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Archive for December, 2012

Aristotle’s Sea Battle and Future Contingents

Posted by allzermalmer on December 18, 2012

This comes from Aristotle’s book “On Interpretation” and is Part 9. It deals with future contingents and statement either being true or not being true, i.e. law of excluded middle.

“In the case of that which is or which has taken place, propositions, whether positive or negative, must be true or false. Again, in the case of a pair of contradictories, either when the subject is universal and the propositions are of a universal character, or when it is individual, as has been said,’ one of the two must be true and the other false; whereas when the subject is universal, but the propositions are not of a universal character, there is no such necessity. We have discussed this type also in a previous chapter.

When the subject, however, is individual, and that which is predicated of it relates to the future, the case is altered. For if all propositions whether positive or negative are either true or false, then any given predicate must either belong to the subject or not, so that if one man affirms that an event of a given character will take place and another denies it, it is plain that the statement of the one will correspond with reality and that of the other will not. For the predicate cannot both belong and not belong to the subject at one and the same time with regard to the future.

Thus, if it is true to say that a thing is white, it must necessarily be white; if the reverse proposition is true, it will of necessity not be white. Again, if it is white, the proposition stating that it is white was true; if it is not white, the proposition to the opposite effect was true. And if it is not white, the man who states that it is making a false statement; and if the man who states that it is white is making a false statement, it follows that it is not white. It may therefore be argued that it is necessary that affirmations or denials must be either true or false.

Now if this be so, nothing is or takes place fortuitously, either in the present or in the future, and there are no real alternatives; everything takes place of necessity and is fixed. For either he that affirms that it will take place or he that denies this is in correspondence with fact, whereas if things did not take place of necessity, an event might just as easily not happen as happen; for the meaning of the word ‘fortuitous’ with regard to present or future events is that reality is so constituted that it may issue in either of two opposite directions. Again, if a thing is white now, it was true before to say that it would be white, so that of anything that has taken place it was always true to say ‘it is’ or ‘it will be’. But if it was always true to say that a thing is or will be, it is not possible that it should not be or not be about to be, and when a thing cannot not come to be, it is impossible that it should not come to be, and when it is impossible that it should not come to be, it must come to be. All, then, that is about to be must of necessity take place. It results from this that nothing is uncertain or fortuitous, for if it were fortuitous it would not be necessary.

Again, to say that neither the affirmation nor the denial is true, maintaining, let us say, that an event neither will take place nor will not take place, is to take up a position impossible to defend. In the first place, though facts should prove the one proposition false, the opposite would still be untrue. Secondly, if it was true to say that a thing was both white and large, both these qualities must necessarily belong to it; and if they will belong to it the next day, they must necessarily belong to it the next day. But if an event is neither to take place nor not to take place the next day, the element of chance will be eliminated. For example, it would be necessary that a sea-fight should neither take place nor fail to take place on the next day.

These awkward results and others of the same kind follow, if it is an irrefragable law that of every pair of contradictory propositions, whether they have regard to universals and are stated as universally applicable, or whether they have regard to individuals, one must be true and the other false, and that there are no real alternatives, but that all that is or takes place is the outcome of necessity. There would be no need to deliberate or to take trouble, on the supposition that if we should adopt a certain course, a certain result would follow, while, if we did not, the result would not follow. For a man may predict an event ten thousand years beforehand, and another may predict the reverse; that which was truly predicted at the moment in the past will of necessity take place in the fullness of time.

Further, it makes no difference whether people have or have not actually made the contradictory statements. For it is manifest that the circumstances are not influenced by the fact of an affirmation or denial on the part of anyone. For events will not take place or fail to take place because it was stated that they would or would not take place, nor is this any more the case if the prediction dates back ten thousand years or any other space of time. Wherefore, if through all time the nature of things was so constituted that a prediction about an event was true, then through all time it was necessary that that should find fulfillment; and with regard to all events, circumstances have always been such that their occurrence is a matter of necessity. For that of which someone has said truly that it will be, cannot fail to take place; and of that which takes place, it was always true to say that it would be.

