Search found 963 matches

by Speakpigeon
Sat May 25, 2019 7:52 pm
Forum: Logic and Philosophy of Mathematics
Topic: How do we say this using the notation conventions of mathematical logic?
Replies: 6
Views: 290

Re: How do we say this using the notation conventions of mathematical logic?

Traditionally, the definition of the notion of validity relies on the notion of truth: An inference is valid if and only if the truth of the conclusion follows from the truth of the premises.
I understand that you choose a definition of truth relying on the notion of validity.
Am I wrong?
EB
by Speakpigeon
Sat May 25, 2019 10:23 am
Forum: Logic and Philosophy of Mathematics
Topic: Any science of logic?
Replies: 105
Views: 3225

Re: Any science of logic?

Univalence wrote:
Fri May 24, 2019 6:00 pm
Speakpigeon wrote:
Fri May 24, 2019 4:35 pm
Then you're using the word "logic" to mean not logic but thinking, possibly rational thinking I wouldn't know. Therefore, equivocation.
Distinction without a difference.
Seems you've run out of anything rational to say.
EB
by Speakpigeon
Sat May 25, 2019 10:22 am
Forum: Logic and Philosophy of Mathematics
Topic: Any science of logic?
Replies: 105
Views: 3225

Re: Any science of logic?

You cannot predict how many cell phones will be produced and sold next year, but every cell phone works because the principles of electronics that define the millions of events that must occur for them to work are determined by principles which are absolute, and known. Nobody knows all possible cau...
by Speakpigeon
Fri May 24, 2019 4:35 pm
Forum: Logic and Philosophy of Mathematics
Topic: Any science of logic?
Replies: 105
Views: 3225

Re: Any science of logic?

Logic has been understood from the start as an incomplete representation of human thought. We can't even get off the conceptual ground here. That is not how I think about logic. For starters - it hasn't been 'understood' since we are still busy trying to understand it. Then you're using the word "l...
by Speakpigeon
Fri May 24, 2019 10:50 am
Forum: Logic and Philosophy of Mathematics
Topic: Any science of logic?
Replies: 105
Views: 3225

Re: Any science of logic?

No. That's for maths to "describe decision-making under uncertainty". We are going to get nowhere with this "that's somebody else's problem" attitude. Does your mind make decisions? Mine does. I am pretty sure yours does too. Any description of 'logic' that doesn't describe the process of decision-...
by Speakpigeon
Thu May 23, 2019 5:34 pm
Forum: Logic and Philosophy of Mathematics
Topic: Any science of logic?
Replies: 105
Views: 3225

Re: Any science of logic?

Univalence wrote:
Thu May 23, 2019 2:50 pm
Modern "so called logic" is an attempt to describe decision-making under uncertainty.
No. That's for maths to "describe decision-making under uncertainty".
Formal logic is an attempt to describe logic. Except of course mathematical logic isn't really formal logic at all.
EB
by Speakpigeon
Thu May 23, 2019 5:30 pm
Forum: Logic and Philosophy of Mathematics
Topic: Any science of logic?
Replies: 105
Views: 3225

Re: Any science of logic?

I don't think anybody ever claimed Boole's algebra would somehow be unrepresentative or untrue of human logic. Russel did, and he was right. He refers specifically to Boole's 1854 An Investigation of the Laws of Thought , pointing out that human thought involves much more than logic. You think Bool...
by Speakpigeon
Thu May 23, 2019 5:15 pm
Forum: Logic and Philosophy of Mathematics
Topic: A junior high school level of understanding of logic
Replies: 31
Views: 895

Re: A junior high school level of understanding of logic

Premise(A) All dogs are mammals. Premise(B) All mammals breathe. Conclusion(C) All dogs breathe. A B {A, B} ⊢ C ------------- ∴ C So, what is "true" and what is "True(x)" in your example? EB To keep it as simple as possible we can assume the propositional logic notion of true. Every propositional v...
by Speakpigeon
Thu May 23, 2019 10:24 am
Forum: Logic and Philosophy of Mathematics
Topic: Any science of logic?
Replies: 105
Views: 3225

Re: Any science of logic?

So, you think Aristotle's definition of a syllogism doesn't amount to a foundational definition of logic? It is one foundational definition of logic. There are many foundational definitions possible. How would you go about deciding which one is the "correct" foundation? Like how I decide what the t...
by Speakpigeon
Thu May 23, 2019 8:18 am
Forum: Logic and Philosophy of Mathematics
Topic: A junior high school level of understanding of logic
Replies: 31
Views: 895

Re: A junior high school level of understanding of logic

It only takes a junior high school level of understanding of this: Validity and Soundness https://www.iep.utm.edu/val-snd/ A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherw...
by Speakpigeon
Thu May 23, 2019 7:27 am
Forum: Logic and Philosophy of Mathematics
Topic: Any science of logic?
Replies: 105
Views: 3225

Re: Any science of logic?

That's a re-definition of logic, hence, it's equivocation. You can't re-define something you never defined to begin with. Here is Aristotle's definition of a syllogism and hence of logical validity and of deductive logic itself https://en.wikipedia.org/wiki/Argument_from_authority So, you think Ari...
by Speakpigeon
Wed May 22, 2019 6:15 pm
Forum: Logic and Philosophy of Mathematics
Topic: Any science of logic?
Replies: 105
Views: 3225

Re: Any science of logic?

Any inconsistency makes a system 100% illogical. No it doesn't. There are logics which can tolerate some inconsistencies. That's a re-definition of logic, hence, it's equivocation. Here is Aristotle's definition of a syllogism and hence of logical validity and of deductive logic itself: A syllogism...
by Speakpigeon
Wed May 22, 2019 5:40 pm
Forum: Logic and Philosophy of Mathematics
Topic: Any science of logic?
Replies: 105
Views: 3225

Re: Any science of logic?

Any inconsistency makes a system 100% illogical.
Aristotle's syllogistic is logical.
ZFC isn't logic at all. At best, it's a crude approximation.
So, your metrics could be understood as the distance from a given system to logic proper.
EB
by Speakpigeon
Wed May 22, 2019 5:32 pm
Forum: Logic and Philosophy of Mathematics
Topic: A junior high school level of understanding of logic
Replies: 31
Views: 895

Re: A junior high school level of understanding of logic

It only takes a junior high school level of understanding of this: Validity and Soundness https://www.iep.utm.edu/val-snd/ A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherw...
by Speakpigeon
Tue May 21, 2019 9:51 am
Forum: Philosophy of Mind
Topic: Do humans have an inherent capacity to decide that a conclusion follows necessarily from premises?
Replies: 5
Views: 333

Do humans have an inherent capacity to decide that a conclusion follows necessarily from premises?

This is the first of a series of polls concerning logic. The overall idea is to determined whether we share a common notion of the logic of valid reasoning as done by humans. I think that Aristotle's syllogistic can be seen as essentially a simple and rather short catalogue of the kind of arguments ...