# Fundamentals of Formalisation level 1: Basic Logic

(note: we have a study group run­ning a week ahead of this se­ries that adds im­por­tant con­tent. It turns out that to get that con­tent ready on a weekly ba­sis, we would have to cut cor­ners. We pre­fer qual­ity over speed. We also like pre­dictabil­ity. So we de­cided to cut us some slack and pub­lish ev­ery 2 weeks in­stead for the time be­ing)

(re­lat­edly, the challenges sec­tion of this week is not yet com­plete at the time of post­ing, so com­plet­ing those will not yet im­ply a full un­der­stand­ing of the con­tent)

## Ba­sic logic

The big ideas:

• Sen­ten­tial Logic

• Truth Tables

• Pred­i­cate Logic

• Meth­ods of Math­e­mat­i­cal Proof

To move to the next level you need to be able to:

• Trans­late in­for­mal ar­gu­ments into for­mal logic.

• Eval­u­ate an ar­gu­ment as ei­ther valid or in­valid.

• Ex­plain how to prove an im­pli­ca­tion/​con­di­tional, a con­junc­tion, a dis­junc­tion, and a nega­tion and know what this looks like in­for­mally (i.e. in words and not sym­bols).

Why this is im­por­tant:

This builds the ba­sic knowl­edge you need to be able to pro­duce and un­der­stand math­e­mat­i­cal proof. A firm foun­da­tion in how log­i­cal ma­chin­ery op­er­ates is the best way to be as­sured that a proof you pro­duce or read is cor­rect. This also teaches the ba­sic meth­ods by which a proof is pro­duced.

Without fur­ther ado: you can find the first les­son on our course plat­form.

Every week you have 2 op­tions: do the whole thing, or skip to the “challenges” in the end. The lat­ter op­tion is for those peo­ple that sus­pect they already know the sub­ject. It serves as a means of ver­ify­ing that as­sump­tion.

We hope this track will fa­cil­i­tate as­piring AI Safety re­searchers in their stud­ies. If it leads to even one suc­cess story, it will have been worth it. Maybe that suc­cess story is you!

Happy studying

• Why oh way does this sys­tem make it so need­lessly in­con­ve­nient to par­take in these courses?

I just want to read the lec­ture ma­te­rial on the top­ics that in­ter­est me, and pos­si­bly do some of the ex­er­cises. Why do I need to cre­ate an ac­count for that us­ing a phony email, sub­scribe to courses, take tests with limited num­bers of re­tries, and all of that? I am not aiming to get a for­mal diploma here, and I don’t think you plan on award­ing me any. So why can’t I just… browse the lec­tures in a state­less web 1.0 fash­ion?

• It looks to me as if ihat­es­tatis­tics.com is a for-profit busi­ness sel­l­ing ed­u­ca­tional ma­te­ri­als and sys­tems to uni­ver­si­ties. The de­sign de­ci­sions that make most sense for them are not nec­es­sar­ily the most con­ve­nient for stu­dents. So e.g. they may be keen to be able to dis­t­in­guish one stu­dent from an­other, take mea­sures against cheat­ing, en­courage and/​​or mea­sure “en­gage­ment”, etc. The things they do to that end may be an­noy­ing for stu­dents, but they still do them be­cause they make their ac­tu­ally-pay­ing cus­tomers hap­pier, or make it eas­ier to con­vince in­vestors that they’re do­ing well, or help them plan fu­ture changes.

(In other words, your ques­tion is a bit like “Why oh why do pub­lish­ers charge money for math­e­mat­ics text­books, in­stead of mak­ing them available for free?”.)

[EDITED to add:] For the avoidance of doubt, I en­tirely agree with you that all that stuff is an­noy­ing and that just hav­ing the ma­te­rial made available would be much nicer.

• Thank you for your crit­i­cism. We need more of that.

I am not aiming to get a for­mal diploma here, and I don’t think you plan on award­ing me any.

A pipeline has 2 pur­poses: train­ing peo­ple and iden­ti­fy­ing good stu­dents. We want to do the lat­ter as much as the former. Not just for the sake of the in­sti­tu­tions we ul­ti­mately wish to recom­mend can­di­dates to, but also for the sake of the can­di­dates that want to know whether they are up to the task. We re­cently did a poll on Face­book ask­ing “what seems to be your biggest bot­tle­neck to be­com­ing a re­searcher” and “I’m not sure I’m tal­ented enough” was the most pop­u­lar op­tion by far (dou­bling the next one).

I agree that it looks silly right now be­cause we’re a tiny startup that up­loaded 2 videos and a few guides to some text­books, and it will prob­a­bly be this small for at least a year to come. You got me to con­sider us­ing some­thing more hum­ble in the mean­time. I’ll bring it up in our next meet­ing.

• Cur­rently we can ac­cess all course ma­te­ri­als at once. For the time be­ing, it might be bet­ter to hide the in­com­plete bits so no­body can wan­der ahead and miss things. Slash, it might be bet­ter to force users to try one sec­tion be­fore un­lock­ing the next; oth­er­wise peo­ple might eter­nally put off the hard sec­tions.

That said, the plat­form looks new so it might not sup­port this.