Philosophical Fragments by Adam J. Pearson

By Adam J. Pearson

The mystic and painter Pema Lomos asked me today “what is the opposite of appearance?” I answered that the opposite of appearance is nonappearance. The opposite of a bird appearing in a given place, for instance, is a bird not appearing in that same place.

When we take relative perspectives into account, the situation is more complicated than this simple explanation would suggest, however. Appearance and non-appearance both depend on whose perspective we are considering. If we are considering the perspective of a man sitting on a bench in the park, who first sees no bird appear, but then sees a bird fly in (appear in his field of vision) and then disappear off in the horizon, then it seems that he is constant and the bird appears at one time and disappears at another.

If, however, we consider the perspective of the bird, the situation is reversed; the bird is constant and it is the man who first appears (as the bird enters the park) and disappears (as the bird leaves the park).

We can also take both perspectives into account and say that both the man and the observer are constant for an interval of time (the interval during which they are alive) and that they both pass in and out of each other’s field of vision a they move relative to one another.

The important point in this discussion is that appearance and nonappearance are relative to particular observers. When we consider them in any situation, we need to ask from whose perspective or frame of reference we are considering the matter. Life exists in a dynamic dance between appearance and nonappearance out of the perspectives of particular observers.

The unseen can become the seen and the seen can become the unseen relative to a given pair of eyes.  Events and objects dance in and out of view on different length-scales from the level of great clusters of galaxies to the tiny level of subatomic particles.  Our human eyes are but one set of eyes that are observing this great cosmic dance.

By Adam J. Pearson

When I consider the matter carefully, I do not find any absolute, capital ‘T’ Truths in the world; I find only relative, lowercase ‘t’ truths. Relative truths are dependent on relationships between sentences and states of affairs (ways things are) in the world. Since most states of affairs in the world change, most truths are, therefore, themselves subject to change. A true statement can become false over time.

For example, the statement “there is an apple on the table in my kitchen” might be true right now if there is such an apple on the table. Imagine, though, that I am in a hurry to leave my house and run out with the left wide door open. I return home a few days later and find that a deer has stolen off my apple (and there are delightful deer droppings all over the house)! In this situation, the statement “there is an apple on the table on the table in my kitchen,” which was once true, is now false. This is because its truth depends on its relation to what’s actually present on my table; once the apple leaves that table, the sentence turns from true to false.

Not even mathematical statements can claim the status of absolute Truth because their truth is relative to particular axioms. In geometry, for instance, the truth of the statement “the interior angles of a triangle add up to 180 degrees” depends on the kind of geometrical space you are working within. On a flat Euclidian plane, the statement is true (see Fig 1.1).

Fig 1.1 – A triangle in a flat Euclidian plane – its interior angles add up to 180 degrees.

In contrast, on a spherical, non-Euclidian plane, the statement is false; the internal angles of a triangle mapped on to a sphere add up to more than 180 degrees (see Fig 1.2).

Fig 1.2 – A triangle mapped on to a spherical surface – its internal angles add up to more than 180 degrees.

On a hyperbolic saddle-shaped plane, the statement is also false; the internal angles of a triangle mapped onto a saddle-shaped surface add up to less than 180 degrees (see Fig 1.3).

Fig 1.3 – A triangle mapped on to a saddle-shaped surface – its interior angles add up to less than 180 degrees. 

As the case of the triangle mapped on to different shapes of geometrical surfaces shows, even in mathematics, the truth of a statement depends on the context in which we are considering it and the ways we define its key terms. Within a given system, exactitude and certainty can be established, but the same statement considered in different geometries can have different truth-values. This, as we saw, is the case for the internal angles of the triangle, which add up to exactly 180 degrees on a flat surface, more than 180 degrees on a spherical surface, and less than 180 degrees on a saddle-shaped surface.

Even simple arithmetical statements and simple geometrical statements like a “triangle has three sides” ultimately depend on basic axioms and definitions.  Outside of the realm of pure mathematics, when we are speaking about conditions and types of things and states in the physical universe, the relative nature of truths is all the more apparent. There are scientific laws that hold at certain length-scales, but that break down at the level of the really large (cosmological level) and the really small (quantum level).

The point I am making here is not that ‘no statement is true,’ but that statements are true relative to states of affairs (ways things are) in the world. When the states change, the truth-value of the sentences that depend on them also change. This fragile relativity of truth is an epistemological consequence of the changing nature of our physical universe.

By Adam J. Pearson

Recently, I went to a dinner party and there was a 4 and a half year old girl there. Her name was Beth and she was adorable. She showed me how to play this game with blocks where you have to build pathways for a prince to walk across to his princess and vice versa. She came up with solutions that weren’t in the answer book, but I validated them anyway; they were creative and still made sense.

She laughed uncontrollably for no reason and started singing spontaneously. I couldn’t stop laughing. She called me her big brother. It was so heartwarming. I picked her up and spun her around and put her back down and she started laughing and got dizzy – I put a pillow under her so she wouldn’t hurt herself.

When I had to leave with my family, she clung to my coat. I pretended she was really strong and that I was unable to budge… “Ughhh… Beth, you’re too strong! Big brother has to go home noowwwww…” I said as I strenuously tried to pull myself from her powerful 4 and a half year old hands. She laughed as she pulled my coat and I fell on the ground from her mighty strength. Finally, my family and I left. Her father told me the next day that she had fallen asleep the moment she got home.

