Philosophy 2340
Symbolic Logic



You can upgrade to the latest version of the software from the support pages for the text at If you have any problems with the software, this may clear them up. (You must register your software and make one submission first; then you can log into your account and download the software from there.)

I think everyone should be able to get the software up and running on their own computers. (Even Linux users can run it under Wine.) But if for some reason this doesn't work, or you don't have a computer, you can also use it on the computers in the computer labs or in the library. (You can't install software on lab computers, but you can run it right off the CD. I believe that you could also install it to your network drive.) If you take this approach, you should save your homework assignments on your network drive, not on the local machine, so that you will be able to get to them from any lab computer.

Places to Get Help

The TLEARN page for the course: log onto TLEARN at (If Symbolic Logic I doesn't show up in your list of classes, let me know and I'll add you to the list of participants.) Some of the same material is on my web site for the course at, but there will be some materials on TLEARN that aren't on the web site. In both places I have notes on some of the chapters and tips on some of the homework problems.

The official "hints and solutions" page for the text, at

Me. I have office hours and an email address; don't hesitate to make use of them. If you want to email me about a world or a proof file, take a screen shot and attach it to your email so I can see what's going on. (If it's a proof file, make sure that line numbers are shown before sending it to me. You can also just attach the proof or world file to an email if you like, but it may take me longer to get to it, since if I open your email on a device on which I don't have the software installed, I won't be able to see what you've done.)

General Advice on Homework

Always do the "You Try It" exercises, whether I assign them to turn in or not.

When doing an assignment, have the grade report sent only to yourself until you're sure you're ready to submit it for a grade.

When doing an assignment, submit the first problem (or the first part of a problem, if it has more than one) before doing any more. Make sure it's correct before moving on to the next one. If you're making some sort of small mistake, this can prevent you from making the same mistake on dozens of problems!

If the Grade Grinder says you're wrong, make sure you figure out why and correct the problem. Pay careful attention to any hints the GG offers. If after a reasonable effort to figure out what the problem is, you just don't see what's wrong, send me an email or drop by to ask.

Don't wait until midnight on the night before the assignment is due to get started. Starting late will guarantee that you don't have time to get help if you need it! Start the assignment as soon as possible after the class in which we discuss the material. That way you can email or come by if there's a problem.

Chapter 1 Notes

We can construct different first-order languages to talk about different things. Chapter 1 takes a look at first-order languages for talking about our authors' children; about sets; about arithmetic; and, the one we'll use the most, about the "blocks world" of the Tarski's World program.


Also called "individual constants" or "names"

Each constant must name an object (no "empty" names)

No constant can name more than one object (no ambiguous names)

However, an object may have more than one name


Each predicate has a specific "arity" or number of argument places

For every object (or sequence of objects), there's a yes or no answer as to whether a predicate applies to that object (no vague predicates)

Atomic Sentences

An atomic sentence is a predicate of arity n, followed by a left parenthesis, followed by n comma-separated constants, followed by a right parenthesis.


We can construct first-order languages to talk about anything we want to. Many of our examples will use the Blocks Language. But the text also introduces a first-order language for talking about the authors, their children, and their pets; a first-order language for talking about arithmetic; and a first-order language for talking about sets.

One of the hw problems involves the language for sets. Sets are collections of things, some of which may be other sets. A simple set: {2, 5, 7} is a set with three members, all of which are numbers. Things get a little trickier if we consider sets some or all of whose members are themselves sets.

Consider the set c = {1, 3, {2, 5, 7}}. How many members (also called elements) does it have? Answer: three. Two of its elements are numbers; one of its elements is a set, namely the set {2, 5, 7}. Question: is 5 an element of c? Answer: no. It's an element of an element of c, but not itself an element of c.

Last update: January 16, 2015. 
Curtis Brown | Symbolic Logic I | Philosophy Department | Trinity University