I absolutely loved my training in formal logic – I didn’t to begin with (it looked suspiciously like maths and equations, and I thought I’d left that behind) but when I got the hang of it, it felt like a beautiful and powerful tool to examine and dismantle sentences and arguments (in the sense of ‘making an argument for something’, not shouty disagreements). I feel like it ought to be taught at an early age in schools, but that’s a side issue.
Formal logic is basically a way of reducing potentially complex sentences to their fundamental logical parts. Once you do that, it’s much easier to examine the logical steps that take you from one to the next – or that fail to do so. So, for example, following all the rain this summer, I’ve decided to always take an umbrella with me if it’s raining. You can actually express this incredibly briefly in formal (or symbolic) logic using these tools!
P = it’s raining
Q = taking an umbrella
→ = if (something) then (something else)
Stands for ‘if it’s raining I will take an umbrella’.
We can now form a logical argument! Basically this is taking at least one premise and using it to reach a valid conclusion.
Premise 1: P
→ Q (if it’s raining I’ll take an umbrella)
Premise 2: P (it’s raining)
Conclusion: Q (I’m taking an umbrella)
You can see that this is a really useful standard form and applies to anything you feed into it, like so:
Premise 1: P
→ Q (if it’s Monday I have ballet class)
Premise 2: P (it’s Monday)
Conclusion: Q (I have ballet class)
Premise 1: P
→ Q (if my partner is tall he will hit his head on the doorway)
Premise 2: P (my partner is tall)
Conclusion: Q (he hits his head on the doorway)
See? It’s so simple you’re wondering why I bothered to write you out three different examples. But you’ve just learned an actual proper logical form called Modus Ponens. GOLD STAR 🙂
Just like with maths, there are all sorts of useful rules for switching bits of this statement around so you don’t have to think it through every time. So just as 6 x 7 = 42 means that 42/7 = 6, ‘if P then Q’ also means that ‘if not-Q then not-P’.
Wait, what? Let’s put it back into ordinary language. Assuming I am totally consistent in my umbrella carrying habits, and I *always* carry an umbrella if it’s raining, the fact of me *not* carrying an umbrella (‘not-Q’) therefore means it can’t be raining (‘not-P’). Similarly, look back to those examples above – if I don’t have ballet class, then it’s not Monday; if my partner doesn’t hit his head on the doorway, he’s not tall.
Premise 1: P
Premise 2: not-Q
You’ve just learned a second logical form! This one is called Modus Tollens. Another gold star 🙂
So you can see there are standard forms for logical arguments, and they’re so standard they have names. These are watertight forms of reasoning, assuming what you put into them is valid (I could write out a logical argument including ‘if I quit my job I will become a famous lion tamer’, but that wouldn’t make it true!). This is known as being ‘truth-preserving’ – the way formal logic works, as long as the premises you put into it are true, then the conclusion will also be true, no matter what. There are also standard forms for logical fallacies – faults, whether intentional or otherwise, in reasoning from the premises to the conclusion.
Let’s keep looking at the umbrella example. We’ve established that ‘if P then Q, not-Q, therefore not-P’ works absolutely fine. Shouldn’t it work the other way round, too? ‘it’s not raining’ therefore ‘I won’t take an umbrella’? BZZZZT nope. There is absolutely nothing in any of those premises anywhere to suggest that I’m not some umbrella-carrying obsessive who always carries an umbrella when it’s raining, but also often carries one in blazing sunshine. That goes for the other examples, too – I might have ballet class on Monday AND Tuesday nights, my not-tall partner might be on stilts or a pogo stick or just bouncy and still hit his head.
These aren’t trick questions or ways to catch you out. This is exactly how formal logic is useful – you look only at what’s actually there, not your own personal inferences or assumptions about what’s ‘probably’ true.
Formal logic is great fun to use to take apart arguments, especially those put forward by politicians who at best use convincing rhetoric rather than logic. It’s not really very useful in your personal life, unless you’re surrounded by people who’d take kindly to being told that their feelings are illogical. Although if you do try that, film the reaction. And be ready to run.
What does this have to do with poly?
Er, yes, good point. Longest introduction ever.
What this is leading up to is an informal logical fallacy called the No True Scotsman fallacy, which comes up in all sorts of ways in discussions around poly relationships (whether it’s poly vs monogamous, or ‘my poly’ vs ‘your poly’). Yes, if you know the difference between formal and informal errors, you’ll already have realised that all that formal logic stuff i just wrote is only tangentially connected to this. So shoot me. Formal logic is my idea of fun 😛
Anyway! No True Scotsman is basically an attempt to cling on to an assertion or claim in the face of evidence against it. Logically, if you claim “all A are B” and then are presented with an example of A that is not B, you ought to accept that “all A are B” is not true, and at best “some A are B”. Instead, the No True Scotsman fallacy involves someone redefining A in direct response to the example, specifically to exclude the example.
Courtesy of philosopher Antony Flew via Wikipedia:
Imagine Hamish McDonald, a Scotsman, sitting down with his Glasgow Morning Herald and seeing an article about how the “Brighton Sex Maniac Strikes Again”. Hamish is shocked and declares that “No Scotsman would do such a thing”. The next day he sits down to read his Glasgow Morning Herald again; and, this time, finds an article about an Aberdeen man whose brutal actions make the Brighton sex maniac seem almost gentlemanly. This fact shows that Hamish was wrong in his opinion but is he going to admit this? Not likely. This time he says, “No true Scotsman would do such a thing”.
Hamish redefined his original point specifically to exclude an example that would otherwise have proved him wrong. His original point relied on ‘Scotsman’ being what most people would understand it (someone born in Scotland or of Scottish parents). His second point redefined it as ‘born in Scotland/of Scottish parents AND not capable of committing brutal sex crimes’.
This may ring more true if I put it into a form most people who’ve come out as non-monogamous have encountered:
“No one in a loving relationship would be happy for their partner to have sex with other people.”
“I love my partner very much, she loves me, and I think her boyfriend is awesome and I’m happy they have a good sex life.”
“That’s not real love, you’re just deluding yourself. When you really fall in love with someone, you’ll understand.”
Again, this is redefining the original point – the original idea of ‘loving relationship’ relies on the commonly understood definition of love, without reference to monogamy or non-monogamy. The second idea redefines a loving relationship to ALSO include monogamy.
You also end up with a similar problem in the tedious ‘true polyamory’ debates. There’s always a moment when someone explains their particular relationship structure, and someone else pops up to say ‘ah, well that’s not true polyamory’. To be fair, being a relatively new word, polyamory doesn’t quite have a universally accepted definition, so sometimes it’s genuine confusion. But sometimes it’s just silly (‘my girlfriend is really spiteful and belittles me in front of my wife’ ‘that’s not really polyamory’ – yes it is, but it’s also a shitty polyamorous relationship. Those happen too.)