Beth reminded me that happiness can always be found in our present moment, that we can have great fun with the smallest things. Adult life is more complicated than the life of a child; we have more responsibilities, but we need not lose touch with the spontaneity, joi de vivre, wonder, curiosity, and love for fun that children reveal to us. We need to always remember that while adults have many lessons for children, children have many lessons for adults as well. Our challenge is to balance our adult knowledge with those beautiful and innocent lessons from children that point the way to a fulfilling life.

By Adam J. Pearson

Today, Ernie Jacobo asked me a fantastic question. His question was “why is logic so vital to human life?”

Logic separates invalid arguments from valid arguments. If the premises are true and the arguments are valid, then we have sound arguments. Sound arguments allow us to move from trustworthy premises to new conclusions. Logic is vital for the progress of all sciences and all inquiries into matters of life that admit of logical analysis.

Of course, logic has its limits; it can’t tell us if premises are true or false, only if they fit together in a way that allows us to validly derive a given conclusion from them.

Moreover, logical units, like sentences, can only handle discrete pieces of information at a time; thus, they must always leave something out. Logic places bits of information into frames so that we can handle them with our limited human rational capacities, but what is left out of the frame is always greater than what is encompassed by it.

With that said, discursive, word-based thinking without logic is muddied, confused, vague, ambiguous, and prone to drawing conclusions from premises from which they do not follow.  Logic provides a reliable structure for our reasoning.  It ensures that we are validly inferring what our premises bear out.  It helps us to detect flaws in poor arguments just based on the way their sentences fit together.  It is a kind of safety net for our thinking.

Of course, just as a net has holes through which some things fall, so does logic.  Logic tells us that given sentences with certain truth-values arranged as premises and conclusions, certain arguments are either valid or invalid. It does not tell us, however, whether a given sentence is true or false; for that, we must look beyond logic into, for instance, empirical verification.  We need to look to the data, or as Bertrand Russell used to say, “to the facts.” These facts are outside the scope of logic; the domain of logic is the basic logical structures of sentences, not their contents.

By Adam J. Pearson

Fig 1.1 – The Universe. Each white dot represents a Supercluster of galaxies. 

Today, I started reading an amazing astronomy textbook entitled The Cosmic Perspective. The opening of the book really put the size of the Earth in cosmic perspective. If you think the Earth is the center of the universe and tremendously important in a universal sense, consider this:

In the vast universe, there are countless ‘superclusters’ in which groups of thousands upon thousands of galaxies are tightly packed together together. Superclusters are giant structures that loosely form giant chains and sheets that resemble strands in a giant cosmic spiderweb.

Between the vast superclusters are voids containing few, if any galaxies at all. The universe is itself “the sum total of all matter and energy, encompassing the superclusters and voids and everything withing them” (The Cosmic Perspective, 4th ed., pp. 2).

Fig 1.2. – Our Neighbouring Superclusters – In this image, you can see the Virgo Supercluster or Local Supercluster relative to the Superclusters that are located around us.  These are our cosmic neighbours, each composed of countless groups of galaxies. 

In our own Local Supercluster (also known as the Virgo Supercluster), there are even denser packs of galaxies called ‘groups’ or ‘galaxy clusters‘ (groups of galaxies with more than a few dozen members). Our own Milky Way Galaxy is one among 40 other galaxies in what we call the Local Group. We call it “Local” because the galaxies in this group are located, relative to the entire universe, closest to ‘home.’

Fig. 1.3 – Inside the Virgo Supercluster or Local Supercluster - This is a diagram of the inside of the Virgo Supercluster. Each dot represents a group of galaxies. The Local Group is the group within which our own Milky Way Galaxy is located.  

Fig 1.4 – Inside the Local Group – This image depicts the inside of the Local Group of galaxies and the galaxies immediately located around our own Milky Way.  All of the above images are from The Atlas of the Universe. 

Within the Milky Way, there are more than 100 billion stars of which our Sun is but one. Our own solar system orbits this relatively small star, the Sun. This solar system is located a little over halfway from the galactic center to the edge of the Milky Way’s galactic disk.

Fig. 1.5 – The Milky Way Galaxy – This is an artist’s rendition of the Milky Way Galaxy with the position of our Sun identified. 

Fig 1.6 – The Orion Arm of the Milky Way Galaxy – This is an image of the Orion Arm of the Milky Way Galaxy in which our Sun is located. Notice how small of a dot our Sun is within the larger arm. 

Within the solar system, our home planet, the Earth, orbits the Sun. It is the fifth-smallest planet in our solar system. Upon this planet, we, human beings, move like tiny ants in the great, unfathomably large vastness of the universe.

Upon this small rock, we live, and move, and have our being.  We visit coffee shops and go to school and work in offices and get into arguments and cry and laugh and smile and live and die.  And all around us, billions of galaxies whirl, each containing billions of stars with billions upon billions of planets and moons orbiting them.  Our home, the Earth, is like a tiny grain of sand on a gigantic cosmic beach.  And we are like infinitesimally small bacteria moving upon that tiny grain of sand.

Fig. 1.7 – The Earth – Our home planet, the fifth-smallest planet in our solar system.

Fig 1.8. – An Aerial View of Montreal – the city within which I presently sit, 13.75 ± 0.13 billion years after the Big Bang, 4.54 billion years after the formation of the Earth, 23 years after my birth, writing the article that you are now reading.