Plausible Denial

Bill Vallicella considers an inconsistent triad:

1. Every free agent is a libertarianly-free (L-free) agent.

2. God is ontologically simple (where simplicity is an entailment of aseity and vice versa).

3. There are contingent items of divine knowledge that do not depend on divine creation, but do depend on creaturely freedom.

Bill says, "(3) cannot be plausibly denied." He doesn't give any reasons for thinking this. The problem with this, of course, is that exactly the opposite judgment has been made by most major figures in the history of philosophy: Augustine, Bonaventure, Aquinas, Scotus, Descartes, Malebranche just to name a few, all clearly deny that (3) is even remotely plausible: there are no contingent items independent of divine creation, although some of those items of divine creation also depend on creaturely freedom. Most of them give reasons for thinking this. Now this does raise some important questions with respect to the relation between divine action and creaturely action; but this is precisely why philosophers through history have tended to focus on that problem rather than the sort of problem raised above.

The Cupola of a Proposition

An amusing typo:

Indeed, the book concludes, logicians often think of things like the cupola of a proposition "almost as if it were a living, conscious entity, capable of declaring for itself what it chose to mean."

Apparently the copula is indeed a living, conscious entity, capable of declaring for itself what it chose to mean; and apparently it chose to be a dome. I am charmed by the thought of a proposition having architectural features.

Starmaker

I am: Olaf Stapledon Standing outside the science fiction "field", he wrote fictional explorations of the futures of whole species and galaxies.

Which science fiction writer are you?


I think I took this before, a couple of years ago, and got the same result. (ht)

Poem Draft

Gods and Graces

The gods and graces in my head
are singing in the choir-loft.
Their fearless faces, heaven-bred,
empassioned, raise the quavers soft
that spark to life the sweeping sky
and overpour the waiting earth;
above the fishful seas soar high
the songs that bring creation's birth.

School of Moral Cultivation

The equality of married persons before the law, is not only the sole mode in which that particular relation can be made consistent with justice to both sides, and conducive to the happiness of both, but it is the only means of rendering the daily life of mankind, in any high sense, a school of moral cultivation. Though the truth may not be felt or generally acknowledged for generations to come, the only school of genuine moral sentiment is society between equals....Citizenship, in free countries, is partly a school of society in equality; but citizenship fills only a small place in modern life, and does not come near the daily habits or inmost sentiments. The family, justly constituted, would be the real school of the virtues of freedom. It is sure to be a sufficient one of everything else. It will always be a school of obedience for the children, of command for the parents. What is needed is, that it should be a school of sympathy in equality, of living together in love, without power on one side or obedience on the other. This it ought to be between the parents. It would then be an exercise of those virtues which each requires to fit them for all other association, and a model to the children of the feelings and conduct which their temporary training by means of obedience is designed to render habitual, and therefore natural, to them. The moral training of mankind will never be adapted to the conditions of the life for which all other human progress is a preparation, until they practise in the family the same moral rule which is adapted to the normal constitution of human society.

John Stuart Mill, The Subjection of Women, Chapter Two

Pride of Prime's Enjoyment

Morning, Midday, and Evening Sacrifice
by Gerard Manley Hopkins

The dappled die-away
Cheek and the wimpled lip,
The gold-wisp, the airy-grey
Eye, all in fellowship -
This, all this beauty blooming,
This, all this freshness fuming,
Give God while worth consuming.

Both thought and thew now bolder
And told by Nature: Tower;
Head, heart, hand, heel, and shoulder
That beat and breathe in power -
This pride of prime's enjoyment
Take as for tool, not toy meant
And hold at Christ's employment.

The vault and scope and schooling
And mastery in themind,
In silk-ash kept from cooling,
And ripest under rind -
What life half lifts the latch of,
What hell stalks towards the snatch of,
Your offering, with despatch, of!

Inference Rules for Complex Predicates

By a complex predicate I mean a predicate such as one has in the following:

Every student in the class is clever or married.

Tom is both a mayor and a father.

Such complex predicates in effect break up into two types: conjunctive and disjunctive. In principle, it is possible to have conditional predicates as well; English is not very favorable to them, but they occasionally show up. They are a particular kind of disjunctive predicate.

