15 Facts
(Modified on 2026-08-11)
2,658 words
fact
- An event or thing known to have happened or existed.
- A truth verifiable from experience or observation.
- A piece of information.
— Collins English Dictionary (2014)
In natural English, the word “fact” is used to denote something known with certainty. This makes “facts” a powerful rhetorical device. If we assert that some knowledge is a “fact,” we are asserting that that knowledge is unassailable. Incontrovertible. Anyone who disagrees is foolish; “Everybody knows” it’s true (and you are a fool if you disagree). However, as we’ve already learned, we cannot ever know the Truth with 100% certainty. There are no facts! In good scientific rhetoric, we never claim to know the Truth.
In theory, saying “there are no facts” makes a lot of sense. In practice, it is very difficult to communicate, or do anything, without reference to “facts.” For example, which of the following paragraphs would you rather read?:
- The Well-Tempered Clavier is possibly a collection of documents which probably represent pieces of music. They may have been written by J.S. Bach, who probably lived in Germany from approximately 1685–1750. There is a greater than 99% chance that the collection consists of 24 pairs of pieces, labeled “prelude” and “fugue” respectively. At least one scholar has claimed that each of the 24 pairs of pieces are written in a different key, covering what might be considered all possible keys.
- The Well-Tempered Clavier is a collection of pieces by German composer J.S. Bach (1685–1750). The collection consists of 24 preludes and 24 fugues, one in each possible major and minor key.
Obviously, the first paragraph above is more epistemologically sound than the second, as it refuses to claim to know anything for sure. However, that first paragraph is also painfully tiresome to read—and for no real gain. There is lots of knowledge that “everybody” agrees on, and it is a waste of time to pretend otherwise. The trick is to use “facts” without compromising our scientific credibility.
Assumptions
In order to conduct and communicate about research, we must assume certain “facts.” These assumptions may be wrong or incomplete (All models are wrong, but some are less wrong, right?) but are necessary. Deciding which assumptions we can make is an important part of research methodology, and we should always endeavor to identify, articulate, and criticise any assumptions we make. One of the great dangers in human cognition is failing to recognize when we are making invalid assumptions. If we base our reasoning on invalid assumptions, our conclusions can be completely wrong, even if our logic is perfect. Ultimately, all deductive knowledge is predicated on assumed facts or axioms. This means our research is always provisional—if our assumptions are true, then our conclusions might be true.
Now, even if you are confident in certain assumptions, there are still rhetorical considerations: Will your audience (of skeptical scientists) agree with your assumptions? Will your readers accept your “facts,” or will they question them? If a reviewer believes you’ve made invalid assumptions, they will reject your work. However, if you make reasonable assumptions, no one will mind.
The claim that J.S. Bach lived from 1685–1750 could conceivably be wrong—perhaps the records from that period were faulty, or there is confusion regarding whether they used the Gregorian or Julian calendar at the time, or perhaps an early scholar simply miswrote a date and it has been copied by everyone since then. However, these dates are widely and consistently used in many sources, relying on the authority (and presumed competence) of actual scholars who studied J.S. Bach’s life. Presenting Bach’s dates or nationality as uncertain in a paper would not only be a waste of time, but would actually be confusing to our readers. Basic “facts” in encyclopedias are generally going to be safe to assume.
Making Assumptions
How do we know what we can assume in a research paper? As is often the case, there is no hard and fast rule. It depends on 1) how credible your audience will find the assumption and 2) how critical the assumption is to your argument.
Do you need a citation for the statement “guitar is heavily used in Rock music”?—Probably not. What about “most people enjoy listening to music”?—Again, probably not. But what about “Rock was the most popular genre in the world between 1960–2000”? That seems plausible, but I’m not sure. If I’m not sure, how many of my readers won’t be sure either? It’s probably not a safe assumption.
The most important consideration is how crucial an assumption is to your conclusions. If your research relies on certain assumptions, you better make sure they are rock solid: both that you are confident they are reasonable and that none of your readers will object to them. On the other hand, if an assumption is tangential to the main point, your readers might not care, even if they disagree with the assumption. You might also consider the rhetorical role of an assumption in your argument: in the introduction to a paper, you might make some grandiose (“big picture”) statements. Here, readers might forgive some weak assumptions because the goal is just to make general points and set the stage for your research. However, in your Methodology section or a statistical analysis, making the same weak assumptions could be red flags for reviewers. For example, if I started off my paper introduction by saying “Rock was the most popular genre in the world in the 1970s,” that claim might be accepted. On the other hand, if I did a statistical analysis of music from the 1970s and based my analysis on this same assumption, I might have a problem.
