Saturday, February 25, 2006

Ockham on Past and Future

The latest exhibit in the Logic Museum is a parallel Latin English translation of Ockham's theory of past and future tenses, in chapter 7 of book II of his Summa Logicae. Find it here. It is connected with the discussion going on below concerning the problem of supplying truth conditions for past and future tense propositions.

Wednesday, February 22, 2006

Rain tomorrow

"There is some actual state of affairs which constitutes its now being the case that it’s possible that it rain tomorrow"

But is this actual state of affairs is the same state of affairs as the state of affairs which will obtain when it rains tomorrow? This seems to be the argument.

1. A statement must be true or false, and so there must be conditions under which it is true.

2. To state the conditions when a given proposition is true, is to say what IS the case, if it IS true. Merely to state the truth conditions is to specify something that exists now.

3. Thus statements about the future can be reduced to statements in the present tense. For if the truth condition obtains, the statement that it obtains, is true now. If it does not obtain, the statement that it does not obtain, is true now.

But why should the truth conditions be in the present tense? I agree that a proposition like 'Tom thinks it will rain tomorrow' says something about the present. It says that Tom has a certain thought, right now, in the present. Similarly 'the weather forecaster says it will rain tomorrow' says something about what the person on the TV says, now. Likewise 'It is causally determined that it will rain tomorrow'. Similarly also for 'it is possible that it will rain tomorrow', which says something about the speaker's present state of knowledge.

But 'it will rain tomorrow' doesn't say anything about the present. 'It will rain tomorrow' is true if and only if it WILL rain tomorrow.

Saturday, February 18, 2006

Locke on Truths of Reason

And here is Locke on the distinction between truths of reason and truths of fact, from Bk 4 ch xi, 13 ' Of our Knowledge of the Existence of Other Things'

13. Only particular propositions concerning concrete existences are knowable. By which it appears that there are two sorts of propositions:—(1) There is one sort of propositions concerning the existence of anything answerable to such an idea: as having the idea of an elephant, phoenix, motion, or an angel, in my mind, the first and natural inquiry is, Whether such a thing does anywhere exist? And this knowledge is only of particulars. No existence of anything without us, but only of God, can certainly be known further than our senses inform us. (2) There is another sort of propositions, wherein is expressed the agreement or disagreement of our abstract ideas, and their dependence on one another. Such propositions may be universal and certain. So, having the idea of God and myself, of fear and obedience, I cannot but be sure that God is to be feared and obeyed by me: and this proposition will be certain, concerning man in general, if I have made an abstract idea of such a species, whereof I am one particular. But yet this proposition, how certain soever, that “men ought to fear and obey God” proves not to me the existence of men in the world; but will be true of all such creatures, whenever they do exist: which certainty of such general propositions depends on the agreement or disagreement to be discovered in those abstract ideas.

The distinctions that Locke makes (see previous post) are therefore as follows:

1. propositions which are truths of reason, but merely trifling or verbal;

2. propositions which are truths of reason, but where the predicate is not actually contained in the subject, but is a necessary consequence of it;

3. propositions which are simply matters of fact, not deducible by reason alone.

Locke on Analytic vs Synthetic

Here is a passage from the Essay (Bk IV, c. viii, 8) that is suggestive of the Analytic / Synthetic distinction.

8. … We can know then the truth of two sorts of propositions with perfect certainty. The one is, of those trifling propositions which have a certainty in them, but it is only a verbal certainty, but not instructive. And, secondly, we can know the truth, and so may be certain in propositions, which affirm something of another, which is a necessary consequence of its precise complex idea, but not contained in it: as that the external angle of all triangles is bigger than either of the opposite internal angles. Which relation of the outward angle to either of the opposite internal angles, making no part of the complex idea signified by the name triangle, this is a real truth, and conveys with it instructive real knowledge.

Friday, February 17, 2006

Hume's Fork

Spur writes here

Leibniz and Hume have the same basic distinction in mind, between those truths which are necessary and can be known a priori, and those which are contingent and can only be known a posteriori. The two philosophers use slightly different terminology, and Leibniz would balk at Hume's use of 'relations between ideas' in connection with truths of reason only, but the basic distinction seems to me to be the same.

But the question is more difficult, and is related to a change in logic that happened at the very beginning of the early modern era. The scholastic logicians said that in a proposition (which for them meant a sentence) the predicate is affirmed or denied of the subject. 'Subject' and 'predicate' here are objectively existing things.

Influenced by Descartes, Antoine Arnauld argued that it is not one THING that is predicated of another thing, but one IDEA that is predicated of another idea. Locke (who studied Arnauld's logic carefully) introduced this to the English world (Book IV of the essay is the locus classicus). For example, he sets its down as a principle, that all our knowledge consists in perceiving certain agreements and disagreements between our ideas.

