Truth suffers from too much analysis

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.














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.”
