Bill Vallicella – Page 503 – Maverick Philosopher

Logical Form and the Supposed Asymmetry of Validity and Invalidity: A Defense of Symmetry

For the 'Londonistas,' Ed and David, partners in logical investigations. We are unlikely ever to agree, but clarification of differences is an attainable and worthwhile goal, here, and in every arena of controversy. Have at it, boys.

………….

1. Suppose someone reasons as follows. 'Some Englishmen are Londoners; therefore, some Londoners are Englishmen.' To reason is one thing, to reason correctly another. So one can ask: Is this specimen of reasoning correct or incorrect? This is the sort of question with which logic deals. Logic is the study of inference and argument from a normative point of view. It seeks to articulate the criteria of correct and incorrect reasoning. It is analogous to ethics which seeks to articulate the criteria of correct and incorrect action.

2. We all take for granted that some reasoning is correct and some incorrect, and we are all more or less naturally good at reasoning correctly. Almost everyone grasps immediately that if Tom is an Englishman and some Englishmen are Londoners, it does not follow that Tom is a Londoner. What distinguishes the logician is his reflective stance. He reflects upon reasoning in general and tries to extract and systematize the principles of correct reasoning. 'Extract' is an apt metaphor. The logician develops a theory from his pre-theoretical understanding of argumentative correctness. As every teacher of logic comes to learn, one must already be logical to profit from the study of logic just as one must already be ethical to profit from the study of ethics. It is a matter of making explicit and raising to the full light of awareness what must already be implicitly present if the e-duc-ation, the drawing out into the explicit is to occur. This is why courses in logic and ethics are useless for many and positively harmful for some. But they do make some of us more logical and more ethical.

3. Correctness in deductive logic is called validity, and incorrectness invalidity. Since one can argue correctly from false premises and incorrectly from true premises, we distinguish validity from truth. Consider the following argument:

Some Englishmen are Londoners
——-
Some Londoners are Englishmen.

We say of neither the premise nor the conclusion that it is either valid or invalid: we say that it is either true or false. And we do not say of the argument that it is true or false, but that it is either valid or invalid. We also speak of inferences as either valid or invalid.

4. What makes a valid argument valid? It can't be that it has true premises and a true conclusion. For there are invalid arguments that satisfy this condition. Some say that what makes a valid argument valid is the impossibility of the premises' being true and the conclusion false. Theirs is a modal explanation of validity. Equivalently,

D1. Argument A is valid =df necessarily, if A's premises are all true, then A's conclusion is true.

This necessity is plainly the necessity of the consequence (necessitas consequentiae), not the necessity of the consequent (necessitas consequentiis): in the majority of cases the premises and conclusion are all contingent propositions.

The modal explanation of validity in (D1) is fine as far as it goes, but it leads to the question: what is the ground of the necessity? If validity is explained by the RHS of (D1), what explains the necessity? What explains the necessitas consequentiae of the conditional on the RHS of (D1)?

Enter logical form.

The validity of a given valid argument evidently resides in something distinct from the given argument. What is this distinct something? It is the logical form of the argument, the argument form. The form F of an argument A is distinct from A because F is a universal (a repeatable) while A is a particular (an unrepeatable). Thus the form

All S are M
All M are P
——-
All S are P

is a one-in-many, a repeatable. It is repeated in every argument of that form. It is the form of indefinitely many syllogisms, although it is not itself a syllogism, any more than 'All S are M' is a proposition. A proposition is either true or false, but 'All S are M' is neither true nor false. To appreciate this, bear in mind that 'S' and 'M' are not abbreviations but placeholders. If the letters above were abbreviations, then the array above would be an (abbreviated) argument, not an argument form. An argument form is not an argument but a form of indefinitely many arguments.

Now validity is a property of argument forms primarily, and secondarily of arguments having valid forms. What makes a valid argument valid is the validity of its form:

D2. Argument A is valid =df A is an instance of a valid argument form.

D3. Argument form F is valid =df no instance of F has true premises and a false conclusion.

Validity is truth-preserving: a valid argument form will never take you from true premises to a false conclusion. (Exercise for the reader: show that invalidity is not falsehood preserving.) In sum, an argument is valid in virtue of having a valid form, and a form is valid if no argument of that form has true premises and a false concusion. The logical form of a valid argument is what makes it impossible for the premises to be true and the conclusion false.

5. If a valid argument is one with a valid form, one will be tempted to to say that an invalid argument is one with an invalid form. Call this the Symmetry Thesis:

ST. If an argument is an instance of a valid form, then it is valid, and if it is an instance of an invalid form, then it is invalid.

But there are examples that appear to break the symmetry, e.g.:

If God created something , then God created everything.
God created everything.
——-
God created something.

This argument fits the pattern of the formal fallacy, Affirming the Consequent:

If p then q
q
——-
p.

But the argument also has a valid form:

Every x is such that Cgx
——-
Some x is such that Cgx.