Yet this view leads to an impossible conclusion; for we see that both deliberation and action are causative with regard to the future, and that, to speak more generally, in those things which are not continuously actual there is potentiality in either direction. Such things may either be or not be; events also therefore may either take place or not take place. There are many obvious instances of this. It is possible that this coat may be cut in half, and yet it may not be cut in half, but wear out first. In the same way, it is possible that it should not be cut in half; unless this were so, it would not be possible that it should wear out first. So it is therefore with all other events which possess this kind of potentiality. It is therefore plain that it is not of necessity that everything is or takes place; but in some instances there are real alternatives, in which case the affirmation is no more true and no more false than the denial; while some exhibit a predisposition and general tendency in one direction or the other, and yet can issue in the opposite direction by exception.

Now that which is must needs be when it is, and that which is not must needs not be when it is not. Yet it cannot be said without qualification that all existence and non-existence is the outcome of necessity. For there is a difference between saying that that which is, when it is, must needs be, and simply saying that all that is must needs be, and similarly in the case of that which is not. In the case, also, of two contradictory propositions this holds good. Everything must either be or not be, whether in the present or in the future, but it is not always possible to distinguish and state determinately which of these alternatives must necessarily come about.

Let me illustrate. A sea-fight must either take place to-morrow or not, but it is not necessary that it should take place to-morrow, neither is it necessary that it should not take place, yet it is necessary that it either should or should not take place to-morrow. Since propositions correspond with facts, it is evident that when in future events there is a real alternative, and a potentiality in contrary directions, the corresponding affirmation and denial have the same character.

This is the case with regard to that which is not always existent or not always nonexistent. One of the two propositions in such instances must be true and the other false, but we cannot say determinately that this or that is false, but must leave the alternative undecided. One may indeed be more likely to be true than the other, but it cannot be either actually true or actually false. It is therefore plain that it is not necessary that of an affirmation and a denial one should be true and the other false. For in the case of that which exists potentially, but not actually, the rule which applies to that which exists actually does not hold good. The case is rather as we have indicated.”

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Avicenna’s Response to Meno’s Paradox

Posted by allzermalmer on December 18, 2012

Avicenna (Ibn-Sina) was an Arabic philosopher who wrote a book called The Healing. In Book 1, the sixth  chapter is called “On the Manner of Apprehending (iābah) Unknown [Things] (al-majhūlāt) from Known [Things] (al-malūmāt).” This is a response to Meno’s Paradox presented to Socrates about learning or coming to obtain new knew knowledge. The response of Avicenna is translated into English by Michael E. Marmura

“Every seeking (malab) of these [unknown things] is only achieved by means of existing, realized things. Here, however, there is a place for doubt, namely, that [with respect] to the thing whose entity (al-dhāt) is nonexistent [and] whose existence is impossible, how is one to conceive it so as to answer the question “What is it?” when asked about it, so that thereafter one could ask “Does it exist?” For if no meaning (manan) for it is realized in the soul, how can one judge it to be either realized or not realized, when the impossible has no form in existence? How, then, would a form of it be taken into the mind so that that conceived thing would constitute its meaning?

[To this] we say: this impossible [thing] is either (a) singular, having  neither composition nor separability [of parts] (wa lā tafīl), [or (b) composite]. If [(a), singular], it would not be at all conceivable except by some kind of analogy (muqāyasa) with the existent and in relation to it. This would be similar to our saying “vacuum” and “the contrary of God.” For vacuum is conceived as belonging to bodies as though a recipient, and the contrary of God would be conceived as belonging to God in the way the hot relates to the cold. Thus the impossible would be conceived in terms of a possible thing to which it relates, being conceived in relation to it and likened to it. In itself, however, it is neither conceivable nor intellectually apprehendable (lā maqūlan), nor would it have any being (wa lā dhāta lahu).

As for [(b)], which has some sort of composition and separable parts, such as the goatstag, the phoenix, or a human that flies, what is first conceived is their separable parts whose existence is not impossible. Thereafter there is conceived for the parts some kind of connections, analogous to the connections that obtain for the separable parts of existing composite entities. There would thus be three things, two of them consisting of parts, where each by itself [can] exist, and the third a composition of them. This in some respect is a conceived composition, because composition inasmuch as it is a composition is one of the things that exist. In this way it yields the meaning signifying the nonexistent’s name. Thus the nonexistent is only conceived because of the prior conception of existing things.

