from the falsity of its contrary. To infer the truth of a proposition from the falsity of its contrary is a fallacy.

I hope this helps. I apologize for the length of the explanation. St. Thomas could have done it a million times better in about 1% of the space.

In Domino,
-FJR.

-------------------------

Dear professor,

You stated that:

The second condemned proposition you cite is a simple proposition (not compound), but it is singular in quantity, not universal or particular, and, therefore, the Square of Opposition does not work either. It can be phrased this way (without loosing its essential meaning) so that it is clear that it is singular:

THE best constitution of public society [...] IS something that requires that human society be conducted and governed without regard being had to religion any more than if it did not exist; or, at least, without any distinction being made between the true religion and false ones.

I thought that this was a universal proposition since it seems to refer to not any society in particular, but the concept of society in the abract viz. it's "best" constitution.

[You also said that:]

Because the condemned proposition,

The best constitution of public society and civil progress ARE things that require that human society be conducted... false ones.

is false, its contradictory,

The best constitution of public society and civil progress ARE NOT things that require that human society be conducted... false ones.

must be true.

If it does not make much sense it is simply because it remains in "logical form." Let us translate it to normal English:

The best constitution of public society and civil progress DOES NOT altogether require that human society be conducted and governed without regard being had to religion any more than if it did not exist; or [...] without any distinction being made between the true religion and false ones.

In other words, the best constitution of society does not require indifferentism. This is the truth that we can logically infer [from the condemned proposition.]


I thought that the contradictory of the proposition above would revolve around the word "without" in such a way that it would read:

The best constitution of public society and civil progress altogether require that human society be conducted and governed WITH regard being had to religion any more than if it did not exist; or, at least, without any distinction being made between the true religion and false ones.

Does this not seem to be the contradictory of the assertion that society ought to be governed "WITHOUT" those conditions?

It seems that the contradictory that you formed would be implicitly allowing for the fact that sometimes religious indifference is the best constitution of society, but I thought this was the very thing Pius IX was censuring. As such, a liberal could theoretically glean from the above contradictory proposition that since we have evolved to a certain point in history, religious indifference of governments is always the best constitution, much like Dignitatis Humanae asserted. Would not the whole force of the condemnation be vitiated?

Yours,
M.S.

----------------------

Matthew,

A few points:

1) It seems to me that the third condemned proposition is singular (not universal) because its subject refers to a singular entity, namely, "THE best constitution." If the subject were "ALL constitutions" then it would be a universal proposition. If it were "SOME constitutions" then the proposition would be particular. The quantity of a proposition is identical to the quantity (or distribution) of the subject.

It is true that sometimes we utilize an abstract term to mean the whole class. For instance, when we say "man is rational" we mean "all men are rational." However, if we qualify the subject "man" by saying it is the "best," as in "the best man will win," then we don't mean "all men will win" but "one man will win." Usually, "the best x" refers to a single x and not to the whole class. I think that is what is going on in this (condemned) proposition. That's why I interpreted it as a singular proposition.

2) Let us suppose the condemned proposition is universal (A). At least in the case of A, E, I, and O propositions, the way you find the contradictory of a proposition is by reversing BOTH its quantity and quality, and leaving the subject and predicate terms untouched.

So, imagining it was an A proposition, I will re-write it with QUANTITY AND QUALITY INDICATORS in caps and will bold the subject and predicate terms:

ALL constitutions of public society and civil progress ARE things that altogether require that human society be conducted and governed without regard being had to religion any more than if it did not exist; or [...] without any distinction being made between the true religion and false ones.

If that were the condemned proposition, then the only way I could find the contradictory is by changing the quantity from universal to particular (i.e., change "ALL" to "SOME") and changing the quality from affirmative to negative (i.e., change "ARE" to "ARE NOT"). Furthermore, I would absolutely have to leave the subject and predicate terms untouched. So the contradictory (O) would look like this:

SOME constitutions of public society and civil progress ARE NOT things that altogether require that human society be conducted and governed without regard being had to religion any more than if it did not exist; or [...] without any distinction being made between the true religion and false ones.

To put it more briefly and in logical form, if the condemned proposition were:

ALL constitutions ARE things that require indifferentism" (which would be condemned, i.e., false).

Then its contradictory would be:

SOME constitutions ARE NOT things that require indifferentism" (which would be true, because it is the contradictory of a false proposition).

And that's all that you would be able to infer from the condemned A proposition. To infer anything else would be a fallacy.

3) Now, there is something extremely important that you MUST understand. When you say that "Some s are not p" you are NOT implying that "Some s are p." That would also be a fallacy. These two types of proposition (I and O) are sub-contraries. You may not infer the truth of one subcontrary from the truth of the other (although you may infer the truth of one from the falsity of the other). For example, it is certainly true that "Some Thomists are not amoebas" (I, for one, am not), you may not thereby infer that "Some Thomists are amoebas." However, knowing that "Some Thomists are amoebas" is false, you could infer that "Some Thomists are not amoebas" is true.

Now, this applies even if the condemned proposition is singular, as I had interpreted it. In the same way that one cannot infer the truth of a particular affirmative (I) from the truth of a particular negative (O), one also cannot infer the truth of a particular affirmative (I) from the truth of a singular negative. I had said that the condemned proposition was singular:

"THE best constitution IS something that requires indifferentism" (false, i.e., condemned).

Then, to get the contradictory, I merely reversed the quality to negative; the quantity, however, being singular, cannot be reversed:

"THE best constitution IS NOT something that requires indifferentism." (true, i.e., the contradictory of a false proposition).

You were alarmed that I would affirm this last proposition (the contradictory), because you thought it would imply that SOME constitutions other than the best one DO require indifferentism. But to think that way is to commit the same fallacy. From the fact that SOME constitutions (for example, the best one) DO not require indifferentism (I), one cannot infer that SOME constitutions DO NOT require indifferntism (O).

In the end, it does not matter what how you interpret the quantity of the condemned proposition:

  • a. If it is universal affirmative (A), then the contradictory will be a particular negative (O), from which you cannot infer a particular affirmative (I).
  • b. If it is singular affirmative, then the contradictory will be a singular negative, from which you cannot infer a particular affirmative (I).

So, either way, you will not be able to infer the I statement:

"SOME constitutions ARE things that require indifferentism" (product of a fallacy).

Let me know what your thoughts are on this.

Best,
-FJR.

---------------

Dear Professor,

You have hit the nail on the head, the fallacious inference of a particular affirmative. It's like a revelation! I was bothered by something, but I couldn't quite put my finger on it. Essentially this gentleman was trying to assert that since the contradictory of the condemned proposition didn't necessarily logically exclude all constitutions, we could infer that some constitutions require religious indifferentism. The universal call of Dignitatis Humanae for civil religious indifferentism, based upon the dignity of man, is what is under discussion. Now, if this is a practical pastoral judgment based upon historic facts, then we could merely quibble about the prudence of such an idea. But on the other hand, if it is a theoretical doctrine, universally valid, or the ideal form of government and it's relation to religion, then we have a real problem. If you have time, the discussion would be greatly enriched by your participation.

Yours,

M.S.

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