(Example adapted from Gerald J. Massey, "The Fallacy behind Fallacies," Midwest Studies in Philosophy VI (1981), pp. 489-500)

So which is it? Is the argument valid or invalid? It can't be both and it can't be neither. One option is to abandon the Symmetry Thesis and maintain that having a valid form is sufficient for an argument to be valid, but that having an invalid form is not sufficient for it to be invalid. One would then be adopting the following Asymmetry Thesis:

AT. Having a valid form suffices for an argument to be valid, but having an invalid form does not suffice for an argument to be invalid.

Another option is to hold to the Symmetry Thesis and maintain that the Massey argument is really two arguments, not one. But before exploring this option, let us consider the unintuitive consequences of holding that one and the same argument can have two different forms, one valid, the other invalid.

6. Consider any valid syllogism. A syllogism, by definition, consists of exactly three different propositions: a major premise, a minor premise, and a conclusion. So every valid syllogism has the invalid form: p, q, ergo r. Generalizing, we can say that any argument whose validity hinges upon the internal subpropositional logical structure of its constituent propositions will instantiate an invalid form from the propositional calculus (PC). For example, any argument of the valid form, Some S are P; ergo, Some P are S, is an instance of the invalid PC form, p, ergo q.

To think of a valid syllogism as having the invalid form p, q, ergo r is to abstract away from the internal subpropositional logical structure that the syllogism's validity pivots on. But if this abstraction is permitted, one may permit oneself to abstract away from the requirement that the same terms in an argument be replaced by the same placeholders. One might then maintain that

All men are mortal
Socrates is a man
——-
Socrates is mortal

has the invalid logical form

All Fs are Gs
a is an H
——-
a is a G

But why stop there? By the same 'reasoning,' the Socrates syllogism has the invalid form:

All Fs are Gs
a is an H
——-
b is an I.

But if one abstracts away from the requirement that the same term or sentence be replaced by the same placeholder, then we get the result that the obviously valid

Tom is tall
——-
Tom is tall

has the valid form p ergo p and the invalid form p ergo q. Here we are abstracting away from the fact that a proposition entails itself and ascending to the higher level of abstraction at which a proposition entails a proposition. After all, it is surely true that in our example a proposition entails a proposition.

I submit, however, that our example's having an invalid form is an intolerable result. Something has gone wrong. Surely the last argument has no invalid form. Surely one cannot lay bare the form of an argument, in an serious sense of 'argument,' if one abandons the requirement that the same term or sentence be replaced by the same placeholder. To do that is to engage in vicious abstraction. It is vicious because an argument in any serious sense of the term is not just a sequence of isolated propositions, but a sequence of propositions together with the idea that one of them is supposed to follow from the others. An argument in any serious sense of the term is a sequence of propositions that has the property of being putatively such that one of them, the conclusion, follows from the others, the premises. But no sequence of propositions can have this property if the argument's form allows for different terms/propositions to have different placeholders.

7. So I suggest that we abandon the Asymmetry Thesis and adopt the Symmetry Thesis according to which no valid argument has any invalid forms. Let me now try to motivate this proposal.

An argument form is an abstraction from an argument. But it is also true that an argument is an abstraction from a concrete episode of reasoning by a definite person at a definite time. Clearly, the same argument can be enacted by the same person at different times, and by the same or different persons at different times. I can 'run through' the argument that the null set is unique any number of times, and so can you. An argument in this sense is not a concrete episode of arguing (reasoning) but a sequence of propositions. A proposition, of course, is not the same as a sentence used to express it.

Now I grant that an argument taken in abstraction from an episode of reasoning (and as the content of that reasoning) can instantiate two or more argument forms. But I deny that a concrete episode of reasoning by a definite person at a definite time can instantiate two or more argument forms. So my claim is that while an argument in abstracto can have two or more forms, an argument in concreto, i.e. a concrete episode of reasoning cannot have more than one form. If this form is valid the argument in concreto is valid. If invalid, the argument in concreto is invalid. To illustrate:

Suppose I know that no Democrat supports capital punishment. Then I learn that Jones is a Democrat. Putting together these two pieces of information, I infer that Jones does not support capital punishment. By 'the concrete episode of reasoning,' I mean the reasoning process together with its content. One first thinks of the first proposition, then the second, then one infers the third, and all of this in the unity of one consciousness. The content is the argument considered in abstraction from any particular diachronic mental enactment by a particular person at a particular time. The reasoning process as a datable temporally extended mental process is also an abstraction from the concrete episode of reasoning which must include both, the reasoning and its content.

Now the concrete episode of reasoning embodies a pattern. In the example, I reason in accordance with this pattern:

(x) (Fx –> ~Gx)
Fa
——-
~Ga

Which is also representable as follows:

No Fs are Gs
a is an F
——-
a is not a G.

The pattern or logical form of my concrete episode of reasoning is assuredly not: p, q, ergo r. This is consistent with saying that the argument in abstracto instantiates the invalid form p, q, ergo r in addition to the valid form above.

