Applied Deliberation

These perspectives offer a glimpse into the way I see the world.

On Life

It is an indisputable fact that pollution and global warming have become enormous global problems. While making precise estimates at such scale is difficult, the biggest human contributors are still known to be the mining, manufacturing and livestock industries [1], [2].

I cannot possibly fix these problems by myself, but I can at least try to lead by example, as long as doing so does not require making it my sole goal in life. This does not mean relegating to virtue signaling on this website, but rather making concrete lifestyle choices.

To that end, I avoid producing waste by only buying what I need and selling or giving away things I no longer need. If something breaks, I always consider repairing or repurposing it before throwing it away. It is quite unfortunate how so many products — especially consumer electronics — are designed to be difficult or impossible to repair these days.

On another note, I follow a mostly vegetarian diet, because it is a decent compromise between sustainability and convenience, not to mention that factory farming makes me uneasy. I am not too strict or pushy about my diet, however, and I would certainly never throw away perfectly good food for ideological reasons.

One more thing worth bringing up is that I only travel when I have a good reason to, such as meeting people or going to work. Even though I have a driver’s license, I prefer traveling short distances by bicycle or by using public transportation.

Noteworthy communities that espouse similar values include

• the Extinction Rebellion,
• the Right to Repair coalition and
• Open Source Ecology.

On Culture

Intellectual property laws give software companies the power to exploit their customers using malicious proprietary programs and academic publishers the means to keep laypeople from having affordable access to publicly funded research. Such laws also stifle the creative freedom of small artists and waste resources on pointless lawsuits between large corporate entities. Overall, intellectual property laws create artificial scarcity, which slows down collective progress [3].

I vehemently oppose intellectual property laws and their manifestation as copyrights, patents, trademarks and trade secrets. Cultural works should be free for anyone to use, modify and redistribute without legal, social or technological restrictions. This is why I support free software projects and favor using free licenses for my own works as well.

While the principles of free cultural works may seem economically unviable, it should be noted that the word free refers to libre (being free of restrictions) rather than gratis (being free of charge). There is no contradiction in the production or distribution of free cultural works costing money. Indeed, even I have made money by writing free software.

Communities supporting free cultural works include

• the Free Software Foundation,
• Creative Commons and
• many hackerspaces, such as Hacklab.

On Media

The world is more connected than ever before, but loneliness and social isolation are still on the rise [4]. While new technologies, such as smartphones and the Internet, seem to be exacerbating these problems [5], [6], it is worth pondering why this might be the case by looking at the situation from a few different angles.

Parasocial interaction is a psychological phenomenon, where a passive audience member forms an illusory relationship with the persona of a performer [7]. In the context of mass media, such as radio, television or live streaming, it is not uncommon to see parasocial relationships between celebrities and their fans.

There is nothing inherently wrong with following your favorite celebrities or empathizing with their fabricated struggles, but it is not a healthy substitute for social interaction [8]. Relying on just parasocial interaction deprives you of reciprocation and distorts your self-image over time. As an extreme example, it is quite disheartening to see lonely men obsess over live streams of pretty girls with cat ears and donate their earnings to said girls in a desperate plea to be noticed.

The issues relating to parasocial interaction are not limited to mass media, as similar concerns and exploitation arise from the use of traditional social media [9]. While social media services may work as publishing platforms or chatrooms, the predominant way to use most such services consists of browsing through other people’s posts and clicking the like button or leaving a short comment. This is not only an unnatural way to stay in touch with people, but also erodes the norm that conversations should be private.

It is not a coincidence that social media services encourage putting your whole life on display and reward you for carrying out all kinds of inane tasks. They do this by design, because your unrelenting attention is what keeps them operating. Without your engagement, there would be no personal information to sell and no eyes to look at their targeted advertising. This is the essence of surveillance capitalism [10].

Being treated like a rat in an operant conditioning chamber is not the only downside of surveillance capitalism. By giving your personal information to a third party, you are also putting yourself at risk, if — or rather, when — your information gets leaked, because software security is a farce. Constant exposure to targeted advertising also influences your thoughts, even if you actively attempt to ignore it [11]. Advertising would not be so profitable if it did not work.