Scope of assumptions
Most research papers are published in places (journals, proceedings, etc.) targeting a specific field. Different fields (and sub fields) will be more comfortable with different assumptions. Part of your research education is getting to know what people in your (sub)field assume, or don’t. However, watch out! It can be very easy to think an idea is “general knowledge” when it is actually very specific to your field, subfield, sub-subfield, or even just your circle of collaborators. As a musician, you might be surprised what is obvious knowledge to you that is not obvious to non-musicians, or musicians who play different instruments/styles. Generally, the safest approach is to err on the side of honesty and clarity: if you aren’t sure, acknowledge your assumptions.
One of the great things about scientific rhetoric is that, because we know our assumptions might be wrong, we don’t have to get attached to them or worry too much if they are justified in general. Rather, we can choose to work with assumptions that make sense (to us and our readers) in the context of our research. For example, imagine if you are studying the differences between rhythm in spoken language and in music. You might assume that all musical rhythms follow a metric pulse and all speech doesn’t. This might not be a safe assumption in general—for example, the Alap in Hindustani classical music is not metric, and spoken poetry is. However, if the data you use in your study is all sampled from 1) best seller audio books and 2) the Billboard Hot 100, then your assumption might be reasonable given those datasets.
Writing assumptions
If you’re not sure if a “fact” is safe to assume, there are two things you can do: you can attempt to either support the fact or hedge the fact.
Supporting assumptions
You can support an assumption by making an argument to justify it. In most papers, there are a few theoretically important assumptions that you’ll need to justify. You might spend several sentences or paragraphs in your introduction laying out these arguments. For less important assumptions, you might just include a sentence or a few extra words here and there in your text. You might say things like:
For our purposes, the exact year of Bach’s birth is irrelevant.
Due to the use of enharmonic notes like Ab and G#, there are arguably more than 24 keys; however, Bach wrote and titled the Well-Tempered Clavier specifically to highlight the equivalence of keys in the (at the time) novel tuning system. Thus, treating enharmonic keys as identical is consistent with the intent of the composer.
Since our participant pool is made up entirely of American college students, we assume that all of our participants who identify as musicians are familiar with Western pitch names and enharmonic spellings.
Saying something like “for our purposes” or “in the context of this research” is not always necessary, but is a good way of clarifying the scope of your assumptions.
Justifying the logic of your assumptions can take up a lot of space in a paper. To streamline things, you can also support your assumptions or “facts” through citation. Cite a reputable, preferably scholarly, source which supports your assumption. For example, you could cite an encyclopedia for J.S. Bach’s dates.
Obviously, when we try to “support” a fact/assumption, we can’t decisively prove it to be True. Our goal is simply to convince our readers that the assumption is reasonable for the purposes of our study. That, even if an assumption may be questionable, it is good enough for now and won’t bias/invalidate our actual results. In some cases, it can be sufficient to just say “another researcher did it this way, so we are doing it the same way.”
Consider again the statement “most people enjoy listening to music.” For most purposes, this statement is probably something you can safely assume. However, if this statement is crucial to your research in some way, having a citation might be worthwhile.
Hedging assumptions
In some cases, we either can’t find good support for an assumption or we simply don’t want to bother because it’s relatively unimportant. In these cases, it’s best to simply emphasize that the assumption is not a “fact,” only an assumption. The simplest hedge is to just say “we assume x.” This communicates to your readers that you are aware that the assumption may be wrong.
A hedge is a purposeful choice to make your argument seem weaker, which seems like a bad idea right? Only if the reader doesn’t think of the problem themselves! If you point out the assumption before the reader thinks of it, this enhances your credibility. This sort of hedging is an essential part of good scientific rhetoric. By clarifying the strengths and weaknesses of your assumptions, you allow your readers to properly judge the validity of your work.
Piano Keys
Consider this “fact”:
Pianos have 88 keys.