The point I am making is this. If we take an argument in abstraction from the concrete episode of reasoning in which it is embodied, then we may find that it instantiates more than one form. There is no denying that every valid syllogism, considered by itself and apart from the mental life of an agent who thinks it through, instantiates the invalid form p, q, ergo r. But no one who reasons syllogistically reasons in accordance with that invalid form. Syllogistic reasoning, whether correct or incorrect, is reasoning that is sensitive to the internal subpropositional logical structure of the syllogism's constituent propositions. The invalid form is not a form of the argument in concreto.

One must distinguish among the following:

The temporally extended event of Jones' reasoning. This is a particular mental process.
The content of this reasoning process, the argument in abstracto as sequence of propositions.
The concrete episode of reasoning (i.e. the argument in concreto) which involves both the reasoning and its content.
The verbal expression in written or spoken sentences of the argument.
The form or forms of the argument in abstracto.
The verbal expression of a form or forms in a form diagram(s).
The form of the argument in concreto.

My point, again, is that we can uphold the Symmetry Thesis if we make a distinction between arguments in the concrete and arguments in the abstract. But this is a distinction we need in any case. The Symmetry Thesis holds for arguments in the concrete. But these are the arguments that matter because these are the ones people actually give.

Applying this to the Massey example above, we can say that while the abstract argument expressed by the following display has two forms, one invalid, the other valid:

If God created something , then God created everything.
God created everything.
——-
God created something

there is no one concrete argument, no one concrete episode of reasoning, that the display expresses. One who reasons in a way that is attentive to the internal subpropositional structure of the constituent propositions reasons correctly. But one who ignores this internal structure reasons incorrectly.

In this way we can uphold the Symmetry Thesis and avoid the absurdities to which the Asymmetry Thesis leads.

Homo Homini Lupus: The Red Army Rape of German Women, Spring 1945

The best antidote to the leftist-progressivist fantasy that man is basically good is the study of history, including the history of leftist-progressivist atrocities. Here is an excerpt from Antony Beevor's book on the fall of Berlin. "They raped every German female from eight to 80."

Capital Punishment and the Difference between Conservatives and Leftists

The difference springs to the eye by comparison of this morally sane piece by Peter Hitchens and this one by Hendrik Hertzberg.

Hendrik makes no mention of the crime, the victim, and her horrible death. Instead, typical leftist that he is, he invests his interest in the perceived underdog without any consideration of why the dirty dog is in his inferior position. Hitchens puts the emphasis where it belongs. Hendrik:

The classic justifications for the death penalty have not changed much over the centuries. There is retribution—an eye for an eye, a life for a life. There is deterrence—this is what awaits you if you transgress. And there is awe—a graphic demonstration of the ultimate power of the state.

No talk of justice, but a shabby suggestion that the principle that the punishment must fit the crime is to be interpreted as a narrow lex talionis injunction, as if the death penalty is in every case like the barbarity of gouging out the eye of the eye-gouger.

There is also something curious about leftists, who are totalitarians from the ground up, the top down, and from side to side, worrying about the ultimate power of the state. These are same moral cretins who want to use the power of the state to force florists and caterers to violate their consciences.

Anyone who doesn't see the moral necessity of the death penalty in certain carefully circumscribed cases, anyone who thinks that it is always and everywhere and in principle immoral, is morally obtuse.

Kant, Supererogation, and Imperfect Duties

Can Kant's ethical scheme accommodate the supererogatory?

If obligatory actions are those that one is duty-bound to perform, a supererogatory action is one that is above and beyond the call of duty. Michael A. Monsoor's throwing himself on a live grenade to save his Navy SEAL buddies is a paradigmatic example. But in a wide sense, a supererogatory act is any act, however trifling, that is in excess of what is morally required, any act that is morally good but the nonperformance of which is not morally bad.

One idea worth exploring is that there is room for supererogatory acts in Kant's scheme under the rubric of imperfect duties. Kant tells us that ". . . by a perfect duty I here understand a duty which permits no exception in the interest of inclination . . . ." (Grundlegung zur Metaphysik der Sitten, AA 421, fn) A perfect duty can be either towards oneself or towards another. Kant gives the prohibition of suicide as a perfect duty to oneself and the prohibition of deceitful promises as a perfect duty towards others. These are proscriptions that admit of no exception, and I take it that perfect duties are perfect in that they are exceptionless: in no circumstance may one take one's own life, and in no circumstance may one make a deceitful promise. If so, then imperfect duties are prescriptions that admit of exceptions. This interpretation fits the examples Kant gives (423-424). There is the duty to oneself of cultivating one's talents, and the duty to to others of benevolent assistance. Both of these duties are prescriptions and both admit of exceptions. My general duty to cultivate my talents is not a duty to cultivate all my talents, or even any particular talent. And the duty of benevolent assistance cannot be a duty to assist everyone. Paul Guyer's reading is similar:

In the Groundwork, Kant's principle of morality gives rise to a fourfold classification of duties, resulting from the intersection of two divisions: between duties to oneself and to others, and between perfect and imperfect duties. Perfect duties are proscriptions of specific kinds of actions, and violating them is morally blameworthy; imperfect duties are prescriptions of general ends, and fulfilling them by means of performing appropriate particular actions is praiseworthy. The four classes of duty are thus: perfect duties to oneself, such as the prohibition of suicide; perfect duties to others, such as the prohibition of deceitful promises; imperfect duties to oneself, such as the prescription to cultivate one's talents; and imperfect duties to others, such as the prescription of benevolence (4: 422-3, 429-30 ). It is straightforward what a perfect duty prohibits one from doing; it requires judgment to determine when and how the general ends prescribed by imperfect duties should be realized through particular actions.

