Logica Docens – Page 6 – Maverick Philosopher

Vallicella on the Argument for God from Logic

James Anderson responds here to my critique of his and Greg Welty's The Lord of Non-Contradiction: An Argument for God from Logic.

Professor Anderson's combox is open.

The Two Opposites of ‘Nothing’

It is interesting that 'nothing' has two opposites. One is 'something.' Call it the logical opposite. The other is 'being.' Call it the ontological opposite. Logically, 'nothing' and 'something' are interdefinable:

D1. Nothing is F =_df It is not the case that something is F

D2. Something is F =_df it is not the case that nothing is F.

These definitions give us no reason to think of one term as more basic than the other. Logically, they are on a par. Logically, they are polar opposites. Anything you can say with the one you can say with the other, and vice versa.

Ontologically, however, being and nothing are not on a par. They are not polar opposites. Being is primary, and nothing is derivative. (Note the ambiguity of 'Nothing is derivative' as between 'It is not the case that something is derivative' and 'Nothingness is derivative.' The second is meant.)

Suppose we try to define the existential 'is' in terms of the misnamed 'existential' quantifier. (The proper moniker is 'particular quantifier.') We try this:

y is =_df for some x, y = x.

In plain English, for y to be or exist is for y to be identical to something. For Quine to be or exist is for Quine to be identical to something. This thing, however, must exist. Thus

Quine exists =_df Quine is identical to something that exists

and

Pegasus does not exist =_df nothing that exists is such that Pegasus is identical to it.

The conclusion is obvious: one cannot explicate the existential 'is' in terms of the particular quantifier without circularity, without presupposing that things exist.

I have now supplied enough clues for the reader to advance to the insight that the ontological opposite of 'nothing,' is primary.

Mere logicians won't get this since existence is "odious to the logician" as George Santayana observes. (Scepticism and Animal Faith, Dover, 1955, p. 48, orig. publ. 1923.)

From the Laws of Logic to the Existence of God

James N. Anderson and Greg Welty have published a paper entitled The Lord of Non-Contradiction: An Argument for God from Logic. Having worked out similar arguments in unpublished manuscripts, I am very sympathetic to the project of arguing from the existence of necessary truths to the necessary existence of divine mind.

Here is a quick sketch of the Anderson-Welty argument as I construe it:

1. There are laws of logic, e.g., the law of non-contradiction.

2. The laws of logic are truths.

3. The laws of logic are necessary truths.

4. A truth is a true proposition, where propositions are the primary truth-bearers or primary vehicles of the truth values.

5. Propositions exist. Argument: there are truths (from 1, 2); a truth is a true proposition (3); if an item has a property such as the property of being true, then it exists. Ergo, propositions exist.

6. Necessarily true propositions necessarily exist. For if a proposition has the property of being true in every possible world, then it exists in every possible world. Remark: in play here are 'Fregean' as opposed to 'Russellian' propositions. See here for an explanation of the distinction as I see it. If the proposition expressed by 'Socrates is Socrates' is Russellian, then it has Socrates himself, warts and all, as a constituent. But then, though the proposition is in some sense necessarily true, being a truth of logic, it is surely not necessarily existent.

7. Propositions are not physical entities. This is because no physical entity such as a string of marks on paper could be a primary truth-bearer. A string of marks, if true, is true only derivatively or secondarily, only insofar as as it expresses a proposition.

8. Propositions are intrinsically intentional. (This is explained in the post which is the warm-up to the present one.)

Therefore

9. The laws of logic are necessarily existent, nonphysical, intrinsically intentional entities.

10. Thoughts are intrinsically intentional.

The argument now takes a very interesting turn. If propositions are intrinsically intentional, and thoughts are as well, might it be that propositions are thoughts?

