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Why Formal Logic?
Jonathan Wang
Yearly Sage ⭐
***I love to write, and I also happen to have a little knowledge about the LSAT and law school admissions generally. With JY’s blessing, I have decided that I will scratch my writing itch on a semi-regular basis by posting long-form blog-style pieces on the forums. If you have a topic that you’d like to see me write about, feel free to PM me. And please, discuss the piece freely in the comments below, especially if you disagree – I love to hear other viewpoints and am happy to engage in respectful and reasoned discourse.
My personal philosophy has always been that fundamentals are paramount because they set the groundwork for true understanding, and true understanding is a foolproof way to do well on anything. Some methods out there eschew a deep discussion of formal logic in favor of more ‘holistic’ approaches, relying on the student to supply their experience with the English language instead. I don’t buy it, and here’s why.
First - if the LSAT gave us everything in “if…then” terms, then I would absolutely agree that formal logic would be mostly unnecessary because everyone understands the “if…then” construction on a very basic level. There would still be some purely logical issues that would need to be addressed (for example, thinking that “if A then B” is equivalent to “if not A then not B”), but those could at least theoretically be addressed without resorting to formal logic mapping. Unfortunately, the LSAC is not so accommodating. Semantics plays a huge role on the LSAT, so we can’t just ignore it as if we lived in some idealized world where “if…then” is the only game in town.
Next - if people were naturally proficient at identifying equivalence between statements, I would also agree that learning formal logic would be mostly unnecessary. But unfortunately, that’s not the case either. The number of students who complain that certain arrangements of conditional statement are ‘convoluted’ or ‘complicated’ speaks to the sheer difficulty of that level of translational proficiency for even the most clued-in students, to say nothing of the average person. Sometimes, even a simple reordering of words can be enough to throw the most astute of students. If you’ve ever missed a conditional indicator because it was in the middle of a sentence, then you know exactly what I’m talking about.
Finally – if there were an easier way to give the required background than what currently exists, then I’d embrace that wholeheartedly. Unfortunately, when we’ve got a conditional (if-then) statement, we need an “if” side (sufficient), a “then” side (necessary), and a way to express the relationship between the two (the arrow). I’m really not seeing how this can be made any simpler.
I take a lot of pride in my ability to teach formal logic, but believe me – I would not teach formal logic at all if I could help it. It is one of the least fun parts of the curriculum for the student, and is very difficult to teach well. It took me years to get even reasonably proficient at conveying the concepts. In addition, once learned, most students go through a phase where they try to translate literally every statement into conditional logic, which I then need to scale back, causing more suffering for everyone. I teach it not because I want to, but because I have to.
Formal logic is not an end unto itself. It is not something where as soon as you learn it, you can go crush the LSAT by mapping everything out. Rather, it is the means – the fundamental first step toward actual comprehension of what’s going on. That comprehension facilitates the application of logic to the facts at hand, because now we’re clear about what the facts actually are. This critically important piece is often overlooked – it doesn’t matter how good your logical skills are if you don’t understand the facts correctly, and screwing up the relationship between two elements is one of the surest ways to screw up the facts.
This is why it always amuses me when people ask whether they have to use formal logic in a question if they can ‘just see it’ (or whatever variation of that metaphor they prefer). That’s actually the entire point. Being able to ‘just see it’ means that you’ve already unconsciously used and understood the formal logic – you just don’t perceive it because the translation is already automatic for you. It’s akin to ‘seeing’ the answer to 2+2: it may be automatic for you now, but there was a time where you had to count it out. That you don’t have to count it out now doesn’t mean that you don’t need to know how it works – in fact, it is precisely because you’ve learned how it works that allows you to avoid counting it out. And if you've ever misinterpreted something even though you thought you could "just see it", that's not just some minor mistake - that's a gaping hole in your logical reasoning instincts because that suggests you've internalized faulty fundamentals. It's the equivalent of going through life thinking 2+2 is 5; what you "just see" winds up being confusing at best, and flat-out wrong at worst. How do you fix that? By going back and learning how it actually works.
When you learn formal logic, it’s important to understand why it works the way it does. A lot of methods just teach formal logic as a series of trigger words and rules to memorize, and in that light it’s entirely understandable why there’s so much animosity toward it. In addition to it being remarkably difficult to apply rules we don’t understand, it also just feels arbitrary – like it’s something the LSAC is forcing you to learn just because. Who wouldn’t get frustrated in that situation?
Conversely, when you understand WHY it works the way it does, several things happen. First, you can ‘prove’ to yourself that the theory itself is sound, which (although it sounds dumb) is an important part of internalizing it. Second, you start to synthesize your existing intuition with the explicit underlying mechanics, allowing you to have principled bases for adjusting your intuition. And finally, because you understand the theory and aren’t just memorizing rules, it becomes much easier to apply the rules appropriately in a wide variety of situations. If you don’t understand why things work the way they do, then you’re forever bound to memorizing lists of words and hoping that no variations show up (though even if you do understand the theory, you’ll still have to memorize some words – sadly, there’s no avoiding that).
So, don’t think about formal logic as just sufficients and necessaries, arrows and slashes, contrapositives and other seemingly-arbitrary rules to follow. That approach misses the mark entirely. The only way you’ll ever be able to consistently parse out complicated sentences is if you have a firm grasp on the underlying mechanics, and you can only have a firm grasp on a set of mechanics if you understand the theory behind it. Formal logic is one of the most important elements of the LSAT, so prioritize accordingly.
Bonus points for those of you who unconsciously translated that last bit into formal logic.
My personal philosophy has always been that fundamentals are paramount because they set the groundwork for true understanding, and true understanding is a foolproof way to do well on anything. Some methods out there eschew a deep discussion of formal logic in favor of more ‘holistic’ approaches, relying on the student to supply their experience with the English language instead. I don’t buy it, and here’s why.
