Symbolic logic- is it worthwhile?

[Nihilist]

I am wondering if it is worthwhile studying symbolic logic.

I’ve been reading a few text, like Boole, and it just seems to be putting things which are pretty obvious to regular common sense into symbolic equations. And then I looked at a few other textbooks, and it was just stuff like: “All men are mortal. Peter is a man. Therefore Peter is mortal”- totally obvious, dressed up in algebraic looking symbols.

Is it worth studying this stuff? Or do people just study it to pass exams, being able to understand symbols, and know terminology, and then forget about it?

Does it actually help one to solve a real philosophical problem, with precision? And if so, could you give me an example of where it might come in handy.

 

[polytropos]

Most of it is pretty straightforward. You can probably get by without formal training in it; you would probably pick it up second-hand if you were to read some analytic philosophy.

It isn’t totally useless. Modal logic builds on it and benefits from being formalized and systematized. It can also help one to understand better certain fallacies, like scope fallacies.

For example, suppose someone says, p entails q, and p. Sometimes people will take this to me necessarily q–at least, when they have couched everything in philosophical prose. Often this the necessity of the consequent is a desirable conclusion (ie. this is the case with deductions of transcendental idealism). In other cases, it is not desirable (sometimes it is absurd for q to be necessary).

But if you know that entailment is necessary implication, then you know that “p entails q” is “necessarily (if p, then q)”. So without p being necessary, you cannot get necessarily q. (Actually, even that move is contestable. It has to do with the “modal structure” and is related to whether we should allow axioms S4 and S5. I think the “modally conservative” route is to disallow it, but I am not sure and am not really familiar with the technical arguments for the position.)

There are other benefits to studying logic. One might think more about how to formulate dilemmas using the law of excluded middle and constructive dilemma. In other words, you have “p or ~p” and “p implies q” and “~p implies r”, so “q or r” (where the dilemma of “q or r” may put some strain on your dialectical opponent). There is no reason why you can’t make such an argument without studying formal logic; you just may not think so much in those terms. (For reasons like this, I actually found formal logic pretty useful for studying mathematics, proving theorems, etc. In turn, studying mathematics is useful for philosophy because it is useful in philosophy to find counterexamples to people’s claims, and so much of mathematics can be done via proof by contradiction.)

 

[Oreoracle]

Does it actually help one to solve a real philosophical problem, with precision? And if so, could you give me an example of where it might come in handy.

I’m not sure about philosophical problems, but it’s useful in math.

In particular, stripping statements of their semantical meaning and looking at them symbolically lets you compare different arguments and even entire deductive systems. This is valuable in algebra for exposing similarities among different algebraic structures.

Without the use of symbolism, some connections between concepts aren’t so obvious. To build on polytropos’ example, there are striking similarities between modal logic (the logic of necessity and possibility) and deontic logic (the logic of obligation and permission), as well as dissimilarities. Both are made much more apparent when you use symbolism.

So I guess what I’m trying to say is that we sometimes get so bogged down in semantics that we fail to see how different structures actually exhibit the same patterns. Logic liberates us from such a myopic perspective.

 

[QuestLove]

I am wondering if it is worthwhile studying symbolic logic.

I’ve been reading a few text, like Boole, and it just seems to be putting things which are pretty obvious to regular common sense into symbolic equations. And then I looked at a few other textbooks, and it was just stuff like: “All men are mortal. Peter is a man. Therefore Peter is mortal”- totally obvious, dressed up in algebraic looking symbols.

Is it worth studying this stuff? Or do people just study it to pass exams, being able to understand symbols, and know terminology, and then forget about it?

Does it actually help one to solve a real philosophical problem, with precision? And if so, could you give me an example of where it might come in handy.

It is definitely a course you would have to take in college if you are a math major, computer major or sometimes engineering major.
It may be a useful course if you plan on doing further studies in scientific research.

Think of some of the applications we take for granted: Doing a Boolean search for example in google. Makes life much easier

 

[QuestLove]

I’m not sure about philosophical problems, but it’s useful in math.

In particular, stripping statements of their semantical meaning and looking at them symbolically lets you compare different arguments and even entire deductive systems. This is valuable in algebra for exposing similarities among different algebraic structures.