I will use term-functor logic to characterize them. If I have two terms in my conjunctive predicate, +P and +Q, then I would represent the conjunctive predicate as +<+P+Q>, as in:

-S+<+P+Q>

which says, "All S is P and Q". Conjunctive predicates are commutative, as disjunctive predicates will also be; it makes no difference whether you say +<+P+Q> or +<+Q+P>. Disjunctive predicates are negations of conjunctive predicates; we rule out the one case they disallow. So if I have two terms in my disjunctive predicate, +P and +Q, I will rule out the one case where -P and -Q both occur; the predicate will be -<-P-Q>, as in:

-S-<-P-Q>

which says, "All S is P or Q". Note that -S-<-P-Q> is not equivalent to -S+<+P+Q>, but is a weaker claim. This is because of a key asymmetry between affirmative and negative quality. If there is only one predicate term, they are equally strong: the affirmative includes one thing and excludes one thing, and the negative does the same. You can go back and forth without much concern. But as the terms in the predicate increase, the affirmative excludes more and the negative excludes less. You can always move from a single conjunctive predicate to a single disjunctive predicate; you can never do the reverse. This gives us our first rule of immediate inference for complex predicates:

Conjunctive Predicate Weakening: From any proposition with a conjunctive predicate we can conclude a proposition with the disjunctive predicate that preserves the signs for the terms. For instance, from -S+<+P+Q>, "All S is P and Q," we can conclude -S-<-P-Q>, "All S is P or Q".


But conjunctive predicates and disjunctive predicates still are related by negation; the +<+P+Q> predicate, for instance, is equivalent to the --<+P+Q>. That is, we could have 'De Morgan rules'. There is however no reason to formulate them. De Morgan rules for complex predicates are just the ordinary logical rule of obversion; there is nothing special about it because it makes no logical difference to obversion whether the predicate is complex or not.

We can also move from a conjunctive predicate to a non-conjunctive predicate immediately:

Conjunctive Predicate Simplification: From any proposition with a conjunctive predicate we can conclude a proposition affirmatively predicating one of the conjunct terms of the subject. For instance, from +S+<+P-Q>, "Some S is P and non-Q," we can conclude +S+P, "Some S is P," or +S+(-Q), "Some S is non-Q".

More interesting things happen when we mix more than one premise where there are complex predicates. Here is an elimination rule for disjunctive predicates:

Disjunctive Predicate Simplification: From any universal proposition with a disjunctive predicate we can conclude a proposition affirming one of the disjunct terms of the subject if we combine it with a universal proposition in which the other disjunct term is denied of the same subject. For instance, from -S-<-P-Q>, "Every S is P or Q," and -S-P, "No S is P," we can conclude -S+Q, "Every S is Q".

Note that this is not available for particular propositions; we need to be sure that the predicates are said of the same subject, and particular propositions do not guarantee that. To put this in more technical terms: this rule is an application of the dictum de nullo. Here is an introduction rule for conjunctive predicates:

Conjunctive Predicate Strengthening: From two universal propositions, both of which affirm predicates of a subject, we can conclude a proposition affirming the conjunction of those predicates of the subject. For instance, from -S+P, "All S is P," and -S+Q, "All S is Q," we can conclude -S+<+P+Q>, "All S is P and Q".

As with the previous rule, the quantities must be universal; in technical terms, this rule is a particular application of the dictum de omni, and thus we must be sure we are talking about all of a subject. And finally we want to be able to throw something out if our complex predicate is inconsistent:

Complex Predicate Absurdity: From a universal proposition in which a contradictory predicate is affirmed of a subject we can conclude that the subject does not exist. For instance, from -S+<+P-P>, "Every S is both P and non-P," we can conclude -S, "There is no S".

So let's take an example. Suppose you have the following:

(1) All motion not from another would have to be either per se or per accidens.
(2) No motion not from another could be per se.
(3) All motion per accidens is either violent or natural.
(4) No motion not from another could be violent.
(5) All natural motion is either in some way self-moving or in no way self-moving.
(6) No motion not from another could be in no way self-moving.
(7) No motion that is in some way self-moving is motion not from another.