We now say: if a judgment about a universal is realized for us, its first  realization being self-evident, as, for example, “every human is an animal” and “the whole is greater than the part,” or evident by induction or experiment (tajriba) in the ways things are believed to be true (p.73) without the help of a [demonstrative] syllogism (qiyās), we would know potentially the judgment over every particular beneath it, but we would be ignorant of it in [its] actuality. Thus, for example, we would not know that Zayd, who is in India, is an animal. In actuality we would be ignorant of this because thus far we would have known [it] only potentially, since we have known that every human is an animal. In actuality we would be ignorant of it because one needs to add to this knowledge another knowledge, or two other [instances] of knowledge, for the potential to become actual. This is because we must know that Zayd exists and know that he exists as a human. If then through the senses we attain immediate cognition (marifa) that he exists and that he is a human, without this being sought after (malūban) through a [demonstrative] syllogism or [this being]taught, and if this is connected with [universal] knowledge (ilm), which is realized for us, also without a [demonstrative] syllogism, in [the] manner by which the connection that in itself brings about a third knowledge [takes place], we would then know that Zayd is an animal. It would thus be the case that from the combining of immediate cognition (marifa) and [universal] knowledge (ilm), knowledge [of the specific particular] comes about for us. Of the two, immediate cognition comes about through sensation, [universal] knowledge through the intellect. Immediate cognition would have come to us at a temporal moment, whereas [universal] knowledge is prior to it.

That which comes about from both of them may well have been sought by us, and we [may have] sought its principles, which bring us to it, or it could have been something to which we have been led by reason of the sufficiency of its causes without our seeking it. With all this, the conception of the thing sought after and its principles must precede every instance of it.

It may also happen that it is not like this, but that the judgment of the universal would have come about for us by a [demonstrative] syllogism, and the judgment of the particular would have come about by another [demonstrative] syllogism, such that if the two are combined, a third instance of knowledge is realized. But even if this is the case, the first syllogisms would have been through self-evident premises or else acquired by induction, experiment, or sensory perception without a syllogism, as we will make clear later.

Then, if a questioner should ask someone and say, “Do you know that every dyad is even?” it is known that the answer would be, “I know this.” [The questioner] would then come back and say, “Is what is in my hand even or odd, and is the number of people in such and such a city even or odd?” If it is answered, “We do not know this,” [the questioner] will come back and say, “You then do not know that every numerical dyad is even; for what is in my hand is a dyad, but you did not know that it is even.”

It is said in The Teaching [of Aristotle] that some people have answered this incorrectly, saying, “We only know that every dyad known to us is even.” But this answer is false; (p. 74) for we know that every existing dyad, whether known or not known, is even.

Rather, [our own] response to this would be, “We did not say that we know every dyad that is even, so that if we did not know that [the] two things [in the hands of the questioner] constitute a dyad our statement is contradicted”; we also did not say, “We know of everything that is a pair, that it is a pair, so that [consequently] we know that it is even.”

Rather, we said one of two things: either that every dyad that we know, we know it to be even; or every dyad in itself, whether we know it or not, is in itself even. As for the first disjunct, it is not contradicted by the doubt mentioned. As for the second [disjunct], it consists of general knowledge, not contradicted by our ignorance [of some aspect belonging to it]. This is because even though we do not know whether what is in the hand of so and so is even or not even, the meaning of our knowledge that every dyad is even stands established and is not false. But what we would be ignorant of is included in our potential, not actual, knowledge. Ignorance of it would not be an ignorance in actuality of [all of] what we have. If we come to know that what is in [the questioner’s] hand is a
dyad, and we remember the thing which was known to us, [namely, that every dyad is even,] we would immediately know that what is in his hand is even. What we are ignorant of is other than that which we know. It is not the case that if we do not know whether or not something is even because we do not know whether or not it is a dyad that this falsifies our knowledge that whatever is a dyad is even. We would then have also known that in one respect that thing is even. With this the doubt raised ceases.

It was mentioned that Meno, who addressed Socrates regarding the  nullification of teaching and learning, said to him, “The seeker of some kind of knowledge will either be seeking knowledge of what he [already] knows, in which case his quest would be inconsequential, or else he would be seeking knowledge of what he does not know—[In this case,] how would he know it, once he attains it? This is akin to one who seeks a runaway slave he does not know. If he finds him, he would not recognize him.”

Socrates then undertook in refuting him (p. 75) to present [Meno] with a geometrical figure, establishing for him how the unknown, after being unknown, is captured through the known. This, however, is not logical discourse. For he showed that this is possible, bringing about a syllogism that yielded as a conclusion the possibility of what Meno brought about by a syllogism that yielded other than its possibility. [As such,] he did not resolve the doubt.

