In a previous post from over a year ago, I had tried to highlight the differences between facts and opinions. Even back then, my feeling was that that writeup was mostly redundant and unnecessary, as I assumed pretty much every reasonable person knew the difference. So it came to me as a huge surprise when during a recent conversation with a good friend of mine, one of the smartest and most well-read people I know, I realized that he kept confusing facts with opinions. Hence the urge to write this note.

Our conversation started with a discussion about which one of the more famous ChatBots has a better chance of getting things right. Which naturally led to a series of exchanges about how accurate and factual their training data was. My point was that a large majority of the content on the Internet, even before the ridiculous recent AI boom, was already not accurate or factual. Because, according to some studies, falsehoods have six or seven times higher chance of being read and forwarded than facts. Basically, facts are usually boring, but falsehoods can be quite sensational. And with the advent of the recent AI tools, there is going to be so much more clutter on the Internet that finding accurate information and factual data on it is likely to become a science of its own.

Now, if those AI companies (who themselves, btw, are proliferating like mushrooms), indiscriminately use the Internet content to train their generative models, such models while being likely to reasonably accurately mimic the same content at their outputs, will simply be adding to the nonsensical clutter, much more than providing/summarizing useful information. To quote a now-famous phrase, “your model’s outputs are as reliable as the data it was trained on.”

But things started going downhill from there. We had a brief conversation about the nature of reality, which obviously was too philosophical and way over my head. So we agreed to move on from that level of depth, and limit our conversation to what is relevant to our day-to-day lives. While I was trying to highlight, in some examples, whether we were dealing with facts or falsehoods, my friend kept repeating that I couldn’t say that, and that “your facts are as good as your assumptions.” As I mentioned above, he is very well-read too, so he started referring to the works of some 19th century philosophers, as well the works of Godel (the incompleteness theorem) and Einstein (the theories of relativity), as evidence for his assertion. If it were anybody other than him, I would assume that he was resorting to name dropping to scare me off the conversation. But with him, I knew that he really had some concrete points and arguments in his mind. Still, I was a having a difficult time understanding what he meant.

While, admittedly, I haven’t read much about philosophy and especially the works of philosophers from the previous centuries, I am familiar with some of Godel’s and Einstein’s works. So I was becoming more and more confused about how he was trying to relate those works to our conversation about facts and falsehoods. Because his assertion that the incompleteness theorem or the theories of relativity imply that the thing called “fact” either does not exist or is purely subjective, did not make sense to me at all.

I tried to explain my understandings that none of those theories provide an opinion about whether facts exist or not. Self consistency of a mathematical construct, or lack thereof, has nothing to do with whether the statement “It is raining right here, right now” is true or false, or even if it can take a value other than true or false. The notion that no self-consistent mathematical construct, under certain assumptions that Godel had considered, can exist, does not mean that there are no facts, and that everything is just a subjective reality. I emphasize, again, that we are not discussing at a very deep philosophical level where the very notion of reality is under question. I understand that one may argue that there is nothing in the universe except for a bunch of floating brains that are imagining any and every observation that we believe to be real. Some may even argue that even those brains, and the universe itself, as we know it, does not exist, and there is only a notion of “I”, whatever that is, whose “thinkings”, whatever they mean, are the only things that exist. Or some may assume that we live in a simulation that is imagined and developed by some superior beings.

But whatever our assumption is about the reality, we can never argue, e.g., during a tax audit, that what you, the auditor, believe is an incorrect or false deduction on my tax return documents for a dependent for whom I cannot provide a name or any identifying information, is subjective and only valid from your point of view, but from where I stand, it is nothing but truth. Or even that the deduction that you are seeing on those documents is just your opinion, and in my opinion, that line and the words and the numbers that are written on that line actually do not exist.

To make things simpler, doesn’t the very notion that we sign, under penalty of perjury, that the information we provide on the tax return documents are true and factual, mean that at least at the level of our day-to-day lives and interactions, we all do have a common understanding of what fact and truth is, and what fiction or falsehood looks like? I know some are going to be quick to point out that those statements involving “under penalty of perjury” always come with a qualifier of “to the best of my knowledge.” To which my answer would be, so what? That I may or may not have knowledge about “something” does not provide any information about that “something” itself (including its truth value, whatever that means); it only provides information about the state or level of my knowledge (about that “something”). That is, “to the best of my knowledge” does not mean that the truth, as a quality, is subjective and depends on me as an observer. But rather that my knowledge about that quality is dependent on me as an observer.