There you have Hume's fork. Before, there was the difference between accidental and essential propositions. An essential proposition is where the predicate belongs in the subject by right, as it were. An accidental proposition is whether the predicate belongs in the subject, but possibly may not. It is not relevant whether this can be known or not. There are (as Aquinas notes) essential propositions which cannot be known because mere humans cannot understand the true meaning of the word which signifies the subject. But the notion of a proposition true in itself but unknowable because the 'subject' is unknowable, is impossible where the proposition consists of ideas stuck together.

In summary: Hume's fork is a consequence of the early modern view of the proposition. The scholastic view was that the proposition connects things. The early modern view is that it connects ideas. The distinction between truths of reason and truths of fact only makes sense on the latter view.

There a number of passages which support this argument & I will make a posting in due course.

Wednesday, February 15, 2006

Praedicatum inesse subjecto verae propositionis

'The predicate is included in the subject of a true proposition'. Leibniz says this (in a letter to Arnauld) but of course his use of Latin signals that he is quoting an orthodox principle of the schools.

And the principle has nothing to do with the analytic/synthetic distinction. It has to do with the true/false distinction. If Socrates is the subject, and the subject is bald, and if the proposition states that the predicate 'is bald' is included in the subject (Socrates) then the proposition is true. Otherwise it is false.

What, then, is the analytic/synthetic distinction?

Tuesday, February 14, 2006

Truth in Hell

What on earth is going on here? and particularly here? Fr. Alexis Bugnolo, a Franciscan who is developing an internet library of Scholastic Theology and Philosophy (and good luck to him, I say – this material has lain buried and neglected for too long) is incensed by what he calls a sodomitic slur against St. Anselm in an article in the internet encyclopedia, Wikipedia. The original article, now locked down, is here, and the talk page, which gives a full background to the dispute is here.

Bognolo stirs up a number of demons, which I won't discuss here. It is what he says about truth that interests me. He says 'Wikipedia is not much different that the real lower regions, where demons wittle the hours of their impending ultimate damnation on the Day of Judgement, idling wailing and complaining and arguing among themselves against the pittible [sic], little truth that their darkened intellects can still behold. … Suffice it to say, that at Wikipedia, they are obsessed with a false definition of truth. For them truth is something neutral, between the medium of two personal opinions. They wrongly believe that falsehood does not exist. Now of course such a definition of truth only prevails in Hell, and that is why those who accept the Wikipedia system end up with the sensibilities of devils, who cannot endure anything at all being said that is true, lest someone arrive at the truth.'

Now there are some real problems at Wikipedia - mainly because professional researchers and academics have no incentive to contribute to it, whereas cranks have every incentive. But I don’t think they have a 'false definition of the truth'. Truth is not something neutral. Of two contrary opinions, at least one must be false, and of two contradictory opinions at least one must be true. Wikipedians would not claim otherwise.

But, when the truth is difficult to determine, Wikipedians say that different opinions about the truth must be given, and (in controversial cases like this) the opinions supported by evidence (or references to that evidence). What is wrong with that?

Monday, February 13, 2006

Mesmerized by science

Any philosopher who mentions my work in their Ph.D. thesis is to be recommended, in my view. One such is Oxford philosopher Edward Kanterian. But what Kanterian says here transcends mere self-interest. Here he is, defending the currently unfashionable view that the methods of philosophy are altogether unlike the methods of the sciences. Even more interesting, he says this fashionable view has a transatlantic source.

'American culture is mesmerized by science. It seems to me that all too many American philosophers think that all real problems can be resolved and answered by scientific methods and that philosophy is either continuous with science or at any rate ought to emulate the methods of the sciences. I have the impression that such a view is widespread in America. It is certainly a view that was encouraged by Quine. And most American philosophers seem to think that Quine showed that the analytic/synthetic, a priori/a posteriori, conceptual/empirical distinctions are obsolete, invalid and to be rejected.'

But read for yourself.

Saturday, February 11, 2006

Aquinas on the names of God

Brandon here has pointed out that it is not inconsistent to hold that there are three persons in the Trinity, but only one God. For the following statements are consistent:

Jack has an F
John has an F
Jack /= John
There is only one F

However, this is true so long as we do not read 'is God' in 'the Father is God' as an identity statement, but as something like ' has the divine nature'. If, on the other hand, we read 'God' as a logically proper name, and 'the Father is God' as an identity statement, it is clearly inconsistent to hold that three things (the Father, the Son and the Holy Ghost) are identical with a fourth thing (God).

Is that right? It is certainly consistent with what Aquinas says here, that no name signifying any individual thing is 'properly communicable to many', except by way of similitude; as a person can be called "Achilles". Thus the name 'God', can only be communicated by way of similitude. 'But if any name were given to signify God not as to His nature but as to His "suppositum," accordingly as He is considered as "this something," (hoc aliquid) that name would be absolutely incommunicable; as, for instance, perhaps the Tetragrammaton among the Hebrew; and this is like giving a name to the sun as signifying this individual thing.'