The following invalid syllogism must be avoided: "Every proposition is intrinsically intentional; every thought is intrinsically intentional; ergo, every proposition is a thought." This argument is an instance of the fallacy of undistributed middle, and of course the authors argue in no such way. They instead raise the question whether it is parsimonious to admit into our ontology two distinct categories of intrinsically intentional item, one mental, the other non-mental. Their claim is that the principle of parsimony "demands" that propositions be constued as mental items, as thoughts. Therefore

11. Propositions are thoughts.

Therefore

12. Some propositions (the law of logic among them) are necessarily existent thoughts. (From 8, 9, 10, 11)

13. Necessarily, thoughts are thoughts of a thinker.

Therefore

14. The laws of logic are the thoughts of a necessarily existent thinker, and "this all men call God." (Aquinas)

A Stab at Critique

Line (11) is the crucial sub-conclusion. The whole argument hinges on it. Changing the metaphor, here is where I insert my critical blade, and take my stab. I count three views.

A. There are propositions and there are thoughts and both are intrinsically intentional.

B. Propositions reduce to thoughts.

C. Thoughts reduce to propositions.

Now do considerations of parsimony speak against (A)? We are enjoined not to multiply entities (or rather types of entity) praeter necessitatem. That is, we ought not posit more types of entity than we need for explanatory purposes. This is not the same as saying that we ought to prefer ontologies with fewer categories. Suppose we are comparing an n category ontology with an n + 1 category ontology. Parsimony does not instruct us to take the n category ontology. It instructs us to take the n category ontology only if it is explanatorily adequate, only if it explains all the relevant data but without the additional posit. Well, do we need propositions in addition to thoughts for explanatory purposes? It is plausible to say yes because there are (infinitely) many propositions that no one has ever thought of or about. Arithmetic alone supplies plenty of examples. Of course, if God exists, then there are no unthought propositions. But the existence of God is precisely what is at issue. So we cannot assume it. But if we don't assume it, then we have a pretty good reason to distinguish propositions and thoughts as two different sorts of intrinsically intentional entity given that we already have reason to posit thoughts and propositions.

So my first critical point is that the principle of parsimony is too frail a reed with which to support the reduction of propositions to thoughts. Parsimony needs to be beefed-up with other considerations, e.g., an argument to show why an abstract object could not be intrinsically intentional.

My second critical point is this. Why not countenance (C), the reduction of thoughts to propositions? It could be like this. There are all the (Fregean) propostions there might have been, hanging out in Frege's Third Reich (Popper's world 3). The thought that 7 + 5 = 12 is not a state of an individul thinker; there are no individual thinkers, no selves, no egos. The thought is just the Fregean proposition's temporary and contingent exemplification of the monadic property, Pre-Personal Awareness or Bewusst-sein. Now I don't have time to develop this suggestion which has elements of Natorp and Butchvarov, and in any case it is not my view.

All I am saying is that (C) needs excluding. Otherwise we don't have a good reason to plump for (B).

My conclusion? The Anderson-Welty argument, though fascinating and competently articulated, is not rationally compelling. Rationally acceptable, but not rationally compelling. Acceptable, because the premises are plausible and the reasoning is correct. Not compelling, because one could resist it without quitting the precincts of reasonableness.

To theists, I say: go on being theists. You are better off being a theist than not being one. Your position is rationally defensible and the alternatives are rationally rejectable. But don't fancy that you can prove the existence of God or the opposite. In the end you must decide how you will live and what you will believe.

The Inconclusiveness of Argument

He who can follow an argument will also know how not to be led by it.

Quantificational Uses of ‘Crap’

Crap, diddlysquat, squat, shit, jackshit, jack.

Crap and cognates as universal quantifiers. It is indeed curious that words for excrement can assume this logical role.

'No one owes you crap' = 'No one owes you anything' = 'Nothing is such that anyone owes it to you' = 'Everything is such that no one owes it to you.'

'He doesn't know jack' = 'He doesn't know anything.'

'He doesn't know shit, so he doesn't know shit from shinola.' In its first occurrence, 'shit' functions as a logical quantifier; in its second, as a non-logical word, a mass term.

You Don't Know Jack About Kerouac. A Trivia Test.