Besides advertising, media companies promote certain narratives that their founders or supporters think people should believe. Whether or not there is a grand conspiracy behind the choice of narratives, I am at least personally appalled by the apparent sexualization of culture [12], [13] and idolization of irresponsible lifestyles. Regardless of what the media would have you believe, never having been interested in casual sex or short term relationships does not make me defective or unfit for finding a life partner, just like caring about the environment does not make me a sissy. That would be absurd.

As it stands, I deliberately avoid using mass media and traditional social media, because they do not make me happy. Only a fool would voluntarily subject themselves to something they know is bad for them.

I do not know any communities focusing on these matters, but I would like to. If you know any influential ones, let me know, so that I can list them here!

On Mathematics

If you push a mathematician enough to get them to answer what, in their view, defines mathematics as an activity, they are quite likely to tell you that it is “the study of ZFc axioms and their consequences”. This answer is not only unimaginative, but also indicates that they want you to stop asking uncomfortable philosophical questions. I think stopping is the opposite of what you should do and I am far from the first or most influential person to hold this opinion.

Most mathematicians feel that mathematics has meaning, but it bores them to try to find out what it is.

— Errett Bishop [14]

Let me set up a more elaborate strawman to explain what bothers me with the dismissive attitude towards the foundations of mathematics. Our strawman shall be embodied by a mathematician called Richard, who works in the fashionable field of harmonic analysis and sometimes indulges in recreational combinatorics. He does not care much about philosophy or programming, unless they happen to yield immediately useful applications.

What would Richard answer if you asked him “is 3 a subset of 4”? If he interpreted 3 as the natural number three and 4 as its successor and encoded them using the von Neumann ordinals, then he would tell you that “yes, indeed, 3 is a subset of 4”. Alternatively, if he interpreted 3 and 4 as real numbers or used some other encoding for natural numbers, such as the Zermelo ordinals, then he would tell you that “no, in fact, 3 is not a subset of 4”.

Now, if Richard had any sense left in his head, he would quickly point out that the answer does not actually matter, because the question is meaningless. It would be difficult to disagree with him on this, but do you think he could explain why? That is, do you think he could provide a sensible answer if you asked him “how to systematically distinguish meaningless questions from meaningful ones”? I doubt it, so let us stop picking on Richard and focus on the question of meaning itself.

Throughout the history of mathematics, many schools of thought have emerged to explain the philosophical nature of meaning. I am personally most fond of intuitionism and formalism with flavors of constructivism and finitism, because they are reminiscent of the way physicists see the world and mesh well with the theory of computation. I greatly enjoy theoretical physics and programming, so anything that lets me look at the world through the respective lenses is jolly good.

Even though intuitionism and formalism were once thought of as polar opposites, they actually complement each other quite nicely. In very broad strokes, you could say that intuitionism pertains to the mind as formalism pertains to the machine. Let me provide some background to explain this analogy in more detail.

The question where mathematical exactness does exist, is answered differently by the two sides; the intuitionist says: in the human intellect, the formalist says: on paper.

— Luitzen Brouwer [15]

Intuitionism was originally conceived as an investigation into mathematics as a mental activity. Its main tenet was that mathematics is a creation of the mind and, as such, the only meaningful way to do mathematics is to experience it. While intuitionism has since become associated with constructivism, its answers to the fundamental epistemological and ontological questions have largely remained the same.

The intuitionistic concept of truth differs slightly from its classical counterpart. Classically, the truth of a statement can be established either by constructing concrete evidence for it — resulting in a direct proof — or by showing that the lack of evidence would lead to a contradiction — resulting in an indirect proof. Intuitionistically, only direct proofs are allowed, although the proof may still be of a statement that itself is a refutation. This subtlety comes with some benefits and drawbacks.

The biggest drawback arising from the different concept of truth is probably its slew of counterintuitive consequences. Most notably, the law of excluded middle \(P \vee \neg P\) is no longer true and the principle of double negation \(\neg \neg P \leftrightarrow P\), the rule of material implication \((P \to Q) \leftrightarrow \neg P \vee Q\) and the distributive property \(\neg (\neg P \wedge Q) \leftrightarrow P \vee Q\) are weakened from equivalences to implications. Not all is lost, however, as these properties are still irrefutable and remain true in many special cases. That is, we can still prove \(\neg \neg (P \vee \neg P)\) for arbitrary propositions and \((n = p) \vee \neg (n = p)\) over the natural numbers, among other such things. We just have to be careful not to overgeneralize.