Note that Guyer states that the fulfilling of imperfect duties is praiseworthy. Now it is the supererogatory that we praise: it is inappropriate to praise people for doing what they are obligated to do. How morally absurd to praise a pater familias for paying the rent and putting food on the table! That is what he is supposed to do, what he morally must do. The failure to do such is blameworthy, but the performance is merely required, hence not praiseworthy. Since the fulfilling of imperfect duties is praiseworthy, it seems we can conclude that in Kant the class of supererogatory acts either is or is a proper subclass of the class of imperfect duties.

Further support for this interpretation comes at Grundlegung 429-430 where Kant speaks of "necessary or obligatory duties to others" and a "contingent (meritorious) duty to oneself." In English, 'obligatory duty' smacks of pleonasm, but that might not be the case for Kant's schuldige Pflicht. If duties divide into the obligatory (schuldigen) and the meritorious (verdienstlichen), then we can say that Kant accommodates supererogatory acts under the rubric of imperfect or meritorious duties.

There is more to it than this, of course, and there is a technical literature on this topic only a small amount of which I have read; but I think I can safely say two things: (i) a case can be made for Kant's being able to accommodate the supererogatory, and (ii) Kantians are more hospitable to the supererogatory than are utilitarians.

The Discursive as Distraction

The search for the Real takes us outside ourselves. We may seek the Real in experiences, possessions, distant lands, or other people. These soon enough reveal themselves as distractions. But what about ideas and theories? Are they simply a more lofty sort of distraction? “Travelling is a fool’s paradise” said Emerson. Among lands certainly, but not among ideas?

If I move from objects of sense to objects of thought I am still moving among objects. To discourse, whether in words or in thoughts, is to be on the run and not at rest. But is not the Real to be found resting within, in one’s innermost subjectivity? Discourse dis-tracts, pulls apart, the interior unity.

Noli foras ire, said Augustine, in te redi, in interiore homine habitat veritas. “Do not wish to go outside, return into yourself. Truth dwells in the inner man.”

Why We are ‘Obsessed’ with Guns and Executions

Keith Burgess-Jackson explains in response to a moronic missive he found in the NYT:

To the Editor:

Dear America: Not that I expect to persuade you, but just so you know, most of the rest of the world regards your obsession with guns and executions as barbaric. Don’t say you weren’t told.

VINCE CALDERHEAD
Nairobi, Kenya, April 30, 2014

Note from KBJ: You mean the world that gave us (just off the top of my head, and in no particular order) the Inquisition, the Crusades, human chattel slavery, gladiatorial contests, human sacrifice, conquistadors, Hitler, Stalin, Pol Pot, Mao Zedung, Robespierre, genocide, tribal warfare, the guillotine, the garrote, and the broadaxe? Sorry; we Americans put our murderers to death because, and only because, we value innocent human life. We are "obsessed" with guns because we are obsessed with individual liberty. It you don't like it here, please leave. If you're not here, please shut up and leave us alone.

Well said. The willful stupidity and moral obtuseness of contemporary liberals is perhaps best demonstrated from their lunatic stands on capital punishment and gun control.

Here it is over a year since the 2013 Boston Marathon bombings. Why is Dzhokhar Tsarnaev still alive? We need a judicial fast track for terrorists. Have we lost the will to defend our open way of life, our institutions and traditions?

On Toleration: With a Little Help from Kolakowski

On Whether Some Arguments from Evil Beg the Question

Thesis for consideration: It can reasonably be maintained that some arguments from evil beg the question against theism.

Suppose we consider the following passage from J. J. C. Smart:

It looks as though the theistic hypothesis is an empirically refutable one, so that theism becomes a refuted scientific theory. The argument goes: (1) If God exists then there is no evil, (2) There is evil, therefore (3) It is not the case that God exists. Premiss (1) seems to follow from our characterization of God as an omnipotent, omnsicient and benevolent being. (2) is empirical. We can hardly reject (2). It seems therefore that the theist has to find something wrong with (1) and this is not easy. (J. J. C. Smart and J. J. Haldane, Atheism and Theism, Blackwell 2003, 2nd ed, p. 60)

Smart's argument from evil is plainly valid, being of the form modus tollens. But for an argument to be probative, other conditions must be met. One of these conditions is that the premises be true. Another is that the argument involve no 'informal fallacy' such as equivocation.

So let us ask: how would 'evil' in (1) have to be construed so that (1) comes out true? I suggest that 'evil' must be short for 'gratuitous evil.' But then, to avoid equivocation, we would have to replace 'evil' in (2) with 'gratuitous evil.' The result would be:

1*. If God exists, then there is no gratuitous evil.
2*. There is gratuitous evil.
—
3. It is not the case that God exists.