Addendum (26 February): Steven comments, "I have my doubts about "crap" meaning "anything." I think it means "nothing", but appears in acceptable double-negative propositions which, because of widespread colloquial usage. The evidence I bring forth is the following. "You've done shit to help us" means "You've done nothing to help us," not "You've done anything to help us."

BV: I see the point and it is plausible. But this is also heard: 'You haven't done shit to help us.' I take that as evidence that 'shit' can be used to mean 'anything.' Steven would read the example as a double-negative construction in which 'shit' means 'nothing.' I see no way to decide between my reading and his.

Either way, it is curious that there are quantificational uses of 'shit,' 'crap,' etc!

The Strange World of Simone Weil: God Does and Does Not Exist

In the chapter "Atheism as a Purification" in Gravity and Grace (Routledge 1995, tr. Emma Craufurd from the French, first pub. in 1947), the first entry reads as follows:

A case of contradictories which are true. God exists: God does not exist. Where is the problem? I am quite sure that there is a God in the sense that I am quite sure that my love is not illusory. I am quite sure that there is not a God in the sense that I am quite sure nothing real can be anything like what I am able to conceive when I pronounce this word. But that which I cannot conceive is not an illusion. (103)

What are we to make of writing like this? Contradictories cannot both be true and they cannot both be false. By their surface structure, God exists and God does not exist are contradictories. So, obviously, they cannot both be true if taken at face value.

Faced with an apparent contradiction, the time-tested method for relieving the tension is by making a distinction, thereby showing that the apparent contradiction is merely apparent. Suppose we distinguish, as we must in any case, between the concept God and God. Obviously, God is not a concept. This is true even if God does not exist. Interestingly, the truth that God is not a concept is itself a conceptual truth, one that we can know to be true by mere analysis of the concept God. For what we mean by 'God' is precisely a being that does not, like a concept, depend on the possibility or actuality of our mental operations, a being that exists in sublime independence of finite mind.

Now consider these translations:

God does not exist: Nothing in reality falls under the concept God.

God exists: There is an inconceivable reality, God, and it is the target of non-illusory love.

These translations seem to dispose of the contradiction. One is not saying of one and the same thing, God, that he both exists and does not exist; one is saying of a concept that it is not instantiated and of a non-concept that it is inconceivable. That is not a contradiction, or at least not an explicit contradiction. Weil's thesis is that there is a divine reality, but it is inconceivable by us. She is saying that access to the divine reality is possible through love, but not via the discursive intellect. There is an inconceivable reality.

Analogy: just as there are nonsensible realities, there are inconceivable realities. Just as there are realities beyond the reach of the outer senses (however extended via microscopes, etc.), there is a reality beyond the reach of the discursive intellect. Why not?

An objection readily suggests itself:

If you say that God is inconceivable, then you are conceiving God as inconceivable. If you say that nothing can be said about him, then you say something about him, namely, that nothing can be said about him. If you say that there exists an inconceivable reality, then that is different from saying that there does not exist such a reality; hence you are conceiving the inconceivable reality as included in what there is. If you say that God is real, then you are conceiving him as real as opposed to illusory. Long story short, you are contradicting yourself when you claim that there is an inconceivable reality or that God is an inconceivable reality, or that God is utterly beyond all of our concepts, or that no predications of him are true, or that he exists but has no attributes, or that he is real but inconceivable.

The gist of the objection is that my translation defense of Weil is itself contradictory: I defuse the initial contradiction but only by embracing others.

Should we concede defeat and conclude that Weil's position is incoherent and to be rejected because it is incoherent?

Not so fast. The objection is made on the discursive plane and presupposes the non-negotiable and ultimate validity of discursive reason. The objection is valid only if discursive reason is 'valid' as the ultimate approach to reality. So there is a sense in which the objection begs the question, the question of the ultimate validity of the discursive intellect. Weil's intention, however, is to break through the discursive plane. It is therefore no surprise that 'There is an inconceivable reality' is self-contradictory. It is — but that is no objection to it unless one presupposes the ultimate validity of discursive reason and the Law of Non-Contradiction.