It suggests that our ordinary words for God only signify by description (as philosophers now say) not 'by reference'. But is that right?

Friday, February 10, 2006

Alarm clock dreams

These are discussed in Freud's great work, The Interpretation of Dreams, which I dusted off after a discussion at Bill Vallicella's place here.

These dreams are apparently caused by a stimulus (such as an alarm clock) which the sleeper interprets as an event in the dream (church bells, sleigh bells).

The puzzle of these dreams is that the interpreted event cannot occur any earlier than the stimulus. Yet there is often a complicated chain of events in the dream that leads up to the interpreted event: how can the dreamer aparently compress such a large quantity of material into the short space between the time that the stimulus occurs, and the beginning of the dream events which conclude with the interpreted event?

A famous example is a dream of Maury, which was about the French Revolution. He witnesses frightful scenes of murder, is brought before a revolutionary tribunal, is questioned by Robespierre, Marat and other revolutionary heroes. After some other incidents which he did not remember clearly, he was condemned, and led to the guillotine in front of an immense crowd. He was bound to the plank by the executioner, the blade of the guillotine fell. He felt his head separated from his body, woke up – and found the top of his bed had fallen and had struck his head in the same place as the blade of the guillotine in the dream.

The puzzle is that the story leading up to the dream was long, and presumably must have begun long before the bed head collapsed. But it seems an extraordinary coincidence that an event in the outside world that so resembled a guillotine, should happen at that time.

Another dream, related by Hildebrandt, is of strolling through green fields until the dreamer came to a village. He saw the villagers strolling through the fields with hymn books. It is Sunday! He went to the churchyard to cool down, read some of the tombstones and then watched the bell ringer climb the tower, and watched the bell first stand motionless, then slowly swing, and finally ring so piercingly that he woke up – to his alarm clock.

The puzzle is to explain how a chance event like the alarm clock could so neatly fit into a dream plot that must have begun some time before the event.

Here is a third example: the dreamer is waiting for a long time for a sleigh to arrive. The sleigh finally comes to the door, there were detailed preparations such as the fur rug, the foot muff, until finally the sleigh started off, with such violence that the sleigh bells ring wildly – his alarm clock.

In all of these cases, the interpreted event is the denoument of what appears to be a complex plot, which happens exactly at the right time and place in the dream. Yet the dreamer (we suppose) has no knowledge or foresight of the actual event which is so interpreted.

Possible solutions are 1. That the dream is made up on waking 2. that the dreamer does have fore-knowledge of the external event (though this hardly explains Maury's dream) 3. The person who told the dream was inventing it.

Wednesday, February 01, 2006

Existential Import

'Existential Import' is a term so frequently bandied around (e.g. here and here) that it is worth explaining its correct meaning, and historical context. I have a complete discussion of it here, but it broadly amounts to this: In traditional logic, the sentence or categorial proposition consists of three parts: the predicate which is 'affirmed' or 'denied', the subject of the affirmation or denial, and the copula which signifies whether the predicate is affirmed or denied. The copula was thought to be signified by the verb 'is', (Latin: est). For example, in the proposition 'man is mortal', the verb 'is' signifies that the predicate 'mortal' is affirmed of the subject 'man'. Thus Mill writes

  • Every proposition consists of three parts: the Subject, the Predicate, and the Copula. The predicate is the name [sic] denoting that which is affirmed or denied. The subject is the name denoting the person or thing which something is affirmed or denied of. The copula is the sign denoting that there an affirmation or denial (Mill, System of Logic).

What is now called a general existential proposition, such as 'some men are mortal' was then called a 'particular' proposition. It was not called 'existential', because it was not thought to be existential. A proposition of the form 'A exists' combines the subject 'A' with the verb 'exists'. Since (according to the traditional theory) every proposition consists of subject, predicate and copula, it follows that 'exists' must be a grammatical abbrevation of copula and predicate, and that it really stands for 'is existent' or something similar. If so, it is not the copula 'is' that signifies existence, but the adjective 'existent'.

The question of 'existential import' was traditionally whether a 'particular' proposition such as 'some mountains are golden' implies the corresponding 'existential' proposition 'golden mountains exist'. Mill argued that it does not.

  • That the employment of [the word 'is'] as a copula does not necessarily include the affirmation of existence, appears from such a proposition as this: A centaur is a fiction of the poets; where it cannot be possibly implied that a centaur exists, since the proposition itself expressly asserts that the thing has no real existence. (System of Logic I.iv.1)

Note that this section is called 'Of the Import of Propositions', from which, perhaps, the term 'existential import' derives. There is another discussion of the question in Joyce's manual of traditional logic here.

Note also that the distinction between particular (Some A is B) and existential (Some A-B exists) also corresponds to the distinction made by Alexius Meinong in Chapter III of his master work 'On Assumptions', between being so or 'Sosein', and being or 'Sein'. This is not to be confused with his distinction between 'subsistence' and 'existence'.