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Thank you for this excellent and thoughtful comment. The watch analogy is a perfect, modern formulation of a classic philosophical challenge, and it gets right to the heart of the matter. You've pinpointed the exact place where the Madhyamaka view often seems counter-intuitive, and your concern is entirely valid from a conventional standpoint. To address it fully requires a deep dive into how different Buddhist philosophical schools approach this.

The core of your argument is that by inferring a process (the watch's movement) that occurs outside of your direct perception, you can prove the existence of a mind-independent reality. From a Madhyamaka viewpoint, the flaw in this conclusion is that it mistakes a conceptual inference for an independently existing reality. Let's analyze the components of your deduction using the Prāsaṅgika Madhyamaka method.

First, we analyze the "watch" itself. What is this "watch" that you deduce exists when unobserved? Our concept of it—its mechanics, its purpose, its continuity—is built entirely from prior perceptions and learning. The very idea of a "watch that functions independently" is a concept that is itself dependently arisen. Then, we analyze the "unobserved process." You posit a continuous mechanical movement happening while you weren't looking. But this "continuous movement" is a mental model, an inference that bridges two discrete moments of perception. We don't experience the unobserved process; we conceptualize it. From a Prāsaṅgika perspective, this conceptual bridge is a dependent designation (prajñapti), not an ultimate truth. It's a conventionally useful story we tell ourselves, but it has no inherent, findable reality.

This leads to the crucial question of how a philosophy can accept an external world conventionally while insisting it's ultimately empty. The answer lies in the precise definition of the two truths. For something to be accepted as "conventionally valid," it isn't just a fantasy. It must be functional (the watch keeps time) and part of our shared, everyday experience. This is why Prāsaṅgika thinkers do not deny the functional reality of the world.

This point is central to the perspective of the Tibetan master Tsongkhapa, who was a brilliant systematizer of the Prāsaṅgika view. It is important to nuance the status of this view across Tibetan Buddhism. While the Gelug school, founded by Tsongkhapa, holds Prāsaṅgika as systematically definitive, other major schools have a more varied approach. To be precise, certain Kagyu and Sakya lineages also teach shentong (gzhan-stong, or "other-empty") readings alongside rangtong (Prāsaṅgika, or "self-empty") presentations. The Nyingma school often balances Madhyamaka analysis with the direct experiential teachings of Dzogchen.

Nonetheless, Tsongkhapa's clarification of Prāsaṅgika is profoundly influential. While he is a key figure, he was not alone in defending conventional reality; earlier Indian masters like Bhāviveka and Śāntarakṣita also emphasized the necessity of a robust conventional world. Tsongkhapa's particular genius was in his forceful and detailed systematization. In what is known as his "eight great difficult points" of Madhyamaka (as detailed in texts like his Illumination of the Thought), he specifically includes the non-negation of external objects as a core tenet of the true Prāsaṅgika view. He argued that without a functioning conventional world, the ultimate truth of emptiness becomes a meaningless, nihilistic void. The watch is conventionally valid and functions. The error is only in believing it functions from its own side, with an intrinsic nature (svabhāva) independent of parts, causes, and a designating mind.

This approach of deconstructing experience extends to all phenomena. The Madhyamaka "Middle Way" states that the world isn’t a projection of our minds, but it isn’t totally independent of our minds, either, because it makes no sense to speak of a particular, fixed reality independent of any concept, mental process, or observer. Rather, there is interdependence. An object is seen by a hundred different people like a hundred reflections in a hundred mirrors. But is it the same object? As a first approximation, it is, but it can be perceived in completely different ways by different beings.

Colors, sounds, smells, flavors, and textures aren’t attributes that are inherent to the objective world, existing independently of our senses. The objects we perceive seem completely ‘external’ to us, but do they have intrinsic characteristics that define their true nature? We have no way of knowing, because our only way of apprehending them is via our own mental process. To take an example, what is a white object? Is it a wavelength, a ‘color temperature’, or moving particles? Are those particles energy, mass, or what? None of those attributes are intrinsic to the object; they’re only the result of our particular ways of investigating it.

A classic Buddhist story tells of two blind men trying to understand the color white. One was told it is the color of snow and concluded white was "cold." The other was told it is the color of swans and concluded white went "swish swish." The point is that the world cannot be determined by itself. If it could be, we’d all perceive it in the same way. This isn't to deny reality as we observe it, but simply that no ‘reality in itself’ is conventionally valid. Phenomena are only conventionally valid in dependence on other phenomena.

To appreciate the precision of this view, it's helpful to contrast it with others. Even within Madhyamaka, the earlier Svātantrika school differed. They also accepted a conventional external world, but believed that for a label to be valid, there had to be something findable on the side of the object that justified it—a sort of "barcode" or own-characteristic (svalakṣaṇa). The Prāsaṅgika view, as interpreted by Candrakīrti and Tsongkhapa, rejected this, arguing for a more radical emptiness where valid mental labelling alone is sufficient. 

