Chapter 1. The Nature of Things
“Dhamma” (Pāli) or "Dharma" (Sanskrit) is a term that will be used to refer to things, may they be material or conceptual, forms or names, matter or mind or feeling, big or small, visible or invisible, past or present, born or unborn, etc. A chair, an animal, air, molecules, atoms, nuclei, quarks, beauty, goodness, hatred, happiness, sadness, properties, characteristics, learning, teaching, etc. are all dhamma. We will use the word “dhamma” in both singular and plural forms.
All dhamma have one common characteristic of being in the same state called “anattatā”. Anattatā is another Pali term that means the state of voidness, having no ultimate identity. An automobile is merely an assembly of parts, all of which can be broken down further, down to molecules, atoms, and further.
Dhamma are said to be “saṅkhatadhamma” (or “saṅkhāradhamma”) if they are in two additional states, viz. “aniccatā”, the state of constant change, impermanence, and uncertainty, and “dukkhatā”, the state of constant struggle and instability. Thus, all saṅkhatadhamma that have come into existence (birth) will necessarily transform (decay, getting sick) and eventually go out of existence (disintegration, death). Dhamma that are not saṅkhatadhamma are called “asaṅkhatadhamma” (or “visaṅkharadhamma”).
In Buddha’s own words,
“Sabbe dhamma anattā” ;
“Sabbe saṅkhāra aniccā” ;
“Sabbe saṅkhāra dukkhā”
where "sabbe" means "all".
Mathematically, let D be the set or collection of all things in the universe and beyond. We shall refer to the elements in D as “δ-elements”. A δ-element may be material, conceptual, known, or still unknown. All δ-elements have one common fundamental property, called “α-property”. One way to describe this fundamental property is to say that every δ-element has no ultimate identity. What this means is that when a δ-element is analyzed, the ultimate finding will always be nothingness, emptiness, or void.
The set D can be partitioned into two disjoint subsets:
D = S ∪ A such as S ∩ A = ∅.
Members of S are δ-elements with two additional properties to be described later. Members of A are δ-elements that do not belong to S, i.e. A = D – S. Let us call the elements of S and A “σ-elements” and “α-elements”, respectively. Every σ-element is always in the state of instability and constant decay and we shall refer to this characteristic as “β-property”. Furthermore, every σ-element is dynamic and always in the state of change, and thus transitory; this characteristic of the σ-elements shall be referred to as “γ-property”.
In sum, all δ-elements have α-property and some, the σ-elements, have β-property and γ-property as well, while α-elements have only α-property. In symbols,
S = { δ ∈ D : δ has α-property, β-property, and γ-property }
and
A = { δ ∈ D : δ has only α-property }.
Finally, note that if A = Ø, then D = S . Generally, Buddhists believe that A ≠ Ø. Since the present approach is mathematical and scientific, whether A is a null set awaits proof and/or discovery.
Putting the above two (nonmathematical and mathematical) parts together, it should be obvious that δ-elements, σ-elements, and α-elements refer to dhamma, saṅkhatadhamma, and asaṅkhatadhamma, respectively, while anattatā, dukkhatā, and aniccatā are mathematically referred to as α-property, β-property, and γ-property, respectively. Note, however, that the latter three concepts are undefined, i.e. are not defined in terms of previously defined concepts, but are only described by appealing to intuition and everyday experience. Mathematicians call this kind of concepts “primitive notions”, “primitive terms”, or “undefined terms”. In that view, “dhamma” or “ D ” is also considered as a primitive term. Furthermore, the above three statements made by the Buddha can be viewed as “axioms”, as in mathematics, and “laws” or “principles”, as in physics. In other words, they should be considered as starting points of the presently new discipline being proposed herewith. Those who are familiar with Buddhism know that these axioms or laws, known as “the three universal characteristics of things”, constitute the very core of Buddhism or the heart of Buddha’s teaching. Some serious practitioners of Buddhism even believe that if and when they truly understand these concepts, they would become “enlightened” or would have reached “nibbana” (or nirvana). Therefore, one can consider all that will follow as further illumination for these basic concepts. Since Buddhism is neither a purely logical system nor a philosophy per se, but a discipline with specifically practical training and self-development, the insight to be obtained from its practice will build up one’s intuition for these fundamental notions. In any case, whether the above axioms and primitive terms are sufficient to axiomatize Buddhism or the formalism will lead to an extension of modern science remains to be seen.
1. Since everything is anattā (in the state of void, lacking an ultimate identity), in our daily living we must not cling to anything as if it is real or fix our view to it. We must not fall into a delusion that we can possess it or take it to be ours.
2. Since everything is aniccā (in the state of constant change, impermanent and uncertain), in our daily living we must be nimble, ready to change with situations under the presently moving circumstance. We must be dynamic. How can we live in harmony (and thus at peace) with things in this dynamic world if we are static and resist to changes? In order to harmonize with things around us, we must therefore be dynamic in every nanosecond (so to speak) of our life, as are all the electrons in every atom in our body.
3. Since everything is dukkhā (in the state of constant struggle, unstable), in our daily living we must constantly keep in mind that everything that we come into contact is necessarily decaying, unstable by its own nature, and will eventually disappear. We ourselves are also unstable and decaying as well. This is just the way things are and we are simply powerless to change this natural course. The best we can do is to recognize it and live wisely.
Continuing to . . .
Application to daily living
1. Since everything is anattā (in the state of void, lacking an ultimate identity), in our daily living we must not cling to anything as if it is real or fix our view to it. We must not fall into a delusion that we can possess it or take it to be ours.
2. Since everything is aniccā (in the state of constant change, impermanent and uncertain), in our daily living we must be nimble, ready to change with situations under the presently moving circumstance. We must be dynamic. How can we live in harmony (and thus at peace) with things in this dynamic world if we are static and resist to changes? In order to harmonize with things around us, we must therefore be dynamic in every nanosecond (so to speak) of our life, as are all the electrons in every atom in our body.
3. Since everything is dukkhā (in the state of constant struggle, unstable), in our daily living we must constantly keep in mind that everything that we come into contact is necessarily decaying, unstable by its own nature, and will eventually disappear. We ourselves are also unstable and decaying as well. This is just the way things are and we are simply powerless to change this natural course. The best we can do is to recognize it and live wisely.
Continuing to . . .
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