Without the use of symbolism, some connections between concepts aren’t so obvious. To build on polytropos’ example, there are striking similarities between modal logic (the logic of necessity and possibility) and deontic logic (the logic of obligation and permission), as well as dissimilarities. Both are made much more apparent when you use symbolism.

So I guess what I’m trying to say is that we sometimes get so bogged down in semantics that we fail to see how different structures actually exhibit the same patterns. Logic liberates us from such a myopic perspective.

 

[RedFox0456]

Because I studied mathematics in college, I got nothing out of my symbolic logic class. I went perhaps two weeks or of the entire semester and got a 98% in the course. That said, my friend got a great deal out of the class because he had never been trained in logic or proofs before.

 

[Nihilist]

I’m not sure about philosophical problems, but it’s useful in math.

In particular, stripping statements of their semantical meaning and looking at them symbolically lets you compare different arguments and even entire deductive systems. This is valuable in algebra for exposing similarities among different algebraic structures.

Without the use of symbolism, some connections between concepts aren’t so obvious. To build on polytropos’ example, there are striking similarities between modal logic (the logic of necessity and possibility) and deontic logic (the logic of obligation and permission), as well as dissimilarities. Both are made much more apparent when you use symbolism.

So I guess what I’m trying to say is that we sometimes get so bogged down in semantics that we fail to see how different structures actually exhibit the same patterns. Logic liberates us from such a myopic perspective.

So, looking on the web- Boolean algebra seems really useful- even in IT. It looks quite accessible, too. Could it be applied to moral and theological issues, too?

 

[Nihilist]

Because I studied mathematics in college, I got nothing out of my symbolic logic class. I went perhaps two weeks or of the entire semester and got a 98% in the course. That said, my friend got a great deal out of the class because he had never been trained in logic or proofs before.

Yes, I did a short course on formal logic while studying- and it seems pretty vacuous. Mainly just memorizing a handful of definitions and symbols. I don’t think it said anything that wasn’t already obvious, apart from giving me an arsenal of terms ‘argumentum ad verecundum’, etc. ‘affirming the consequent’.

But, I 'm thinking, there must be something more to it…

 

[RedFox0456]

Yes, I did a short course on formal logic while studying- and it seems pretty vacuous. Mainly just memorizing a handful of definitions and symbols. I don’t think it said anything that wasn’t already obvious, apart from giving me an arsenal of terms ‘argumentum ad verecundum’, etc. ‘affirming the consequent’.

But, I 'm thinking, there must be something more to it…

Well you will be tested and have a chance to get familiar with applying the various rules of logic and identifying logical fallacies. That can be quite helpful if you haven’t had much experience or practice with strict logical arguments before.

 

[Oreoracle]

So, looking on the web- Boolean algebra seems really useful- even in IT. It looks quite accessible, too. Could it be applied to moral and theological issues, too?

My understanding is that Boolean algebra bridges propositional logic with set theory. They offer different ways of expressing the same ideas, and the one you would use would likely depend on the application.

Deontic logic is an extension of propositional logic, and it is intended for the study of obligation and permission. Assuming that you use axioms for the relationship between obligation and permission that reflect your moral views, you could view deontic logic as an extension of Boolean algebra rather than propositional logic if you like, and this deontic algebra could be used to address moral issues. The tricky part is choosing axioms that are appropriate for one’s moral views. As you can imagine, the choice of axioms for deontic logic can be contentious.

That being said, I’m not familiar with the advantages of using an algebraic approach rather than the logical or set-theoretic approaches. In any case, you certainly need to introduce operators to denote the moral content of your logic. For example, let’s say you want a way of expressing that a proposition is “good”. Boolean algebra alone has only three operators, and two of them are binary. We aren’t stating a relationship between propositions, so we would be forced to use the unary operator, negation. But Boolean algebra and propositional logic hold that either a proposition or its negation is true. So if we used negation as the “good” operator, we would be saying that any proposition is either true or good. So we definitely need more than those three operators, which is what deontic logic offers.

 

[Charlemagne_III]

I am wondering if it is worthwhile studying symbolic logic.

Unless you plan to become a professional logician, why bother? I’ve noticed that logicians of my acquaintance often thought they were the brightest bulbs in the room; but after a while of speaking with them you begin to notice they are not any brighter than most people when it comes to most matters of the intellect.

