General Course info
Lorenz Demey - lectures
Lisann Penttila - exercise sessions (TA)
Classes:
Monday - 11 - 13: lecture
Tuesday 11 - 13:
first 3 weeks - 2 hours of lecture
afterwards - 1h of lecture + 1h of exercise
Might be more chaotic due to circumstances, check your schedule regularly!
Also make sure to check where the actual classes are (what rooms)
No recordings of classes!
Toledo has all of the main communication. Slides, textbook, additional course material, discussion boards (teacher doesn’t use message or discussion board, but will answer questions there regularly or correct others if they make a mistake answering, use it or don’t doesn’t matter to him but it’s useful for asking questions and clarifying things), announcements (i.e. culture cancelled)
Can e-mail prof about particular questions, though discussion board is better (more efficient). Contact details can be found on toledo.
Slides will be published after being covered due to the presence of exercises and answers in them.
Textbook
introduction to formal logic, “long” though most of it is a lot of examples and other conveniences.
Toledo + https://www.logicmatters.net/ifl/
Exam:
Pretty standard, closed-book, written exam (open questions, no multiple choice), mix of theoretical questions and exercises (~50/50). Will be based on lectures, and lectures usually give examples of questions that might come on the exam.
Mock exam:
In the course of the semester (early December), grades won’t count towards final result. Good way to prepare for the real exam, and is very representative in terms of modalities, difficulty level, etc.
Natural deduction isn’t mentioned in the mock exam because it’s only given in December, and is very difficult for some people (“hardest part of the course”). Some of the exercises can also be solved using “Tableaux”. The first edition of the textbook uses the latter, while the second uses the former.
Separate day, not one of the lectures.
Model answers (i.e. how to get full marks) will be discussed and shown.
Discussion boards are a good way to double-check your answers, and students’ input will be triple-checked by the teacher.
First group of chapters is informal logic, then PL (propositional logic), then QL (quantitative logic), then modal logic.
Some flexibility in course contents though a lot of the latter years rely on the foundations laid in Logic.
“High fail rate” (yippie!!)
in 2022, out of 124 students registered for the January exam, 21 didn’t participate, 45 failed, 58 passed. 46.8% pass rate from total students, 56.3% from participants. Out of the possible audience of 66 people for the resit exam (66 people), 29 didn’t participate, 16 passed.
Final passing % out of -
registered in the course - 59.7%
participated in exam - 52.9%
Average grade: 10.6/20
What is deductive logic?
The interface for systematically assessing an argument for its validity (what validity is will be elaborated on throughout the entire course).
Cogency:
- narrative cogency (the story makes sense)
- visual cogency (seeing a face in the clouds)
- in logic: validity
An argument is a piece of text in which a conclusion is in some way supported with a number of reason.
The piece of text can be written, spoken, or thought.
The argument (formally) encompasses both the reasons and the conclusion.
”all logicians are smart, Lorenz is a logician, so Lorenz is smart.”
Modus ponens - if, then
Modus normal is “all x are y”, “z is x”, “x is y”.
In an argument there are
- any number of premises
- conclusion (exactly one per argument)
We must allow any number of premises (“be super flexible”), but only ever allow exactly one conclusion. There are generalizations of logic where you may be more liberal with this, but not here.
No recursion (language cannot be self-referential). Otherwise you run into nasty things like
”This sentence is false” or “therefore this argument is not valid”.
inference markers
The conclusion doesn’t have to be at the end;
the premises don’t have to be the beginning.
“Lorenz is smart, since all logicians are smart, and Lorenz is a logician"
"All logicians are smart, so Lorenz is smart, since he is after all a logician”
etc.
because of this, inference markers are very helpful indicators of what’s what.
so, therefore, consequently… indicate a conclusion
since, because, after all… indicate a premise
watch out for terminological ambiguity -
to argue, an argument are ambiguous:
“having a fight” - no reasons are given
”reasoning” - reasons are given
reasoning is everywhere:
in philosophy (metaphysics, epistemology, pol. philosophy…)
in science (STEM)
in daily life (what are we going to eat tonight?)
why is reasoning (and logic) everywhere?
- because we want our beliefs to be true, which will help us act better
- if our beliefs are grounded in reason there is a higher chance they are true
Evaluation of arguments
all humans are mammals, Lorenz is a human, so Lorenz is a mammal
two dimensions to evaluate this argument:
- truth/falsity
- is the first premise true or false?
- is the second premise true or false?
- is the conclusion true or false?
- property of individual sentence in the argument
- evaluation to be made by the philosophers, the biologist, people in daily life… but not the logician
as a logician, our arguments should not require outside knowledge to assess their validity. We are less concerned with the truth of an argument, but rather with its
- validity / invalidity
- does the conclusion really follow from the premises, or not?
- can we proceed from the premises to the conclusion, or not?
- property of an inference step / argument as a whole
- evaluation to be made by the logician
categorical mistakes is basically comparing apples to oranges (i.e. a microphone cannot be even (or odd), because that is a property that fundamentally does not apply)
arguments are not true or false, they are valid or invalid.
validity is at the level of arguments, truth is at the level of premises. You can’t define validity without truth, but truth != validity.
all humans are mammals, Lorenz is a human, so Lorenz is a mammal
this argument is valid
the conclusion follows from the premises, the conclusion is guaranteed from the premises
validity and truth:
if we assume that all premises are true
then we have to agree that the conclusion is true as well
there is no way in which all premises can be true
while the conclusion is false
all Mexicans are Europeans, Lorenz is a Mexican, therefore Lorenz is European.
the argument is also valid, though the premises aren’t true.
Suppose someone agrees with all the premises of a valid argument, but denies the conclusion. This person is contradicting themselves → they are irrational.