Everybody knows that! Right? But is this a reasonable “fact” to assume? Let’s break it down.
Now, pretty much everybody who knows anything about piano will agree that a standard modern piano has 88 keys. Nonetheless, I can think of some reasons why some reviewers might object. The 88-key standard has not always existed—neither Bach, Mozart, nor Beethoven ever played an 88-key keyboard. Even today, electric pianos, keyboards, and some small acoustic pianos don’t always have 88 keys. Does your dataset include older music, or music played on keyboards or synths? If so, the number of keys on the keyboard might be crucial to your research methodology—not something to assume lightly.
The big question is always “could this assumption affect our results?” Let’s say we are training an artificial neural network to classify piano music as being either Mozart or Beethoven. Beethoven played pianos with greater ranges than Mozart did. Thus, our classifier might learn to simply look at the lowest notes in a score to recognize Beethoven. This might work fine but it is pretty mundane; The classifier hasn’t actually “learned” anything about the musical style of Beethoven and Mozart, only that they used different pianos. Does it matter for our research? Maybe not. But only by being critical of an obvious “fact” can you even identify the potential problem.
Let’s assume that you’ve thought about this problem and determined that, for your specific research purposes, it is safe to use the 88-key assumption. How you might use this fact in a research paper? Here are some quotes we could use:
- We set up our neural network to accept an 88-dimension input vector.
- Keyboards have 88 keys, so we use an 88-dimension input vector.
- For the purposes of the this study, we assume that pianos always have 88-keys, and thus use an 88-dimension input vector.
- Though pianos have not always had 88-keys, we assume that using an 88-dimensional input vector will not affect the results.
- Though older composers in the dataset did not use 88-key pianos, our ABC statistical algorithm is not sensitive to zeros in its input. Therefore we pad all scores with zeros as necessary to form consistent 88-dimension input vectors representing all pieces.
What are the advantages of these different options?
The first two options, which implicitly (1.) or explicitly (2.) make the 88-key assumption without any critical discussion, have the advantage of being much shorter. If you have determined that the 88-key assumption doesn’t affect the results, why waste time talking about it? In particular, if you are publishing in an engineering journal, its likely that none of your reviewers will know (or care) how many keys a piano has. However, (1.) is bad precisely because a non-musician engineer wouldn’t know why the input vector is 88-dimensional.
The next two options (3. and 4.) don’t really change anything except that they acknowledge the assumption. They tell your audience that you are aware of the assumption, casting the work as slightly tentative (Be humble), but leave it up to the reader to judge if there is a problem or not. If you are publishing in a (historical) musicology journal, your reviewers will definitely be annoyed if you just say “keyboards have 88 keys” (2.), but simply acknowledging the historical change makes it clearer that you understand the issues and have thought through them. This makes you seem more competent (and humble).
Example (5.) is the fullest explanation, articulating the nature of the potential problem (historical change in keyboard sizes) and why you have determined that the problem won’t affect your results. Now, in your specific subfield, readers who are familiar with the “ABC statistical algorithm” might be competent to judge for themselves that there is no problem with the 88-key assumption, so (2.) might be acceptable. But how confident are you that readers would see that? Even if you are confident that an assumption won’t invalidate your results, acknowledging the assumption can make reviewers more confident in you. If you use examples like (1.) or (2.) above, a reader wouldn’t know that you thought through the problem; In fact, it might appear that you don’t know about the problem at all. By adding more hedging/support/justification, it convinces your reviewers that you know what you are doing.
Finally, let’s not forget that making an assumption like “keyboards have 88-keys” could really be a problem. For example, if your statistical algorithm is sensitive to zeros. In this case, you’d want to (a priori) change your methodology to avoid the problem and explain why you did so in the paper:
- Beethoven and Mozart played pianos with different ranges, which could bias the statistical analysis. Thus, we crop scores to the middle four octaves surrounding middle C, which we are confident that both composers had access to, and thus use a 48-dimensional (12x4) input vector.
Mantras
These mantras are closely connected to mantras we’ve learned before, but each remind us of specific things to keep in mind when writing.
Don’t think in terms of “facts”—this is a slippery slope. Always think in terms of assumptions. The question is, will your colleagues/readers agree that your assumptions are valid?