What does Ñanavira Thera's Notes on Dhamma mean here, about a one-one correspondence?

Question

This is from Ñanavira's Notes on Dhamma:

The notion of sensation, however, as we see from the dictionary's definition, is an abomination from the start—how can one 'perceive the state of one's senses' when it is precisely by means of one's senses that one perceives? (See MANO.) Another individual's perception (with his eye) of the state of my eye may well have, in certain respects, a one-one correspondence with my perception (with my eye) of, say, a tree (or, for that matter, a ghost, or, since the eye as visual organ extends into the brain, a migraine

What does it mean for something to have a one-one correspondence with something else?

How can the state of my eye have a one-one correspondence with my perception? What would be an example of that.

Answer 1

Read the whole note, and understand the prior paragraph and all its footnotes. All of this is written very well!

Please share the whole sentence, if not the whole argument, in your post. The full sentence is

The notion of sensation, however, as we see from the dictionary's definition, is an abomination from the start—how can one 'perceive the state of one's senses' when it is precisely by means of one's senses that one perceives? (See MANO.) Another individual's perception (with his eye) of the state of my eye may well have, in certain respects, a one-one correspondence with my perception (with my eye) of, say, a tree (or, for that matter, a ghost, or, since the eye as visual organ extends into the brain, a migraine); but it is mere lazy thinking to presume from this that when I perceive a tree I am really perceiving the state of my eye—and then, to account for my sensation, inferring the existence of a tree in a supposed 'external' world beyond my experience.

"Another's individual's perception..." is the start of an argument he wishes to rebut. To wit, due to the interpersonal consistency of people's views of the world, we can infer the existence of a world independent of experience, and therefore sensations are real in the sense of reflecting the real physical state of our real sense organs. The "one-to-one" correspondence between his view and another's view, is an exemplar of that interpersonal consistency.

Answer 2

The Buddha defines conduct as:

Dependent on the eye & forms there arises eye-consciousness. The meeting of the three is contact.

Nanavira has fundamentally misunderstood contact here:

In this way, phassa comes to be seen as contact between the conscious eye and forms—but mark that this is because contact is primarily between subject and object, and not between eye, forms, and eye-consciousness.

But for the Buddha, contact requires consciousness. We can understand why the buddha is correct as follows:

We have impingement of object, and sense base, all the time without contact arising. For example, as you peruse this answer, light is reflecting from your device, and other physical objects, in your visual field. But you’re not aware of all of these objects! You need consciousness to create contact.

Thus, sensation of the object you’re conscious of – like these words you’re reading – arises from the meeting of eye consciousness, with the visual form of your device at the eye sense base. All three are necessarily required, arahant or not.

Nanavira is mistaken on consciousness. He incorrectly mistook what western philosophy considers ‘stream of consciousness’, as what the Buddha differently and specifically refers to as instants of sense consciousness that arise and fall away moment to moment.

In contrast to Nanavira's claims here, for the Buddha, sentient experience requires contact arising from the meeting of sense object, sense base, and sense consciousness – whether one is enlightened. Buddha notes that consciousness persists ‘without remainder’, as part of the non-clinging aggregates after enlightenment, until final Nibbana.

Answer 3

Mathematically, in set theory, 1-to-1 correspondence means unique pairing between the elements of one set and those of another such that each and every element if one set is matched/paired with one and only one element of the other such that all elements of the two sets are a "couple".. The sets {apple, h, $} and {9, Tom, Talk} yield the 1-to-1 correspondence (apple, Talk), (h, 9), ($, Tom). This, for sets, implies and is implied by the sets have the same cardinality/size.

From a drive-by what I can gather is, Ñanavira is casting doubts on the common sense notion that there are external objects (a tree, a dog, etc.) that are in 1-to-1 correspondence with the eye's perceptions (images of a tree, a dog, etc.). In essence he's alluding to maya(an "image" in our minds with no object out there to correspond to it, illusion). So here are two sets: The set of external-to-the-mind objects E = {tree, dog} and the set of visual images you have M = {tree, dog, Sara}. Tree in E corresponds with tree in M, dog in E corresponds to dog in M, but there's no Sara in E that corresponds to the Sara in M. The two sets E and M lack a 1-to-1 correspondence relationship.

Answer 4

I disagree with this answer.

He's discussing a different level of cognition. In the first sentence, he admits that contact is defined in terms of the three-fold coming together. But he is discussing a basic assumption underlying the default subjective experience of that contact — i.e. that there is a subject coming into contact with an object. The essay is convincing the reader to abandon the senses of : identification with that subject, and objectification of the object.

While SN 12.44 is stated in terms of Dependent Origination, it's not about the experience of Dependent Origination! It's about how the experience of the world arises. In our experience of the world, visual forms arise via three-fold contact with the eye. That model is key to our conventional experience of the world. But DN 15 (mentioned in Ven. Nanavira's footnote [a]) is about how contact per se arises from name-and-form, independent of any concrete world model, which is why it uses the much more abstract terms of resistance-contact and designation-contact. As he says in footnote [a], resistance-contact isn't five-senses contact (his "cakkhusamphassa &c."). In terms of our direct experience, cognition in terms of forms arising via three-fold contact at the eye is nama — not rupa in its own right — though it concerns rupa. It's a useful model which Ven. Nanavira does not wish to spurn, but Ven. Nanavira contends that to carry the Buddha's program to completion, we must release attachment to any implicit subject/object duality in the background of cognitions which are in terms of that model.

in contrast to what nanavira is stating here, for the buddha, contact arising from the meeting of sense object, sense base, and sense consciousness, is essential for sentient experience whether one is enlightened or not.

He does not deny that! Contact occurs in the arahat. He's just saying that that's not the key issue for purposes of phassanirodha. See footnote [d]:

Phusanti phassā upadhim paticca
Nirūpadhim kena phuseyyum phassā
Contacts contact dependent on ground—
How should contacts contact a groundless one? Udāna ii,4 <Ud.12>

It must, of course, be remembered that phassanirodha in the arahat does not mean that experience as such (pañcakkhandhā) is at an end. But, also, there is no experience without phassa. In other words, to the extent that we can still speak of an eye, of forms, and of eye-consciousness (seeing)—e.g. Samvijjati kho āvuso Bhagavato cakkhu, passati Bhagavā cakkhunā rūpam, chandarāgo Bhagavato n'atthi, suvimuttacitto Bhagavā ('The Auspicious One, friend, possesses an eye; the Auspicious One sees visible forms with the eye; desire-&-lust for the Auspicious One there is not; the Auspicious One is wholly freed in heart (citta)' (Cf. ATTĀ [c].)) (Salāyatana Samy. xviii,5 <S.iv,164>)—to that extent we can still speak of phassa. But it must no longer be regarded as contact with me (or with him, or with somebody). There is, and there is not, contact in the case of the arahat, just as there is, and there is not, consciousness. See CETANĀ [f].

In summary, the key issue for purposes of phassanirodha is the abandonment of the subject/object duality — "I am making contact/contact is made with me". This is how I construed his footnote — "But [contact] must no longer be regarded as contact with me (or with him, or with somebody)."

what the buddha very differently and very specifically refers to as instants of sense consciousness that arise and fall away moment to moment.

Can you point me to the sutta you're thinking of?