One of the great logicians of the 20th Century, Bertrand Russell, did not seem to profit much from the study of logic and mathematics as can be seen in the pitiful arguments he often put forth against the existence of God and the human soul.

For all his talents as a logician, he did not even try to dismantle Pascal’s Wager Argument, and actually confessed that he could not precisely p(name removed by moderator)oint the error of Anselm’s ontological argument, though he was certain it was erroneous. He went full steam against Aquinas’ proofs which he wrongly thought were easy pickings. Aquinas, after Gaunilon, was one of the first to detect Anselm’s deficient logic. It’s not clear that Aquinas benefited much from the study of Aristotle’s logical systems, though he certainly benefited much from studying other writings by Aristotle.

If you plan to be a philosopher, the study of Plato’s dialogues will sharpen your wits far more so than the study of Boolean logic.

 

[Bob_Crowley]

Probably a bit off track, but I seem to remember my old pastor saying that there’d one day be a logical proof of God’s existence, and it will have something to do with zero. If so, then I suspect Boolean Algebra might have something to do with it.

For most people, studying symbolic logic would be a waste of time. They wouldn’t use it. Even the bulk of mathematics falls into that category. For the great majority of the population, basic arithmetic is all they ever use - checking the shopping dockets, working out how much fuel they can buy for $30 (or more likely hitting the $20 and the $10 on the prepay keyboard), checking their speed against the signed limit, cutting the timber once after measuring twice, working out how many palings they need to buy to build the fence, and so on.

But the tools of logic and maths have their use if you’re going to work in the IT industry, engineering, and other professional areas. And I suppose if you intend to be a theologian, you’d need at least a passing acquaintance with philosophy, including symbolic logic.

 

[thinkandmull]

Unless you plan to become a professional logician, why bother? I’ve noticed that logicians of my acquaintance often thought they were the brightest bulbs in the room; but after a while of speaking with them you begin to notice they are not any brighter than most people when it comes to most matters of the intellect.

One of the great logicians of the 20th Century, Bertrand Russell, did not seem to profit much from the study of logic and mathematics as can be seen in the pitiful arguments he often put forth against the existence of God and the human soul.

For all his talents as a logician, he did not even try to dismantle Pascal’s Wager Argument, and actually confessed that he could not precisely p(name removed by moderator)oint the error of Anselm’s ontological argument, though he was certain it was erroneous. He went full steam against Aquinas’ proofs which he wrongly thought were easy pickings. Aquinas, after Gaunilon, was one of the first to detect Anselm’s deficient logic. It’s not clear that Aquinas benefited much from the study of Aristotle’s logical systems, though he certainly benefited much from studying other writings by Aristotle.

If you plan to be a philosopher, the study of Plato’s dialogues will sharpen your wits far more so than the study of Boolean logic.

Hey Charlemagne III, do you think we should start a new thread on Bertrand Russell? And who is Gaunilon by the way?

My math teacher in college said that Russell and Whitehead said they couldn’t think as sharply on others subjects after they wrote their Principles of Mathematics? He told me that truth should make you wiser and smarter on just about every subject.

 

[MPat]

I am wondering if it is worthwhile studying symbolic logic.

I’ve been reading a few text, like Boole, and it just seems to be putting things which are pretty obvious to regular common sense into symbolic equations. And then I looked at a few other textbooks, and it was just stuff like: “All men are mortal. Peter is a man. Therefore Peter is mortal”- totally obvious, dressed up in algebraic looking symbols.

Is it worth studying this stuff? Or do people just study it to pass exams, being able to understand symbols, and know terminology, and then forget about it?

Does it actually help one to solve a real philosophical problem, with precision? And if so, could you give me an example of where it might come in handy.