Mystic and logician seem to be at loggerheads.

Mystic: "There is a transdiscursive, inconceivable reality."

Logician: "To claim as much is to embroil yourself in various contradictions."

Mystic: "Yes, but so what?"

Logician: "So what?! That which is or entails a contradiction cannot exist! Absolutely everything is subject to LNC."

Mystic: "You're begging the question against me. You are simply denying what I am asserting, namely, that there is something that is not subject to LNC. Besides, how do you know that LNC is a law of all reality and not merely a law of your discursive thinking? What makes your thinking legislative as to the real and the unreal?"

Logician: "But doesn't it bother you that the very assertions you make, and must make if you are verbally to communicate your view, entail logical contradictions?"

Mystic: "No. That bothers you because you assume the ultimate and non-negotiable validity of the discursive intellect. It doesn't both me because, while I respect the discursive intellect when confined to its proper sphere, I do not imperialistically proclaim it to be legislative for the whole of reality. You go beyond logic proper when you make the metaphysical claim that all of reality is subject to LNC. How are you going to justify that metaphysical leap in a non-circular way?"

Logician: "It looks like we are at an impasse."

Mystic: "Indeed we are. To proceed further you must stop thinking and see!"

How then interpret the Weilian sayings? What Weil is saying is logically nonsense, but important nonsense. It is nonsense in the way that a Zen koan is nonsense. One does not solve a koan by making distinctions, distinctions that presuppose the validity of the Faculty of Distinctions, the discursive intellect; one solves a koan by "breaking through to the other side." Mystical experience is the solution to a koan. Visio intellectualis, not more ratiocination.

A telling phrase from GG 210: "The void which we grasp with the pincers of contradiction . . . ."

But of course my writing and thinking is an operating upon the discursive plane. Mystical philosophy is not mysticism. It is, at best, the discursive propadeutic thereto. One question is whether one can maintain logical coherence by the canons of the discursive plane while introducing the possibility of its transcendence.

Or looking at it the other way round: can the committed and dogmatic discursivist secure his position without simply assuming, groundlessly, its ultimate and non-negotiable validity — in which event he has not secured it? And if he has not secured it, why is it binding upon us — by his own lights?

Reification and Hypostatization

My tendency has long been to use 'reification' and 'hypostatization' interchangeably. But a remark by E. J. Lowe has caused me to see the error of my ways. He writes, "Reification is not the same as hypostatisation, but is merely the acknowledgement of some putative entity's real existence." ("Essence and Ontology," in Novak et al. eds, Metaphysics: Aristotelian, Analytic, Scholastic, Ontos Verlag, 2012, p. 95) I agree with the first half of Lowe's sentence, but not the second.

Lowe's is a good distinction and I take it on board. I will explain it in my own way. Something can be real without being a substance, without being an entity logically capable of independent existence. An accident, for example, is real but is not a substance. 'Real' from L. res, rei. Same goes for the form of a hylomorphic compound. A statue is a substance but its form, though real, is not. The smile on a face and the bulge in a carpet are both real but incapable of independent existence. So reification is not the same as hypostatization. To consider or treat x as real is not thereby to consider or treat x as a substance.

Lowe seems to ignore that 'reification' and 'hypostatization' name logico-philosophical fallacies, where a fallacy is a typical mistake in reasoning, one that occurs often enough and is seductive enough to be given a label. On this point I diverge from him. For me, reification is the illict imputation of ontological status to something that does not have such status. For example, to treat 'nothing' as a name for something is to reify nothing. If I say that nothing is in the drawer I am not naming something that is in the drawer. Nothing is precisely no thing. As I see it, reification is not acknowledgment of real existence, but an illict imputation of real existence to something that lacks it. I do not reify the bulge in a carpet when I acknowledge its reality.