Putting this in term-functor form we get:

(1) -NA-<-PS-PA>
(2) -NA-PS
(3) -PA-<-V-N>
(4) -NA-V
(5) -N-<-SM-(-SM)>
(6) -NA-(-SM)
(7) -SM-NA

From (1) and (2) we get -NA+PA by Disjunctive Predicate Simplification. From this, (3), and (4) we can get -NA+N by the same rule plus the dictum de omni; another application of the dictum de omni gets us -NA-<-SM-(-SM)>. Combining this with (6) gives us -NA+SM; combining it with (7) gets us -NA+(-SM). Both of those are by Disjunctive Predicate Simplification. Conjunctive Predicate Strengthening lets us put these together to get -NA+<+SM-SM>. Using Complex Predicate Absurdity we draw the only possible conclusion: -NA, which says that there is no such thing as motion that is not from another.

Sommers Notation, Part VIII

(Part VII)

References and Further Reading (Offline)

By Fred Sommers:

An invitation to formal reasoning. The logic of terms, with George Englebretsen). Ashgate, 2000.
The logic of natural language. Clarendon Press, 1982.


By George Englebretsen:

Something to reckon with: the logic of terms. Ottawa: Ottawa University Press 1996.
Essays on the Philosophy of Fred Sommers: In Logical Terms. Edwin Mellen Press, 1990.
Three logicians. Aristotle, Leibniz, and Sommers. Van Gorcum, 1981.
Logical negation. Van Gorcum, 1981.

"Syllogistic: old wine in new bottles," History and Philosophy of Logic 23: 31-35 (2002).
"Logical primitives," Indian Philosophical Quarterly 12: 371-380 (1985).
"Singular terms and the syllogistic," The New Scholasticism 54: 68-74 (1980).
"Notes on the new syllogistic," Logique et Analyse 85-86: 111-120 (1979).

George Englebretsen (ed). The new syllogistic. Peter Lang, 1987.


By Others:

David S. Oderberg (ed). The Old New Logic: Essays on the Philosophy of Fred Sommers. MIT Press, 2005.
Lorne Szabolcsi. Numerical Term Logic. (Englbretsen, ed.) Mellen Press, 2008.


References and Further Reading (Online)

Except for Purdy's review, the following can be found available at these websites:
The Reasoner
Notre Dame Journal of Formal Logic

By Fred Sommers:

“Reasoning: how we’re doing it,” The Reasoner 2.1 (January 2008).
“The world, the facts, and primary logic,” Notre Dame Journal of Formal Logic 34.2: 169-182 (1993).
“Predication in the logic terms,” Notre Dame Journal of Formal Logic 31.1: 106-126 (1989).

By George Englebretsen:

“Formatives,” Notre Dame Journal of Formal Logic 30.3 (1989), 382-389.
“Preliminary notes on a new modal syllogistic,” Notre Dame Journal of Formal Logic 29.3: 381-395 (1988).
“Czeżowski on wild quantity,” Notre Dame Journal of Formal Logic 27.1: 62-65 (1986).
“Singular/general,” Notre Dame Journal of Formal Logic 27.1: 104-107(1986).
“Opposition,” Notre Dame Journal of Formal Logic 25.1: 79-85 (1984).
“Do we need relative identity?” Notre Dame Journal of Formal Logic 23.1: 91-93 (1982).
“On propositional form,” Notre Dame Journal of Formal Logic 21.1: 101-110 (1980).
“The square of opposition,” Notre Dame Journal of Formal Logic 17.4: 531-541 (1976).
“Sommers' proof that something exists,” Notre Dame Journal of Formal Logic 16.2: 298-300 (1975).
“A note on contrariety,” Notre Dame Journal of Formal Logic 15.4: 613-614 (1974).
“Sommers on empty domains and existence,” Notre Dame Journal of Formal Logic 13.3: 350-358 (1972).

By Others:

William H. Friedman, “Calculemus,” Notre Dame Journal of Formal Logic 21.1: 166-174 (1980).

Wallace A. Murphree, “Numerical term logic,” Notre Dame Journal of Formal Logic 39.3: 346-362 (1998).
Wallace A. Murphree, “The numerical syllogism and existential presupposition,” Notre Dame J. Formal Logic 38.1: 49-64 (1997).
Wallace A. Murphree, “The irrelevance of distribution for the syllogism,” Notre Dame Journal of Formal Logic 35.3: 433-449 (1994).

Aris Noah, “Nonclassical syllogistic inference and the method of resolution,” Notre Dame Journal of Formal Logic 34.2: 209-222 (1993).