The biggest benefit arising from the different concept of truth is definitely the consequent refinement of the concept of existence. Classically, it is possible to end up in a situation, where an object exists, but no example of it can be given. This paradox comes up if you try to find a nontrivial ultrafilter on (the powerset of) natural numbers or a well-ordering of the real numbers, for instance. Intuitionistically, such a situation is impossible, because the existence of an object can only be established by providing a concrete example in the form of a proof by construction. If we absolutely need a nonconstructive axiom \(A\) to prove some proposition \(P\), we can still avoid the paradox by using the axiom as a hypothesis and proving \(\Gamma \vdash A \to P\) instead of \(\Gamma, A \vdash P\). We just have to be explicit about our assumptions.

In fact all mathematicians and even intuitionists are convinced that in some sense mathematics bear upon eternal truths, but when trying to define precisely this sense, one gets entangled in a maze of metaphysical difficulties. The only way to avoid them is to banish them from mathematics. This is what I meant by saying that we study mathematical constructions as such and that for this study classical logic is inadequate.

— Arend Heyting [16]

If you think intuitionism is just a tool for reaching ever greater levels of mathematical perversion, let me present another perspective from the direction of moral philosophy. In order to make the presentation more concrete, I will use little George and his fictitious adventures to demonstrate my ideas.

I do not call George little in jest, for he is still a small child and quite a poorly behaved one at that. In an attempt to teach him some manners, his parents have established two strict rules: if George physically fights with other kids or lies to his parents, he will get the stick (or some other punishment that is better for his emotional development).

Despite the risk of punishment, one day George runs up to his parents and proudly proclaims that “I just punched Leo in the mouth for calling me a filthy set-theorist”. Now, what should his parents do? If George is telling the truth, he should be punished for fighting, and if he is not telling the truth, he should be punished for lying. Classical parents would apply the law of excluded middle and punish George for breaking one of the rules, while intuitionistic parents would have to find more evidence before taking action. Similar situations come up in the analysis of legal systems, but let us not get carried away and, instead, move on to formalism.

In logic, there are no morals. Everyone is at liberty to build up his own logic, i.e., his own form of language, as he wishes. All that is asked of him is that, if he wishes to discuss it, he must state his methods clearly, and give syntactic rules instead of philosophical arguments.

— Rudolf Carnap [17]

Formalism refers to the idea that mathematics is a meaningless game of symbol manipulation and does not have any connection to reality. The formalist ideology does not motivate the foundational axioms of mathematics or explain how to interpret their consequences, which makes it compatible with quite a few other philosophies. Jokingly put, formalists subscribe to the idea that “the rules (of inference) are made up and the points (in space) do not matter”.

The lack of philosophical commitment is part of what makes formalism so popular among mathematicians like Richard. However, another big part is played by the recent increase in applications of formal methods to programming language theory, software engineering, systems design and constructive mathematics [18]. It is difficult to argue against things that have repeatedly proven themselves to be unreasonably effective [19].

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.

— Eugene Wigner [20]

I think that we — meaning you, mainly — must continue to try to explain why the logical side of science — meaning mathematics, mainly — is the proper tool for exploring the universe as we perceive it at present.

— Richard Hamming [21]

In summary, intuitionism can be used to describe the rationale and guide the design of the tools afforded to us by formalism. This complementary relationship provides a sensible answer to the question of meaning and has motivated the inception and investigation of several foundational metatheories, such as Martin-Löf type theory [22] and the calculus of inductive constructions [23], [24].

Alas, not all is sunshine and roses in the land of foundational metatheories. Even though we have a decent grasp of truth and existence, the question of identity — or, as it is also known as, equality — is still open and so is the derived concept of uniqueness. Perhaps one day homotopy type theory [25], cubical type theory [26] or some other univalent conjuration will save us from the darkness. Nobody knows, but hope dies last.

Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

— Bertrand Russell [27]

Communities rife with intuitionism and formalism often revolve around

• dependent types,
• univalent mathematics and
• proof assistants, such as Coq or Agda.

References