This also clarifies how Tsongkhapa’s Prāsaṅgika diverges from Yogācāra. Unlike Yogācāra, which in many formulations treats all external appearance as projections of mind, Tsongkhapa insists that functioning external objects are required for any valid cognition: they serve as causal conditions, are witnessed by public consensus, and pass empirical tests. What makes them only conventionally real, he says, is that their existence is established "merely by correct designation" and not by any discoverable essence on the object’s side. However, it is a common oversimplification to equate all of Yogācāra with idealism. Early epistemic Yogācārins such as Dharmakīrti still allowed externals insofar as they exercise causal efficacy (arthakriyā)—real is what produces effects—yet their focus remains the mental image as the direct object of awareness. Later false-aspectarian Yogācāra (Ratnākaraśānti) drops externals altogether, calling the shared world a karmic hallucination. Tsong-khapa rejects both extremes: • a strict physicalist nihilism (uccheda-dṛṣṭi) that treats all mind and karma as nothing more than brain-chemistry, and • a reifying stance — whether naive realism that endows matter with intrinsic substance or an idealism that grants mind or mental images intrinsic substance (śaśvata-dṛṣṭi). His Middle Way lets the watch keep ticking, but only as a dependently-arisen, empty phenomenon: conventionally valid, never self-powered. Even proposals like Yogācāra’s ālaya-vijñāna are, in Candrakīrti’s reading, only conventionally posited; under ultimate analysis they—like external objects—are dependently designated and empty. Gelugpa Prasangikas, on the other hand, do not accept the ālaya-vijñāna.

The Dzogchen tradition, while distinct in its direct, experiential methodology, arrives at a philosophical conclusion that is highly compatible with Prāsaṅgika Madhyamaka. It fully accepts the conventional world of appearances. As the great Dzogchen master Longchenpa famously quipped, when we stop looking at a mountain, it does not just disappear. Longchenpa is explicit that, on the conventional level, we shouldn’t collapse appearances into “only mind.” He distinguishes the perceived appearance (snang ba) from the object that appears (snang yul). The object that appears is not the mind, he argues, because “it remains where it is when one is not in its presence and does not change its position when one goes elsewhere,” and because it shows features like color and shape that the mind itself does not (At the same time, he states that these appearances are also not other than the mind, because no external object can ever be established as separate from the delusory perceptions of the mind.). What is mental is the “mere perceived appearance,” i.e., how the mind registers the object; confusing these two is “reifying deceptive things and assuming them to be true.” This is precisely why, in ordinary life, mountains don’t vanish when you look away, even while they are empty of any intrinsic essence.

Having secured that commonsense point, Longchenpa then performs the ultimate analysis: that phenomena are illusory. He repeatedly uses the eight similes of illusion (dream, magical display, mirage, echo, city of gandharvas, reflection, apparition, etc.) to show that appearances function and seem real, yet are unfindable under analysis — “vividly appearing, but without any reality of their own, like a reflection in a mirror.” When analyzed, the external apprehended object is found to be emptiness, as it dissolves into partless atoms which are themselves non-existent. Objects are realized to be "unreal", "delusory appearances of the mind". To be clear: on the conventional level, outer objects are accepted precisely because they are functional, publicly corroborated, agreed upon by unimpaired senses and worldly consensus. In the Buddha’s own words—later cited by Candrakīrti—‘The world argues with me; I do not argue with the world. What the wise in the world agree exists, I too say exists; what they agree does not exist, I too say does not exist.’ What is rejected is not the functioning world but the reified sense that objects possess some intrinsic essence ‘out there.’ And thus the Buddha also said:, "’All exists’: Kaccana, this is one extreme. ‘All does not exist’: this is the second extreme. Without veering towards either of these extremes, the Tathagata teaches the Dhamma by the middle: {The Buddha then continues with an exposition on Dependent Origination.}".

Dzogchen texts add that Buddhas still employ concepts and can designate individual things conventionally, yet they do not misapprehend these designated phenomena as independently or inherently existing. Many people—even some teachers—assume that full awakening means a permanent mental blankness with no thoughts or concepts. Authoritative Dzogchen texts explicitly deny this. They explain that, even for a buddha, thoughts, labels, and speech can still arise as part of the enlightened display, and that Buddhas still have concepts of individual objects; the difference is that these appearances self-liberate as they arise and these conceptual individual objects are not grasped or reified as independently existing.

Likewise, on the ultimate side, the internal apprehending consciousness—when examined—has no foundation and no root: it is a self-clarity that is ultimately baseless. Thus, under analysis, neither external object nor internal subject can be pinned down. What remains, in Dzogchen terms, is the indivisible unity of primordial purity (ka-dag, emptiness) and spontaneous presence (lhun-grub, the display of appearances).