Well, I can give you an example where I have used it in this forum:

Third, the point is that apostles were martyred. The argument goes on like this:

1. Apostles have chosen to die rather than to deny Catholicism. (premise)
2. Apostles would have known if Catholicism was true. (premise)
3. If someone chooses to die rather than to deny p, that someone believes p to be true. (premise)
4. If someone knows some p to be true, that someone also believes p. (premise)
5. If someone knows some p to be false, that someone does not believe p. (premise)
6. Apostles would have believed Catholicism if and only if it was true (from 2, 4 and 5)
7. Apostles did believe Catholicism was true (from 1 and 3)
8. Catholicism is true (from 6 and 7)

Or symbolically:

1. Martyred(A, C)
2. ( C <=> knows(A, C) ) and ( not C <=> knows(A, not C) )
3. Martyred(x, p) => believes(x, p), for each x, p
4. knows(x, p) => believes(x, p), for each x, p
5. knows(x, not p) => not believes(x, p), for each x, p
6. C <=> believes(A, C)
7. believes(A, C)
8. C

The sixth step (the least obvious) can be shown to follow like this (if I didn’t miss anything - it is not a full natural deduction, as I didn’t want to use temporary assumptions, but it’s close):

1. (p <=> q) and (not p <=> r) [premise, like 2 in previous argument]
2. q => s [premise, like 4 in previous argument]
3. r => not s [premise, like 5 in previous argument]
4. p <=> q [from 1]
5. p => s [from 2, 4]
6. not p <=> r [from 1]
7. not p => not s [from 3, 6]
8. p <=> s [from 5, 7]

(If you don’t trust this proof, you can try entering “((p <=> q) & (-p <=> r) & (q => s) & (r => -s)) => (p <=> s)” in teachinglogic.liglab.fr/DN/index.php and it should construct you a nicer one.)

As you can see, the conclusion does follow, if all premises are granted. If they are not granted - then we have a different discussion…

The argument could have been given without symbols, but using them forced me to make every premise and intermediate step more precise and explicit.

Although it is true that using it is more important in Computer science than in Philosophy.

 

[Charlemagne_III]

Hey Charlemagne III, do you think we should start a new thread on Bertrand Russell? And who is Gaunilon by the way?

My math teacher in college said that Russell and Whitehead said they couldn’t think as sharply on others subjects after they wrote their Principles of Mathematics? He told me that truth should make you wiser and smarter on just about every subject.

I’m fairly played out on Russell, but if you have a specific issue, I’d be interested in it.

Gaunilon was the first critic of Anselm’s ontological argument. He was a contemporary of Anselm.

What you say about Russell and Whitehead together bears studying. Whitehead, though certainly more interested in God than Russell, often soars too high in the clouds of ambiguity to suit me. Russell was clever, but in the end he was tediously clever and a bit more than sarcastic toward the plausibility of God.

I used to be one of his greatest admirers!

 

[inocente]

So, looking on the web- Boolean algebra seems really useful- even in IT. It looks quite accessible, too. Could it be applied to moral and theological issues, too?

Once you’re stated something in Boolean algebra, you can turn it into hardware using just a battery, a bulb and switches connected with wires. Wire AND switches in series, OR in parallel. Which goes to show that logic itself is mundane. The difficulty with a moral or theological issue would be dividing it into parts which can be represented by on/off (true/false) switches. Probably impossible of course, but trying to do helps p(name removed by moderator)oint where the thinking is fuzziest, and so tells you where further analysis is most needed.

 

[thinkandmull]

Charlemagne III I would like to know more about Russell’s arguments on God. Modern science has proven the soul. A tiny unaccountable amount of weight leaves the body when it dies. And people say they remember seeing themselves on operation tables when they had no brain waves going on

 

[Charlemagne_III]

Charlemagne III I would like to know more about Russell’s arguments on God. Modern science has proven the soul. A tiny unaccountable amount of weight leaves the body when it dies. And people say they remember seeing themselves on operation tables when they had no brain waves going on

Here is the text of Russell’s probably most famous essay against God and Christianity. It was originally a lecture that became the title of his most famous book. When I was young I was very impressed by his shallow thinking. After a lifetime of thinking, I graduated to a higher level of insight, at least enough to see through Russell.

users.drew.edu/~jlenz/whynot.html

 

[Rhubarb]

I think logic is worthwhile as a tool to use when assessing arguments. The syllogism used in the OP is very easy to comprehend but not all symbolic arguments are straight forward. Some arguments can be very complex when written out symbolically - especially when using more advanced systems of logic. Contradictions, tautologies and equivilances aren’t always so apparent either.

 

[Charlemagne_III]

Symbolic logic is only going to be understood by people who understand symbolic logic.

So the masters of symbolic logic should prepare to have a very small audience of readers.