Or consider the internal relation being the same color as. If two balls are (the same shade of) red, then they stand in this relation to each other. But this relation is an "ontological free lunch" not "an addition to being" to borrow some phaseology from David Armstrong. Internal relations have no ontological status. They reduce to their monadic foundations. The putatively relational fact Rab reduces to the conjunction of two monadic facts: Fa & Fb. To bring it about that two balls are the same color as each other it suffices that I paint them both red (or blue, etc.) I needn't do anything else. If this is right, then to treat internal relations as real is to commit the fallacy of reification. Presumably someone who reifies internal relations will not be tempted to hypostatize them.

To treat external relations as real, however, is not to reify them. On my use of terms, one cannot reify what is already real, any more than one can politicize what is already political. To bring it about that two red balls are two feet from each other, it does not suffice that I create two red balls: I must place them two feet from each other. The relation of being two feet from is therefore real, though presumably not a substance.

To hypostatize is is to treat as a substance what is not a substance. So the relation I just mentioned would be hypostatized were one to consider it as an entity capable of existing even if it didn't relate anything. Liberals who blame society for crime are often guilty of the fallacy of hypostatization. Society, though real, is not a substance, let alone an agent to which blame can be imputed.

If I am right then this is mistaken:

First, I have given good reasons for distinguishing the two terms. Second, the mistake of treating what is abstract as material is not the same as reification or hypostatization. For example, if someone were to regard the null set as a material thing, he would be making a mistake, but he would not be reifying or hypostatizing the the null set unless there were no null set.

Or consider the proposition expressed by 'Snow is white' and 'Schnee ist weiss.' This proposition is an abstact object. If one were to regardit as a material thing one would be making a mistake, but one would not be reifying it because it is already real. Nor would one be hypostatizing it since (arguably) it exists independently.

Gilson and the Avicennian-Thomistic Common Natures Argument

Chapter III of Etienne Gilson's Being and Some Philosophers is highly relevant to my ongoing discussion of common natures. Gilson appears to endorse the classic argument for the doctrine of common natures in the following passage (for the larger context see here):

Out of itself, animal is neither universal nor singular. Indeed, if, out of itself, it were universal, so that animality were universal qua animality, there could be no singular animal, but each and every animal would be a universal. If, on the contrary, animal were singular qua animal, there could be no more than a single animal, namely, the very singular to which animality belongs, and no other singular could be an animal. (77)

This passage contains two subarguments. We will have more than enough on our plates if we consider just the first. The first subargument, telescoped in the second sentence above, can be put as follows:

1. If animal has the property of being universal, then every animal would be a universal. But:

2. It is not the case that every animal is a universal. Therefore:

3. It is not the case that animal has the property of being universal.

This argument is valid in point of logical form, but are its premises true? Well, (2) is obviously true, but why should anyone think that (1) is true? It is surely not obvious that the properties of a nature must also be properties of the individuals of that nature.

There are two ways a nature N could have a property P. N could have P by including P within its quidditative content, or N could have P by instantiating P. There is having by inclusion and having by instantiation.

For example, 'Man is rational' on a charitable reading states that rationality is included within the content of the nature humanity. This implies that everything that falls under man falls under rational. Charitably interpreted, the sentence does not state that the nature humanity or the species man is rational. For no nature, as such, is capable of reasoning. It is the specimens of the species who are rational, not the species.

This shows that we must distinguish between inclusion and instantiation. Man includes rational; man does not instantiate rational.

Compare 'Man is rational' with 'Socrates is rational.' They are both true, but only if 'is' is taken to express different relatons in the two sentences. In the first it expresses inclusion; in the second, instantiation. The nature man does not instantiate rationality; it includes it. Socrates does not include rationality; he instantiates it.

The reason I balk at premise (1) is because it seems quite obviously to trade on a confusion of the two senses of 'is' lately distinguished. It confuses inclusion with instantiation. (1) encapuslates a non sequitur. It does not follow from a nature's being universal that everything having that nature is a universal. That every animal would be a universal would follow from humanity's being universal only if universality were included in humanity. But it is not: humanity instantiates universality. In Frege's jargon, universality is an Eigenschaft of humanity, not a Merkmal of it.