William C. Purdy, “Review: Fred Sommers, George Englebretsen, An Invitation to Formal Reasoning. The Logic of Terms,” Bulletin of Symbolic Logic 8.1: 97-100 (2002). (available here)
William C. Purdy, “On the question `’do we need identity?'’” Notre Dame Journal of Formal Logic 33.4: 593-603 (1992).
William C. Purdy, “Surface reasoning,” Notre Dame Journal of Formal Logic 33.1: 13-36 (1991).

Three Poem Drafts

Men of Gadeira

The ichor of youth
still stirs our vital blood;
we watch as waves,
stormed by the god,
ripple far, far away.
And here below
the dryads sway,
naiads of kelp,
and chant of days,
now lost, of virtue.

Natural Light

Grasp this world
that God has blessed;
its sparks will make
the mind fluoresce
and in the dark
it still will hold
a phosphorescence
soft and low.

Prayer of the Shadows

Circles of heaven, stop your motion,
everlasting ocean, cease to wave!
Stretch midnight hours to endless years;
from dawn-born tears the shadows save.
Music of heaven, one note alone
play in the sky, one sound and tone,
never to die!

Gersonides on Two Types of Worthy Poems

Their statement that this poem is the most wonderful and choicest of the songs which are Solomon's is very clearly true because there are two types of worthy poems. The first type is a poem which presents a representation of deep things which are difficult to represent, through the use of symbolic representations and allegory. The second type is the poem crafted to draw one to love what ought to be loved and to reject what ought to be rejected. It is clear that the more the poem represents worthy matters which are ever more useful to the attainment of felicity, it is itself more worthy. So, too, with the second type: the more a poem is crafted to draw one to love worthier things and those things useful for the attainment of felicity, the worthier it is itself. In this book these two types of poems have been combined together in the worthiest fashion, for it presents a representation of the ultimate felicity and attracts one to draw near to it and to strive for it with every possible striving.

Levi ben Gershom, Commentary on Song of Songs, Menachem Kellner, tr. Yale UP (1998) p. 118. (Gersonides's notion of felicity is highly philosophical so his commentary ends up being a very interesting discourse on Jewish-Aristotelian epistemology.)

Finlay on Oughts and Ends

Stephen Finlay has an excellent paper, called Oughts and Ends (PDF); in it he argues for a close cousin of the view of 'oughts' that I've argued for here at Siris. He calls it an end-relational view; I think it's clear that it's obviously right in its basic points, although I think there's room for refinement of a couple of points. The only thesis that should be even remotely controversial here is Finlay's Sixth Thesis and his handling of 'ought' simpliciter. But, as I've said before, I find that the reason that the "You can't derive an 'ought' from an 'is'" slogan has such durability is that it has no stable and definite meaning: everyone means something different by it. It's time to put it to bed: it's obviously false as is, and if people mean something that differs from what it says on the surface, they should come out and say it.

In any case, Finlay develops points that I haven't ever developed, and, while I don't agree with every point, he does a good job in going beyond the fairly limited position I've expressly discussed here, on grounds independent of those to which I've appealed.

The Angel in the House (Repost)

This is a slightly revised version of a post that was originally posted in 2008.

Virginia Woolf famously said, "Killing the Angel in the House was part of the occupation of a woman writer." But this has, I think, often been misunderstood. I have often seen the phrase "The Angel in the House" interpreted to mean something about submission, but this is not a plausible gloss. For one thing, in the original poem by Coventry Patmore, whose title Woolf is adapting, submission plays virtually no role: the word and its cognates only arises twice in the poem, and in both cases is used merely as a secondary image for the headlong character of being in love. Patmore also makes use of the common lover's trope that the beloved woman is to be served, so arguably the image moves both ways. For another, this is not at all the point Woolf herself is actually making:

You who come of a younger and happier generation may not have heard of her—you may not know what I mean by the Angel in the House. I will describe her as shortly as I can. She was intensely sympathetic. She was immensely charming. She was utterly unselfish. She excelled in the difficult arts of family life. She sacrificed herself daily. If there was chicken, she took the leg; if there was a draught she sat in it—in short she was so constituted that she never had a mind or a wish of her own, but preferred to sympathize always with the minds and wishes of others. Above all—I need not say it—–she was pure. Her purity was supposed to be her chief beauty—her blushes, her great grace. In those days—the last of Queen Victoria—every house had its Angel.