Plato, on the other hand, undertook to resolve the doubt, saying that  learning is recollection. In this he attempted to convey that the thing being sought had been known prior to the quest and prior to [its] attainment, but it was only being sought because it had been forgotten. Once the investigation led to the thing sought, it was remembered and learned. Thus the seeker would have known something he had [previously] known. It is as though Plato had acquiesced to the doubt and sought toescape from it and fell into an impossibility. This is something we have treated in exhaustive detail in our solution to it in our summary of the book on the Syllogism.

Still with all this we say: if what is being sought after is known for us in every respect, we would not seek it; and if unknown for us in every respect we would not seek it. It is, [however,] known to us in two respects, and unknown in one respect. For it is known to us conceptually in actuality, and known to us potentially in terms of assent. It is unknown to us in being specified with actuality, even though it is also known to us [as] being not specified with actuality. If, then, we have had previous knowledge that every thing which is of a certain character is of that character,  without [that knowledge] having been sought after, but by an inborn rational act, or through sensation, or some other [similar] ways of knowing, we would attain in potentiality knowledge of numerous things. If through sensation we apprehend some of these particulars without our seeking them, they would immediately fall within [the category] of being actual, within the [category] of first knowledge. This, in some respect, would parallel step by step what Meno had brought about in the example of the runaway slave.

For we would know at first the thing sought after conceptually, as we would know the runaway slave at first conceptually. And we know prior to this what would bring us to knowing it by assent, just as we would know the road [taken by the slave] prior to our knowing the place of the runaway slave. For if we follow the path to what is being sought after, and we have had a previous conception of it and of the road leading to it, and [if] we reach it, we would have apprehended the thing sought after. [This is] similar to our travelling path to the runaway slave when we have a previous conception of his self, and of the road leading to him  Once we reach him, we would recognize him, even if we had never seen the runaway slave at all [before]; but we would have conceived for him a distinguishing mark (alāma), [which indicates] that everyone having this mark is a runaway.

If there were added to this some knowledge occurring not by acquisition but coincidentally by observation, or [some knowledge] occurring by acquisition, demonstration, testing, and cognizing, and we found that mark on a slave, we would know that he is a runway.

The distinguishing mark would thus be like the middle term in the  syllogism. Our grasping that distinguishing mark in a slave would be like the minor term. Our knowledge that whoever has this mark is a runaway is akin to the prior occurrence for us of the major premise; and our finding the runaway would be akin to the conclusion. This runaway, moreover, would not have been known to us in every respect; otherwise we would not have sought him. Rather, he was known to us by way of conception, unknown to us as regards [the physical] place [where he is]. Hence, we would be seeking him with respect to his being unknown, not with respect to his being known. Once we recognized him and caught him, there would have occurred through [our] demonstrative quest knowledge of him which [previously] did not exist. This only happened on account of the combination of two causes of knowledge, one being [knowledge of] the way and its leading to him, the second, his being the object of sense apprehension.

The unknown things sought after are similar to this: they are known by the combination of two things. The first is something which is prior for us, namely, that B is A, which parallels the first cause in the example of the runaway slave; the second is a thing which occurs immediately, namely, our sensory cognition that C is B, which equals the second cause in the example of the runaway slave. Just as the two causes there necessitate the apprehension of the runaway slave, similarly the two causes here necessitate the apprehension of what one is seeking. It is not the case that what he, [that is, Meno,] demanded as a condition, [namely,] that whatever is not known in every respect would not be known when attained, is admitted. Rather it is every thing unknown in every respect that is not recognized when attained. If, however, knowledge of a thing which had been known [before] had been pursued, [the prior knowledge of it] would constitute potential knowledge of a part of what is being sought after, it being like a distinguishing mark for it. Itwouldthen only require something to connect with it to change it into actuality. As soon as that which actualizes it is connected with it, the thing sought after is attained.

[Now] that it has been established how mental (dhihnī) instruction and  learning takes place and that this takes place only through previous knowledge, we must have first principles for conception and first principles for assent. If every instruction and learning was through previous knowledge, and every existing knowledge is through instruction and learning, the state of affairs would regress ad infinitum, and there would be neither instruction nor learning. It is hence necessary that we have matters believed to be true without mediation, and matters that are conceptualized without mediation, and that these would be the first principles for both assent and conceptualization.”

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