Since the first subargument fails, there is no need to examine the second. For if the first subargment fails, then the whole Avicennian-Thomist argument fails.

More Fun With Existential Generalization

Intuitively, if something is identical to Venus, it follows that something is identical to something. In the notation of MPL, the following is a correct application of the inference rule, Existential Generalization (EG):

1. (∃x)(x = Venus)
2. (∃y)(∃x)(x = y) 1, EG

(1) is contingently true: true, but possibly false. (2), however, is necessarily true. Ought we find this puzzling? That is one question. Now consider the negative existential, 'Vulcan does not exist.'

3. ~(∃x)( x = Vulcan)
4. (∃y)~(∃x)(x = y) 3, EG

(3) is contingently true while (4) is a logical contradiction, hence necessarily false. The inference is obviously invalid, having taken us from truth to falsehood. What went wrong?

Diagnosis A: "You can't existentially generalize on a vacuous term, and 'Vulcan' is a vacuous term."

The problem with this diagnosis is that whether a term is vacuous or not is an extralogical (extrasyntactic) question. Let 'a' be an arbitrary constant, and thus neither a place-holder nor a variable. Now if we substitute 'a' for 'Vulcan' we get:

3* ~(∃x)( x = a)
4. (∃y)~(∃x)(x = y) 3*, EG

The problem with this inference is with the conclusion: we don't know whether 'a' is vacuous or not. So I suggest

Diagnosis B: Singular existentials cannot be translated using the identity sign as in (1) and (3). This fact, pace van Inwagen, forces us to beat a retreat to the second-level analysis. We have to analyze 'Venus exists' in terms of

5. (∃x)(Vx)

where 'V' is a predicate constant standing for the haecceity property, Venusity. Accordingly, what (5) says is that Venusity is instantiated. Similarly, 'Vulcan does not exist' has to be interpreted as saying that Vulcanity is not instantiated. Thus

6. ~(∃x)(Wx)

where 'W' is a predicate constant denoting Vulcanity.

It is worth noting that we can existentially generalize (6) without reaching the absurdity of (4) by shifting to second-order logic and quantifying over properties:

7. (∃P)~(∃x)Px.

That says that some property is such that it is not instantiated. There is nothing self-contradictory about (7).

But of course beating a retreat to the second-level analysis brings back the old problem of haecceities. Not to mention the circularity problem.

The thin theory is 'cooked' no matter how you twist and turn.

Are the Laws of Logic Empirical Generalizations?

London Ed raises the question whether logic is empirical.

That puts me in mind of the old idea of John Stuart Mill and others that the laws of logic are empirical generalizations from what we do and do not perceive. Thus we never perceive rain and its absence in the same place at the same time. The temptation is to construe such logic laws as the Law of Non-Contradiction — ~(p & ~p) — as generalizations from psychological facts like these. If this is right, then logical laws lack the a priori character and epistemic ‘dignity’ that some of us are wont to see in them. They rest on psychological facts that might have been otherwise and that are known a posteriori.

London Ed might want consider this reductio ad absurdum:

1. The laws of logic are empirical generalizations. (Assumption for
reductio)
2. Empirical generalizations, if true, are merely contingently
true. (By definition of ‘empirical generalization’: empirical generalizations
record what happens to be the case, but might not have been the case.)
Therefore,
3. The laws of logic, if true, are merely contingently true.
(From 1 and 2)
4. If proposition p is contingently true, then it is possible
that p be false. (Def. of ‘contingently true.’)Therefore,
5. The laws of logic, if true, are possibly false. (From 3 and 4)Therefore,
6. LNC is possibly false: there are logically possible worlds in which ‘p&~p’ is true.
(From 5 and the fact that LNC is a law of logic.)
7. But (6) is absurd (self-contradictory): it amounts to saying that it is logically possible that the very criterion of logical possibility, namely LNC, be false. Corollary: if
laws of logic were empirical generalizations, we would be incapable of defining ‘empirical generalization’: this definition requires the notion of what is the case but (logically) might not have been the case.