As for the theories of relativity, while it is true that according to those theories there is no absolute frame of reference, a frame that some could refer to as the true frame or the God’s frame or anything like that, and that the numeric values of certain measurements of certain “attributes” of objects in relation to space and time are relative and can be different from one frame to another, it does not say anything about whether those attributes themselves “actually” exist or not. If anything, the very notion that there are deterministic transformations (talking about objects and events at macroscopic levels) that we can use to convert the numeric values of the measurements of one observer (in one frame of reference) to the ones of another observer (in another frame of reference), may be considered as an evidence for the existence of a unique underlying “attribute” (please note that by this, I do not mean its numeric value). Otherwise, if the observations of different observers were purely subjective and only dependent on the observer, how could we predict the numeric values of one observer’s measurement based on the information we have about the measurement results of another observer and the relative motion of the two observers?

To make the long story short, I provided the following example, and asked him what he thought about it: “Imagine someone committing a crime, e.g., murdering another person in broad daylight, and in front of many many witnesses, whose testimonies all agree with each other. Even more, there are video and audio recordings of the incident that anyone can examine after the fact, and see what happened, for themselves. On the last day of the trial, and as their last statement in the court, that person stands up and addresses the judge and the jury as following: whatever those witnesses observed and testified to, are subjective and valid only to those witnesses. Even whatever you can observe in those video and audio recordings is subjective and valid only from your point of view. But from my point of view, there was no murder, there was no victim, heck there was no such day, at all. And that you cannot convict me based on your subjective facts or realities while mine are different from yours. Even more, fact or reality does not even exist, so there is no basis on which you can convict me of anything.”

My friend’s response was that he would convict that person if it were up to him, like anybody else would in that situation. But that that conviction itself would not be a fact and could change with additional information in the future, as it has happened many times in the past. It was at that point that I realized we had been discussing or arguing about different things, and that he had been confusing facts with opinions. It is, of course, well known that courts rulings are not facts, but opinions. In fact, most court rulings actually start with explicit mention of that, e.g., “It is this court’s opinion that …” And this is not limited to lower courts. Even the Supreme Court’s rulings are also opinions, not facts, as they often clearly state that it in the ruling itself.

It is true that the justice system deals with facts and the laws, but that not make their rulings facts. In the federal court system, fact finding is the job of the district courts. They are the ones that examine the evidence and witness testimonies. In criminal cases, often a jury is also involved and makes conviction decisions. And the ultimate ruling of the court stating the verdict and the sentence are based on those fact findings, and by contrasting them against the applicable laws. If appealed, the upper courts, both appellate and Supreme, do not usually examine the evidence or ask for witness testimonies. They usually accept the fact findings of the lower courts, but they may have a different “opinion” when it comes to contrasting those facts with the applicable laws.

Take for example the case of Colorado voters against Donald Trump in 2024, where the voters asserted that Section 3 of the Fourteenth amendment prohibited Trump from running for president because of his involvement in the January 6th (2021) insurrection. The district court determined that, as a matter fact, Trump did engage in that insurrection by aiding or abetting the insurrectionists, but as a matter of law, Section 3 of the 14th amendment may not apply, because it only applies to the “officers” of the United States, and the president is probably not an “officer” of the United States. One might argue that that opinion was an obvious evasion from ruling against Trump, maybe based on fear of retribution. But the finding of the facts was clear. Based on this fact finding of the lower court, the Colorado Supreme Court ruled against Trump and ordered the Colorado Secretary of State to exclude Trump from the ballot. Of course, the case went all the way up to the US Supreme Court which ruled against the Colorado Supreme Court and allowed Trump to be on the ballot. But these rulings of the courts were all “opinions” not facts. The only fact there was the one that was identified by the lower court, that Trump did indeed engage in that insurrection.

What I am trying to get at is that confusing facts with opinions is a serious problem, and is not limited to a specific group or sector of the society. Anybody can fall into that trap. And that such confusions are usually the main sources of misunderstandings. Sometimes we discuss things without having the same understanding of the facts surrounding them. Such discussions are doomed to end in misunderstanding instead of consensus, because the parties are in “fact” (pun intended) talking about different things. Sometimes we discuss opinions that are not formed based on facts at all, such as religious believers, or opinions on vague notions such as beauty or taste. These discussions are also headed nowhere. How can you convince someone that something is beautiful, or that something needs to be respected? In such cases, there is no way to set a common ground to base our arguments on. But there are also times that we avoid conversations by claiming that everyone is entitled to their opinions, or by saying “let’s agree to disagree.” If the subject of those conversations is the truth or falsehood of some statement, the assertions that everyone is entitled to their opinions, or “let’s agree to disagree” are just not applicable. You cannot agree to disagree on facts. Yes, you can have your own opinions. But you cannot have your own facts.

So, now I believe when my friend repeatedly said “your facts are as good as your assumptions,” what he really meant was that “your opinions about something are as good as your knowledge about the facts surrounding that something.” I should check this with him next time we meet, but for now, I think that is a fair assumption.

Let me end this note with this: That I have written these words is a fact. That you are now reading these words is a fact too. These are not things that we can agree to disagree on. But the messages that these words convey are my opinions. On those, we can agree to disagree.