Dzogchen reframes this union of the two truths through the lens of rigpa—often translated as “knowledge” (vidyā)—as spontaneous presence (lhun grub) naturally arising from the empty basis of primordial purity (ka‑dag). Spontaneous presence is presented as the display “out of which all phenomena of saṃsāra and nirvāṇa arise, and into which they are absorbed,” i.e., the whole field of appearances or conventional reality. In classical Dzogchen, the inseparable pair ka‑dag (primordial purity) and lhun‑grub (spontaneous presence) plays the same structural role that the two truths (ultimate/conventional) play in Madhyamaka, though the idiom is more experiential: ka‑dag ≈ emptiness (ultimate) and lhun‑grub ≈ the ceaseless display of appearances (conventional). Thus, saying that lhun‑grub is Dzogchen’s way of talking about dependent arising is broadly correct—provided we remember Dzogchen stresses lhun‑grub’s “already‑complete,” uncontrived spontaneity, whereas Madhyamaka usually presents a step‑wise conditioning. In Madhyamaka terms (MMK 24:18), dependent origination = emptiness = the Middle Way: “Whatever is dependently co‑arisen, that is explained to be emptiness; that, being a dependent designation, is itself the Middle Way.” Dzogchen agrees that appearances are empty and dependently arisen, but adds an experiential distinction: the twelve‑link chain driven by avidyā is afflicted dependent origination, whereas the ceaseless, effortless display of lhun‑grub is described as unafflicted causality (unafflicted dependent origination)—the way appearances manifest from rigpa without ignorance (See: https://www.awakeningtoreality.com/2009/10/dzogchen-rigpa-and-dependent.html). Caveat (Dzogchen and “two truths”): Dzogchen uses ka‑dag / lhun‑grub to functionally mirror ultimate/conventional, yet classic sources emphasize that, in the direct view of rigpa, two truths are not asserted as a final division; even Nyingma/Dzogchen commentaries that do speak of “two truths” do so to show their inseparability (appearance/emptiness), and then immediately point beyond conceptual fabrication. 

Regarding the brain and the Hard Problem of Consciousness, the Madhyamaka analysis would be applied to the brain itself. How do we know of the brain? Through diagrams, scans, and scientific explanations. In every case, the "brain" as an object of knowledge is part of the same perceptual triad: an organ, an object, and a consciousness. Therefore, the brain cannot be the ultimate, independent, physical substrate for mind. Rather than "sidestepping" the Hard Problem, the Madhyamaka approach shows that the problem itself evaporates. Because "brain," "mind," and "causation" are all seen as equally dependently designated constructs, the dualistic framework that creates the Hard Problem is shown to be a conceptual error from the start.

It is also crucial to note that classical Buddhism—including Nāgārjuna—does not treat consciousness as a late-stage product of grey matter. In Abhidharma and Madhyamaka alike, each moment of mind is said to arise from the immediately preceding moment of mind, not from physical substance; matter is merely one of many cooperative conditions. This continuity of the mind-stream (saṃtāna) across death underpins the standard Buddhist teaching of rebirth (see example) —a cycle Nāgārjuna takes for granted when he speaks of karma’s “non-ceasing” causal efficacy. Because mind is neither a permanent soul nor a neuronal epiphenomenon, strict physicalism counts as one of the “annihilationist extremes” (uccheda-dṛṣṭi) already rejected in the early suttas and reiterated by Nāgārjuna. Conversely, positing an eternal, self-contained consciousness would fall into the opposite extreme of eternalism. His Middle Way avoids both by analysing the mind-brain-world nexus exactly as he analyses the watch: conventionally valid and functional, dependently originated, and empty of intrinsic essence. So when you see a watch ticking after you look away, Buddhism happily says: yes, causally efficient processes continue outside your present cognitive frame—but neither those processes, nor the mind that later cognises them, are reducible to a self-standing physical substrate.

Finally, you raise the most important concern: that this nonduality is just a subjective experience, "confined to within the mind." From the Prāsaṅgika perspective, the nonduality being pointed to is not the merging of a subject (mind) with an object (the world).

It is the realization that the very concepts of "subject" and "object" are themselves empty, dependently arisen imputations. The goal is not to dissolve the world into the mind (idealism) or to see the mind as a product of the world (physicalism). The goal is to see that the very boundary we draw between "in the mind" and "outside the mind" is a conceptual fabrication. Only one who has attained enlightenment recognizes an object’s ultimate nature – that it appears, but is devoid of any intrinsic existence – as the direct contemplation of absolute truth transcends any intellectual concept or duality. It's also important to add one subtle but critical Madhyamaka point: even that state of enlightened gnosis is itself seen as empty of inherent existence, thus avoiding any final lapse into positing a new absolute.

So, the nonduality Nāgārjuna points to is not a state within the mind; it is the collapse of the conceptual framework that creates the illusion of an "inner mind" and an "outer world" in the first place. The "problem" of the watch's independent functioning only exists if you first grant the watch and the mind an independent, inherent existence that they do not actually possess.

Thank you again for a fantastic question that gets to the very core of the issue.