The resulting argument is valid, and (1*) is plainly true, unlike (1) which is not plainly true, but false. That (1) is false can be seen from the fact that an omniqualified God could easily permit the existence of an evil that was necessary for the attainment of a greater good. So it is just false to say, 'If God exists, then there is no evil.'

But (1*) is plainly true. Now it may be — it is epistemically possible that –(2*) is also true. The reformulated argument would then be sound. A sound argument, by definition, is a deductive argument that is both valid in point of logical form and whose premises are all of them true. And for the record, a proposition p is epistemically (doxastically) possible for a subject S if and only if p is logically consistent with what S knows (believes).

But note that a sound argument will be probatively worthless if it begs the question, if it is such that one cannot know a premise to be true without already knowing the conclusion to be true. So let us ask a very simple question: How does one know that (2*) is true? Smart tells us that (2) is empirical. 'Empirical' is a term of epistemology. It is applied to those propositions that are known from experience, by observation via the senses and their instrumental extensions (microscopes, telescopes, etc.) Now I am willing to grant that (2) — There is evil — is an empirical truth. (2), however, is not what Smart needs to make his argument work. He needs (2*). But is (2*) an empirical truth? Can one know from experience (whether inner or outer) that there is gratuitous evil? Is gratuitousness an empirical attribute of the evils one experiences?

Consider the evil of intense pain. I am acquainted with pain by 'inner sense.' And I am willing to grant arguendo, though it is not quite obvious, that I am acquainted empirically with the evil of intense pain. But I am surely not acquainted empirically with the gratuitousness of experienced evils. Gratuitousness is no more an empirical attribute than the createdness of the natural world. It is not evident to the senses that nature is a divine creation. Similarly, it is not evident to the senses that instances of evil are gratuitous. Is it not epistemically possible that they are all non-gratuitous?

To say that an evil is gratuitous is to say in effect that it is an evil inconsistent with the existence of the omniqualified God. It is to say that it is an evil that no such God could have a morally sufficient reason for permitting. Clearly, one cannot 'read off' such a complex relational attribute from any instance of evil.

The conclusion I am driving towards is that Smart's argument supra is question-begging. For in order to know that premise (2*) is true, I must know that the conclusion is true. That is, to know that there are gratuitous evils, I must know that God does not exist. For if God exists, then then there are no gratuitous evils.

Smart tells us above that the theistic hypothesis is empirically refutable. But I say Smart is mistaken: he needs (2*) for his argument to work, but this proposition — There is gratuitous evil — is not empirical. It may be true for all that, but it is not knowable by experience. You may be convinced that it is true, and I won't blame you if you find it much more plausible than the truth of 'God exists'; but it is not an empirical truth, if it is a truth. It is an interpretation imposed upon the data. It is as metaphysical as 'God exists.'

More on Sensible Properties and Constituent Ontology

A reader asks:

Suppose I said that blue is not a Peter-van-Inwagen property, but a sensible property. Suppose also that I said that we see 1) substances and we see 2) their colors, and we see 3) the fact that substances are colored (and this last point amounts to not much more, if anything at all more, than the claim that we see both substances and their colors). I take it you would agree with these points.

There are some difficult questions here. No doubt we see material meso-particulars. I see a cat, a keyboard, a lamp. But do we see substances? 'Substance' is a theoretical term, of Aristotelian provenience, not what I call a 'datanic' term. If a cat is a bundle of universals, or a bundle of tropes, or a diachronic bundle of synchronic bundles of Castanedan guises, then a cat is not a substance. It is a Moorean fact that there are cats and that we see them; it is not Moorean fact that there are substances and that we see them. But let's set this problem aside.

A black cat sleeps on my desk. I see the cat and I see black (or blackness if you will) at the cat: I see black where the cat is. Contrary to what you suggest, there is more to a cat's being black than a cat and blackness even if the blackness is seen exactly where the cat is and nowhere else. For a cat's being black involves, in addition to the cat and black, the first's BEING the second. Note that a cat's being black is a fact, but neither a cat nor blackness is a fact.

This give rise to a puzzle. I see the cat, and I see black where the cat is. But do I see the cat's BEING black? Do I literally see (with my eyes) the fact of the cat's being black? And if I don't, how do I know that the cat IS black?

But let's set this vexing cluster of problems aside as well.

But then suppose that you discover that I think that colors are per se nowhere. They are not located in space in the way that substances are. When you turn your eye to something colored, geometrically speaking, you turn your eye only to the thing that is colored, but not the color of the thing, for this has no per se spatial location and therefore has nothing to do with the geometry of space beyond being the sensible property of something that has something to do with the geometry of space. Nonetheless, we see colors and we see the things that are colored. Would you find this view problematic? If so, why? Would you think that in making color only accidentally spatial that I depart from constituent ontology? I would like to think that I do not, for I say that both being an ox and being blue are parts of what it is to be a blue ox.