Woolf goes on to describe the experience of a woman writing a review of a book by a man. She takes up the pen to be critical, and the Angel slips in behind her and whispers, "As a woman you should be sympathetic, tender, tactful, gentle, etc.; you should be pure, not saying what you think but always saying what you ought." It's not submission but this ethereal, unreal purity that is the reason the Angel in the House must be killed by the woman writer; it is an image of woman that is inhuman and threatens to rip out the heart from any woman's writing. It's an image of woman so unreal that, if taken as a standard, it is dishonest:

For, as I found, directly I put pen to paper, you cannot review even a novel without having a mind of your own, without expressing what you think to be the truth about human relations, morality, sex. And all these questions, according to the Angel of the House, cannot be dealt with freely and openly by women; they must charm, they must conciliate, they must—to put it bluntly—tell lies if they are to succeed. Thus, whenever I felt the shadow of her wing or the radiance of her halo upon my page, I took up the inkpot and flung it at her. She died hard. Her fictitious nature was of great assistance to her. It is far harder to kill a phantom than a reality.

And this is why 'Angel in the House' is a good label for what Woolf is trying to describe. There really isn't anything dishonest about Patmore's poetry, but the image of woman presented in The Angel in the House is simultaneously real and mythological. It is Patmore's wife, but it is Patmore's wife pitched to cosmic significance, used as a model for a goddess:

But when I look on her and hope
To tell with joy what I admire,
My thoughts lie cramp'd in narrow scope,
Or in the feeble birth expire;
No mystery of well-woven speech,
No simplest phrase of tenderest fall,
No liken'd excellence can reach
Her, thee most excellent of all,
The best half of creation's best,
Its heart to feel, its eye to see,
The crown and complex of the rest,
Its aim and its epitome.
Nay, might I utter my conceit,
'Twere after all a vulgar song,
For she's so simply, subtly sweet,
My deepest rapture does her wrong.
Yet is it now my chosen task
To sing her worth as Maid and Wife;
Nor happier post than this I ask,
To live her laureate all my life.

There is in a sense nothing wrong with this in itself, or, at least, nothing that even Woolf herself would have thought wrong with this on its own: this is literary depiction and trope. The problem arises not with the image, but with an image like this becoming a standard to which women are expected to hold themselves to (and, more than this, a standard to which they hold themselves). For it is a lover's fantasy, a romantic myth, a pretty painting by a man who wants to laud the excellences of his wife; it is not a woman, and it is something no woman can actually be. It's all the difference between serving as a model for a painting of Aphrodite and expecting yourself to be Aphrodite. But Woolf notes that something like this image, not perhaps Patmore's own but something closely analogous, is taken not merely as a picture for which a woman can be a model, but as the standard for what a woman should be. It becomes not merely art that they can inspire but the state to which they are expected to aspire. And no one can hold themselves to such a standard without dissimulation. You should be pure -- more pure by far than any woman can be; and if that's the standard of what a woman is to be, well, what option is there but lies and deceit? It will tear the honest heart out of what you do.

So the woman writer must kill the Angel in the House, this standard of purity whispering in her ear, and be -- what? Woolf doesn't think the answer is easy at all. We'd naturally say that she should just be a human woman. But Woolf thinks this a superficial answer:

I mean, what is a woman? I assure you, I do not know. I do not believe that you know. I do not believe that anybody can know until she has expressed herself in all the arts and professions open to human skill.

After all, we are really talking about a standard for what a woman should be. The Angel in the House can't be that standard. But merely take that away and you don't automatically have a woman who knows what she should be. You either have a woman who doesn't know what it is to which she can aspire, or who finds herself faced with yet another unreal phantom standard which must yet again be slain:

These were two of the adventures of my professional life. The first—killing the Angel in the House—I think I solved. She died. But the second, telling the truth about my own experiences as a body, I do not think I solved. I doubt that any woman has solved it yet. The obstacles against her are still immensely powerful—and yet they are very difficult to define. Outwardly, what is simpler than to write books? Outwardly, what obstacles are there for a woman rather than for a man? Inwardly, I think, the case is very different; she has still many ghosts to fight, many prejudices to overcome. Indeed it will be a long time still, I think, before a woman can sit down to write a book without finding a phantom to be slain, a rock to be dashed against.