First - if the LSAT gave us everything in “if…then” terms, then I would absolutely agree that formal logic would be mostly unnecessary because everyone understands the “if…then” construction on a very basic level. There would still be some purely logical issues that would need to be addressed (for example, thinking that “if A then B” is equivalent to “if not A then not B”), but those could at least theoretically be addressed without resorting to formal logic mapping. Unfortunately, the LSAC is not so accommodating. Semantics plays a huge role on the LSAT, so we can’t just ignore it as if we lived in some idealized world where “if…then” is the only game in town.
Next - if people were naturally proficient at identifying equivalence between statements, I would also agree that learning formal logic would be mostly unnecessary. But unfortunately, that’s not the case either. The number of students who complain that certain arrangements of conditional statement are ‘convoluted’ or ‘complicated’ speaks to the sheer difficulty of that level of translational proficiency for even the most clued-in students, to say nothing of the average person. Sometimes, even a simple reordering of words can be enough to throw the most astute of students. If you’ve ever missed a conditional indicator because it was in the middle of a sentence, then you know exactly what I’m talking about.
Finally – if there were an easier way to give the required background than what currently exists, then I’d embrace that wholeheartedly. Unfortunately, when we’ve got a conditional (if-then) statement, we need an “if” side (sufficient), a “then” side (necessary), and a way to express the relationship between the two (the arrow). I’m really not seeing how this can be made any simpler.
I take a lot of pride in my ability to teach formal logic, but believe me – I would not teach formal logic at all if I could help it. It is one of the least fun parts of the curriculum for the student, and is very difficult to teach well. It took me years to get even reasonably proficient at conveying the concepts. In addition, once learned, most students go through a phase where they try to translate literally every statement into conditional logic, which I then need to scale back, causing more suffering for everyone. I teach it not because I want to, but because I have to.
Formal logic is not an end unto itself. It is not something where as soon as you learn it, you can go crush the LSAT by mapping everything out. Rather, it is the means – the fundamental first step toward actual comprehension of what’s going on. That comprehension facilitates the application of logic to the facts at hand, because now we’re clear about what the facts actually are. This critically important piece is often overlooked – it doesn’t matter how good your logical skills are if you don’t understand the facts correctly, and screwing up the relationship between two elements is one of the surest ways to screw up the facts.
This is why it always amuses me when people ask whether they have to use formal logic in a question if they can ‘just see it’ (or whatever variation of that metaphor they prefer). That’s actually the entire point. Being able to ‘just see it’ means that you’ve already unconsciously used and understood the formal logic – you just don’t perceive it because the translation is already automatic for you. It’s akin to ‘seeing’ the answer to 2+2: it may be automatic for you now, but there was a time where you had to count it out. That you don’t have to count it out now doesn’t mean that you don’t need to know how it works – in fact, it is precisely because you’ve learned how it works that allows you to avoid counting it out. And if you've ever misinterpreted something even though you thought you could "just see it", that's not just some minor mistake - that's a gaping hole in your logical reasoning instincts because that suggests you've internalized faulty fundamentals. It's the equivalent of going through life thinking 2+2 is 5; what you "just see" winds up being confusing at best, and flat-out wrong at worst. How do you fix that? By going back and learning how it actually works.
When you learn formal logic, it’s important to understand why it works the way it does. A lot of methods just teach formal logic as a series of trigger words and rules to memorize, and in that light it’s entirely understandable why there’s so much animosity toward it. In addition to it being remarkably difficult to apply rules we don’t understand, it also just feels arbitrary – like it’s something the LSAC is forcing you to learn just because. Who wouldn’t get frustrated in that situation?
Conversely, when you understand WHY it works the way it does, several things happen. First, you can ‘prove’ to yourself that the theory itself is sound, which (although it sounds dumb) is an important part of internalizing it. Second, you start to synthesize your existing intuition with the explicit underlying mechanics, allowing you to have principled bases for adjusting your intuition. And finally, because you understand the theory and aren’t just memorizing rules, it becomes much easier to apply the rules appropriately in a wide variety of situations. If you don’t understand why things work the way they do, then you’re forever bound to memorizing lists of words and hoping that no variations show up (though even if you do understand the theory, you’ll still have to memorize some words – sadly, there’s no avoiding that).
So, don’t think about formal logic as just sufficients and necessaries, arrows and slashes, contrapositives and other seemingly-arbitrary rules to follow. That approach misses the mark entirely. The only way you’ll ever be able to consistently parse out complicated sentences is if you have a firm grasp on the underlying mechanics, and you can only have a firm grasp on a set of mechanics if you understand the theory behind it. Formal logic is one of the most important elements of the LSAT, so prioritize accordingly.
Bonus points for those of you who unconsciously translated that last bit into formal logic.
Comments
http://7sage.com/discussion/#/categories/sage-advice
Thanks.
More people need to see this
https://media2.giphy.com/media/Jv4Te8YylM3Pa/giphy.gif
Bumping the heck out of this post.
ohmygersh you used Paper Mario in your GIF! And the one from TYD, nonetheless!
Best game ever! It was a very long, but great post! Was it about PM:TYD?
I see PM:TYD in everything.
And this post to me stresses all the more to take your time with the curriculum. So many people worry that their pace is "too slow," when in reality, your pace needs to be determined (and I'd argue exclusively) by your level of understanding. Take it from me - I skimmed past parts of the curriculum, as I came to 7Sage after having studied for a few months. Not approaching the formal logic in the way described here is what cost me a score higher than what I obtained - that and just an overall disregard for an absolute, insatiable desire for understanding every single detail.
Great read after the Advanced Logic section of the core curriculum, which I'm about to go do over again now!