The view you sketch strikes me as incoherent. You cannot coherently maintain both that blue (of some definite shade) is a sensible property and that blue is nowhere. If blue is sensible, then it is sensible at some location or other. Therefore, blue cannot be nowhere.

Note that if there is a PVI-property of blueness, it could not itself be blue. Abstract objcts don't come in colors. So what good is it? What work does it do? You are still going to need the blueness of the blue cup. PVI-blueness is ontologically otiose, a metaphysical fifth wheel if you will. The blueness at the cup, by contrast, is blue! Right? If you deny that there is any blue blueness at the cup, are you then prepared to say that the cup is devoid of sensible properties?

Will you say that the blue cup is sensibly bluein virtue of instantiating PVI-blueness? How would that work? PVI-blueness is not a Platonic exemplar. It is not itself blue. How can a particular's instantiating it explain the particular's being sensibly blue?

Could blueness be accidentally spatial? I don't see how. Either it is necessary spatial, and in consequence thereof, sense-perceivable, or it is necessarily nonspatial in the manner of an abstract object. A blue wall is accidentally blue, but blueness, I should think, is necessarily spatial. And I do think you would be departing from constituent ontology if you were to hold that blueness is accidentally spatial.

From Racists to Sexists

Image credit. (HT: Bill Keezer) By the way, I am grateful to all my correspondents. Don't take it amiss if I forget to credit you by name. And of course some of you I do not mention by name for your own protection.

If you send me something, but don't want it posted, just say so and I will honor your request. Otherwise, everything you send me is potential blog fodder.

In these "times that try mens' souls" one has to be very careful. But there is also such a thing as civil courage.

A Question About Constituent Ontology: Sensible Properties as ‘Parts’

The following from a reader. I've edited it for clarity.

Here is a quick question for you: suppose someone were to grant you that there is the sensible character blue that you say that there is, a character of your coffee cup, but then still wanted to know why it is "in" or a "constituent" of a substance such as a cup. So, take this person to have read and understood your argument about nude particulars and to have said: "Indeed, whatever red is, it cannot be an abstractum, for certainly something of the sort could never enter into visual experience. Nor could "the fact that" some sensible particular stands in an instantiation relation to such an abstract object enter into visual experience, for we theorize such metaphysical facts, we do not see them. So I grant that blue is a visible property, but why should we say that blue, so characterized is "in" or is a "constituent" of a sensible particular item?"

Well, one assumption I am making is that a certain form of nominalism is untenable. Suppose someone said that what makes a blue object blue is that English speakers apply the predicate 'blue' to it. Nelson Goodman actually maintains something as crazy as this in one of his books. (Intellectual brilliance and teaching at Harvard are not prophylactic against silliness.) Why is it crazy? Because it is the metaphysically antecedent blueness of the thing in question, my trusty coffee cup, for example, that grounds the correctness of the application of 'blue' to the cup. I am tempted to say that this realism is just Moorean common sense.

In other words, 'blue' is true of the cup because the cup is blue. And not the other way around. It is false that the cup is blue because 'blue' is true of it. Obviously, this use of 'because' is not causal, as causation is understood by most contemporary philosophers. But neither is it logical. It is not logical because it does not express a relation that connects a proposition to a proposition. It expresses an asymmetrical relation of metaphysical grounding. This relation is a relation between what is at most a proposition-like entity such as a concrete fact or state of affairs and a proposition.

The truthmaker of 'This cup is blue' cannot be anything of a linguistic nature. (More generally, it cannot be anything of a representational nature.) And yet something makes our sample sentence true. There must be a truthmaker. It would be silly to say that the sentence is "just true." Given that there must be a truthmaker, it is going to involve the cup and the property, both construed as 'real,' i.e., extramental and extralinguistic. There is more a truthmaker than this, but we don't need to go into this 'more.'

My reader grants that blue is a visible property. One literally sees the blueness of the cup. This is not a Platonic visio intellectualis. It is not a seeing with the 'eyes' of the mind, but a seeing with the eyes of the head. Now if this is the case, then the property I see when I see a blue cup as blue cannot be an item off in a realm apart. It cannot be a denizen of a Platonic topos ouranos, and I am not peering into such a heavenly place when I see blue. Blueness cannot be an abstract object as many contemporary philosophers use this phrase.

Now if I see the blueness where the cup is, and when the cup is (although only at times at which the cup is in fact blue), then the pressure is on to say that blueness is some sort of 'proper part' of the cup, albeit in an extended, unmereological sense of 'part.' It can't be the whole of the cup because the cup has other empirically detectable properties such as being hot and smooth and of such-and-such weight and electrical conductivity. What other options are there?

Reflecting on the data of the problem, I come to the following conclusions: The blueness is real: it is extramental and extralinguistic. It is empirically detectable; hence it cannot be an abstract object. The blueness is detectable at the cup, not at some other place. The blueness is not identical to the cup.

We can account for the data by saying say that the blueness of the cup is an ontological constituent of the cup. Is there a better theory?