Asserting and Arguing: Analysis of an Example and Response to Novak

In my earlier posts on this topic here and here I did not analyze an example. I make good that deficit now.

Suppose a person asserts that abortion is morally wrong. Insofar forth, a bare assertion which is likely to elicit the bare counter-assertion, 'Abortion is not morally wrong.' What can be gratuitously asserted may be gratuitously denied without breach of logical propriety, a maxim long enshrined in the Latin tag Quod gratis asseritur, gratis negatur. So one reasonably demands arguments from those who make assertions. Here is one:

Infanticide is morally wrong
There is no morally relevant difference between abortion and infanticide
Ergo
Abortion is morally wrong.

Someone who forwards this argument in a concrete dialectical situation in which he is attempting to persuade himself or another asserts the premises and in so doing provides reasons for accepting the conclusion. This goes some distance toward removing the gratuitousness of the conclusion. But what about the premises? If they are mere assertions, then the conclusion, though proximately non-gratuitous (because supported by reasons), is not ultimately non-gratuitous (because no support has been provided for the premises).

Of course, it is better to give the above argument than merely to assert its conclusion. The point of the original post, however, is that one has not escaped from the realm of assertion by giving an argument. And this for the simple reason that (a) arguments have premises, and (b) arguments that do dialectical work must have one or more asserted premises, the assertions being made by the person forwarding the argument with the intention of rationally persuading himself or another of something.

Our old friend Lukas Novak proposes a counterexample to (b): the reductio ad absurdum (RAA)argument. If I understand him, what Novak is proposing is that some such arguments can be used to rationally justify the assertion of the conclusion without any of the premises being asserted by the producer of the argument. Suppose argument A with conclusion C has premises P1, P2, P3. Suppose further that the premise set entails a contradiction. We may then validly conclude and indeed assert that either P1 is not true or P2 is not true or P3 is not true. We may in other words make a disjunctive assertion, an assertion the content of which is a disjunctive proposition. And this without having asserted P1 or P2 or P3. What we have, then, is an argument with an asserted conclusion but no asserted promises.

I think Professor Novak is technically correct except that the sort of RAA argument he describes is not very interesting. Suppose the asserted conclusion is this: Either the null set is not empty, or the null set is not a set, or the Axiom of Extensionality does not hold, or the null set is not unique. Who would want to assert that disjunctive monstrosity? An interesting RAA argument with this subject matter would establish the uniqueness of the null set on the basis of several asserted premises and one unasserted premise, namely, The null set is not unique, the premise assumed for reductio.

So I stick to my guns: 'real life' arguments that do dialectical work must have one or more asserted premises. Novak's comment did, however, give me the insight that not every premise of a 'real life' dialectically efficacious argument must be asserted.

Now back to the abortion argument. My point, again, is that providing even a sound argument for a conclusion — and I would say that the above argument is sound, i.e., valid in point of logical form and having true premises — does not free one from the need to make assertions. For example, one has to assert that infanticide is morally wrong. But if no ground or grounds can be given for this assertion, then the assertion is gratuitous. To remove the gratuitousness one can give a further argument: The killing of innocent human beings is morally wrong; (human) infants are innocent human beings; ergo, etc. The first premise in this second argument is again an assertion, and so on.

Eventually we come to assertions that cannot be argued. That is not to say that these assertions lack support. They are perhaps grounded in objective self-evidence.

Note that I am not endorsing what is sometimes called the Münchhausen trilemma, also and perhaps better known as Agrippa's Trilemma, according to which a putative justification either

   a. Begets an infinite regress, or
   b. Moves in a circle, or
   c. Ends in dogmatism, e.g., in an appeal to self-evidence that can only be subjective, or in an appeal to authority.

All I am maintaining — and to some this may sound trivial — is that every real-life argument that does dialectical work must have one or more asserted premises. And so while argument is in general superior to bare assertion, argument does not free us of the need to make assertions. I insist on this so that we do not make the mistake of overvaluing argumentation.