Saturday Night at the Oldies: Two ‘Sentimental’ Songs

Fleetwood Mac, Sentimental Lady

Thelonious Monk, I'm Getting Sentimental Over You. Wow!

There are of course others with 'sentimental' in the title, but I post only what I like.

The Politics of Impassibility

This just over the transom:

I hope you don’t mind my seeking your help on an issue related to the history of philosophy. I and a few friends are have a disagreement re: the origin of belief in divine apatheia.

In Manana: Christian Theology from a Hispanic Perspective, Justo Gonzalez discusses the political motivations behind the origin and development of the concept. His claim is that belief in divine impassibility merely reflects the desire for permanence (of power) on the part of the ruling class so that Athenian politics is responsible for the philosophical development of the belief, a projection onto God of the political aspirations of the elite.

The question of how apatheia got adopted/revised by Christians isn’t so much my concern at this point (as legitimate a question as it is). I’m interested in Gonzalez’s history and whether and to what extent he’s right in supposing apatheia was a projection onto the divine being of the political aspirations for the permanence of the city and its ruling class.

Does that ring true with your understanding? Thoughts?

Well, if it serves my political interests to believe that p, that leaves open the question whether p is true or false. Suppose I am a member of the royal court. Then it would serve my earthly interests if the masses were to believe that the king rules by divine right. But one cannot show that the king does not rule by divine right by showing that the interests of the ruling class are served by that belief's being widespread.

So there are two logically independent questions. Does the holding of a belief serve interests? Is the belief true? To say that the questions are logically independent is to say that both an affirmative and a negative answer to the first is consistent with both an affrmative and a negative answer to the second.

If God exists, then he is either impassible or not. This question cannot be decided by showing, assuming that it could be shown, that widespread belief that God is impassible would help legitimate the dominance of the ruling class. (I am having a hard time imagining how such an abstruse doctrine could get a grip on the popular mind. Does Joe Sixpack think about such things?)

The bolded thesis supra is a 'weasel' thesis. Gonzalez does not state unambiguously that the impassibility doctrine is nothing other than an expression of class interests, and therefore either false or unsupportable by reasons. But that is probably what he means.

If that is what he means, then he is guilty of the logical/epistemological error of confusing the holding of a belief with the propositional content of a belief. It is a concern of the sociology of knowledge to study the incidence of beliefs as states of people, their causes and effects and modes of transmission. But the evaluation of belief contents as to truth, falsehood, consistency, inconsistency, rationality, etc., does not belong to the sociology of knowledge.

There is nothing new about the move Gonzalez appears to be making. It's old hat. It is the standard Marxist rubbish of reducing belief systems to systems of ideology in the service of class interests. But if all is ideology in the service of class interests, then so is the system of Marxist beliefs. In which case it is a self-vitiating system of beliefs if not outright self-refuting.

Islam versus Chess

Holy moly! Perhaps Brandeis University ought to ban chess playing on campus lest some adherent of the 'religion of peace' take offense.

Jews dominate chess. I wonder if that is part of the explanation of the irrational animosity of Islamists to the game of kings and the king of games.

Lukasiewicz on Logical Form

London Ed writes,

I read and excerpted the chapter. I am not mistaken. Also, what he says seems correct to me.

He claims that logic is not formal, insofar as it is concerned with the 'laws of thought'. He says "Thought is a psychical phenomenon, and psychical phenomena have no extension. What is meant by the form of an object that has no extension?" I can't fault this.

I take it that the argument is this:

1. Only spatially extended objects have forms.
2. Neither acts of thinking, nor such objects of thought as propositions, are spatially extended.
Therefore
3. If logic studies either acts of thinking or objects of thought, then logic is not a formal study, a study of forms.

If this is the argument, I am not impressed. Premise (1) is false. L.'s notion of form is unduly restrictive. There are forms other than shapes. Consider a chord and an arpeggio consisting of the same notes. The 'matter' is the same, the 'form' is different. In a chord the notes sound at the same time; in an arpeggio at different times. The arrangement of the notes is different. Arrangement and structure are forms. Examples are easily multiplied.

Nor, he says, is it the object of logic to investigate how we are thinking or how we ought to think. "The first task belongs to psychology, the second to a practical art of a similar kind to mnemonics". And then he says "Logic has no more to do with thinking than mathematics has". Isn't that correct?

We can agree that logic is not a branch of psychology: it is not an empirical study and its laws are not empirical generalizations. LNC, for example, is not an empirical generalization. But a case can be made for logic's being normative. It does not describe how we do think, but it does prescribe how we ought to think if we are to arrive at truth. If so, then logic does have a practical side and issues hypothetical imperatives, e.g., "If you want truth, avoid contradictions!"

In a similar vein he notes the formalism of Aristotelian logic. The whole Aristotelian theory of the syllogism is built up on the four expressions 'every' (A), 'no' (E), 'some' (I) and 'not every' (O). "It is obvious that such a theory has nothing more in common with our thinking than, for instance, the theory of the relations of greater and less in the field of numbers". Brilliant.

Why do you call it "brilliant"? Husserl and Frege said similar things. It's old hat, isn't it? Psychologism died with the 19th century at least in the mainstream. Given propositions p, q, logic is concerned with such questions as: Does p entail q? Are they consistent? Are they inconsistent? We could say that logic studies certain relations between and among propositions, which are the possible contents of judgings, but are not themselves judgings or entertainings or supposings or anything else that is mental or psychological.

Again, on the need for logic and science to focus on the expression of thought rather than 'thought', he says "Modern formal logic strives to attain the greatest possible exactness. This aim can be reached only by means of a precise language built up of stable, visually perceptible signs. Such a language is indispensable for any science. Our own thoughts not formed in words are for ourselves almost inapprehensible and the thoughts of other people, when not bearing an external shape [my emphasis] could be accessible only to a clairvoyant. Every scientific truth in order to be perceived and verified, must be put into an external form [my emphasis] intelligible to everybody."

I can't fault any of this. What do you think?

Sorry, but I am not impressed. It is fundamentally wrongheaded. First of all this is a howling non sequitur:

1. Logic does not study mental processes;
Therefore
2. Logic studies visually perceptive signs.

Surely it is a False Alternative to suppose that logic must either study mental processes or else physical squiggles and such. There is an easy way between the horns: logic studies propositions, which are neither mental nor physical.

In my last post I can gave two powerful arguments why a perceptible string of marks is not identical to the proposition those marks are used to express.

L. speaks of an external form intelligible to everybody. But what is intelligible (understandable) is not the physical marks, but the proposition they express. We both can see this string:

Yash yetmis ish bitmish

but only I know what it means. (Assuming you don't know any Turkish.) Therefore, the meaning (the proposition), is not identical to the physical string.

There is also an equivocation on 'thought' to beware of, as between thinking and object of thought. As you well know, in his seminal essay Der Gedanke Frege was not referring to anything psychological.

I will grant L. this much, however. Until one has expressed a thought, it is not fully clear what that thought is. But I insist that the thought — the proposition — must not be confused with its expression.

The real problem here is that you wrongly think that one is multiplying entities beyond necessity if one makes the sorts of elementary distinctions that I am making.

Logical Form, Instantiation, and Pattern-Matching

David Brightly comments:

We can't say that an argument is invalid because it instantiates an invalid form. The argument Socrates is a man; all men are mortal; ergo Socrates is mortal instantiates the invalid form a is F; all Hs are G; ergo a is G, but modulo equivocation, it is truth-preserving. Instantiation of form is just pattern-matching, and the argument does match the pattern of the invalid form.

I reject this of course.The sample argument is an example of correct reasoning. But anyone who argues in accordance with the schema argues incorrectly. Why? Because the schema is not truth-preserving. Therefore the sample argument does not instantiate the invalid form.

I don't think Brightly understands 'truth-preserving.' This is a predicate of argument forms, primarily, and the same goes for 'valid' and 'invalid.' Here are some definitions:

D1. An argument form is truth-preserving =df no argument of that form has true premises and a false conclusion.

D2. An argument form F is valid =df F is truth-preserving.

D3. A particular argument A is valid =df A instantiates a valid form. (This allows for the few cases in which an argument has two forms, one valid and one invalid.)

D4. A particular argument A is invalid =df there is no valid form that it instantiates.

Now what is it for an argument to instantiate an argument form? To answer this question we need to know what an argument is. Since deductive arguments alone are under consideration, I define:

D5. A deductive argument is a sequence of propositions together with the claim that one of them, the conclusion, follows from the others, the premises, taken together.

If the claim holds, the argument is valid; if not, invalid.

Now the main point for present purposes is that an argument is composed of propositions. A proposition is not a complex physical object such as a string of marks on paper. Thus what you literally SEE when you see this:

7 + 5 = 12

is not a proposition, but a spatiotemporal particular, a physical item subject to change: it can be deleted. But the proposition it expresses cannot be deleted by deleting what you just literally SAW. That suffices to show that the proposition expressed by what you saw is not identical to what you saw. Whatever propositions are (and there are different theories), they are not physical items.

What's more, you did not SEE (with your eyes) the proposition, or that it is true, but you UNDERSTOOD the proposition and that it is true. (A proposition and its being true are not the same even if the proposition is true.) So this is a second reason why a proposition is not identical to its physical expression.

Now what holds for propositions also holds for arguments: you cannot delete an argument by deleting physical marks, and you cannot understand an argument merely by seeing a sequence of strings of physical marks.

An argument is not a pattern of physical marks. So there is no question of matching this physical pattern with some other physical pattern. Instantiation of logical form is not just pattern-matching.

If a sentence contains a sign like 'bank' susceptible of two or more readings, then no one definite proposition is expressed by the sentence. Until that ambiguity is resolved one does not have a definite proposition, and without definite propositions no definite argument. But once one has a definite argument then one can assess its validity. If it instantiates a valid form, then it is valid; if it instantiates an invalid form, then it is invalid.

It is as simple as that. But one has to avoid the nominalist mistake of thinking that arguments are just collections of physical items.