To put it aphoristically, the mind's discursivity needs for its nourishment intuitive inputs that must be affirmed but cannot be discursively justified.

Abbreviations, Place-Holders, and Logical Form

It is one thing to abbreviate an argument, another to depict its logical form. Let us consider the following argument composed in what might be called 'canonical English':

1. If God created some contingent beings, then he created all contingent beings.
2. God created all contingent beings.
—–
3. God created some contingent beings.

The above is an argument, not an argument-form. The following abbreviation of the argument is also an argument, not an argument-form:

More on Asserting and Arguing

James Anderson comments astutely via e-mail:

I have a worry about your post Asserting and Arguing.

You seem to affirm all of the following:

(1) An assertion is a mere assertion unless argued.
(2) Mere assertions are gratuitous.
(3) The premises of arguments are assertions.
(4) One cannot argue for every premise of every argument.

This is an accurate summary except for (3). I did not say that the premises of arguments are assertions since I allow that the premises of an argument may be unasserted propositions. The constituent propositions of arguments considered in abstracto, as they are considered in formal logic, as opposed to arguments used in concrete dialectical situations to convince oneself or someone else of something, are typically unasserted.

Since the conclusion of an argument cannot be any stronger (or less gratuitous) than its premises, doesn't it follow from these claims that the conclusion of every argument is gratuitous?

Well, if the conclusion follows from the premises, then it has the support of those premises, and is insofar forth less gratuitous than they are. Your point is better put by saying that, if the premises are gratuitious, then the conclusion canot be ultimately non-gratuitous, but only proximately non-gratuitous.

You distinguish between 'making' arguments and 'entertaining' arguments, but that doesn't offer a way out here because the kind of argument required in (1) and (3) is a 'made' argument rather than an 'entertained' argument.

Isn't the answer here to reject (1) and to grant that some assertions (e.g., the assertion that your cats are on the desk) can be neither mere assertions nor argued assertions? We need a category like 'justified' assertions: no justified assertion is a mere assertion and not every justified assertion is an argued assertion.

Professor Anderson has put his finger on a real problem with the post, and I accept his criticism. I began the post with the sentence, "Mere assertions remain gratuitous until supported by arguments." But that is not quite right. I should have written: "Mere assertions remain gratuitous until supported, either by argument, or in some other way." Thus my assertion that two black cats are lounging on my writing table is not a mere assertion although it is and must be unargued; it is an assertion justified by sense perception.

Expressed more clearly, the main point of the post was that ultimate justification via argument alone cannot be had. Sooner or late one must have recourse to propositions unsupportable by argument. Argument does not free us of the need to make assertions. (I am assuming that there is no such thing as infinitely regressive support or circular support. Not perfectly obvious, I grant: but very plausible.)

Asserting and Arguing

Mere assertions remain gratuitous until supported by arguments. Quod gratis asseritur, gratis negatur. That which is gratuitously assertible is gratuitously deniable. Thus one is right to demand arguments from those who make assertions. It is worth pointing out, however, that the difference between making an assertion and giving an argument is not absolute. Since no argument can prove its own premises, they must remain mere assertions from within the context of the argument. No doubt they too can be supported by further arguments, but eventually one comes to ultimate premises that can only be asserted, not argued.

Argument cannot free us of assertion since every argument has premises and they must be asserted if one is making an argument as opposed to merely entertaining one. One who makes an argument is not merely asserting its conclusion; he is asserting its conclusion on the basis of premises that function as reasons for the assertion; and yet the premises themselves are merely asserted. There is no escaping the need to make assertions.

If you refuse to accept ultimate premisses, then you are bound for a vicious infinite regress or a vicious circle, between which there is nothing to choose. (The viciousness of a logical circle is not mitigated by increasing its 'diameter.') This shows the limited value of argument and discursive rationality. One cannot avoid the immediate taking of something for true. For example, I immediately take it to be true, on the basis of sense perception, that a couple of black cats are lounging on my desk: