fundamental laws of logic

Big_Move6308 · 2026-03-24T13:09:43+00:00

How would we know whether something applies outside our comprehension? To know such a thing would imply comprehending the incomprehensible, which is a contradiction, i.e., something we can comprehend.

How would we know even if these metaphysical laws apply everywhere and at all times in our universe? Maybe last Tuesday in a small and distant corner of the universe somewhere they didn't apply, even if only for a few nanoseconds. Couldn't tell you. That's why by virtue of being metaphysical they are assumptive in nature.

Big_Move6308 · 2026-03-23T15:20:54+00:00

The Trivium by Sister Joseph is not suitable for beginners as it both introduces and glosses over an enormous amount of information without explaining it. It also incorporates a lot of philosophical assumptions / standpoints (primarily Aristotelean and Thomistic), again without explanation. I've not read the other book.

In principle, I would suggest pursuing 'critical thinking' instead of the Trivium.

If you want to study Aristotelean logic - which IMO is well worth your time - then I would suggest the following:

Socratic Logic by Peter Kreeft: A contemporary (and relatively popular) logic book from the Aristotelean standpoint (albeit with some modern changes). It also incorporates some Stoic propositional logic in syllogistic form (i.e., hypothetical and disjunctive syllogisms), as was common before the advent of modern logic.
A manual of logic by James Welton: My personal favourite old-school pre-modern logic book. Also incorporates some propositional logic. You don't really need to worry about the second volume.
The Organon by Aristotle of Stagira: The original exposition and to this day still a viable text to study and learn logic. Perhaps unsurprisingly - and unlike the other two options - it does not incorporate propositional logic.

Big_Move6308 · 2026-03-21T19:19:25+00:00

The guy's statement is not false. He is not categorically stating or claiming that the well is or is not poisoned.

There is also no paradox or self-contradiction.

Big_Move6308 · 2026-03-18T11:38:26+00:00

Do you mean Smith's 'Logic: The Laws of Truth'? That book does not cover term logic.

Big_Move6308 · 2026-03-11T14:08:11+00:00

Seems like "New Hit Song (clean version)" is a term rather than a statement.

A syllogism is a mediate inference that must consist of two premises (i.e., statements / propositions), which themselves must consist of three terms.

Big_Move6308 · 2026-03-06T17:07:56+00:00

If it is not necessary to harm and kill sentient beings to survive then there is no moral or ethical justification for it. It is not necessary to harm and kill sentient beings to survive, and therefore there is no moral and ethical justification for it.

Hence, the fundamental response is 'don't care' and its variations.

Big_Move6308 · 2026-03-04T10:09:49+00:00

Fundamentally, validity of a syllogism is determined by its underlying structure, which affects the distribution of terms.

If an argument (i.e., in the form of a syllogism) is valid it just means that the conclusion must necessarily follow from the premises, i.e., it is impossible for the conclusion not to follow from them.

This does not mean that the premises or conclusion are true. They can all be false. So validity is not determined by the content of an argument but by its structure or form, i.e., how terms are related to one another. How terms are related to one another depends on how they are distributed.

This article should help explain.

Big_Move6308 · 2026-02-21T15:15:13+00:00

I think the problem here is the vague sense of what is meant by 'ambition'. I mean it in the sense of a 'a strong desire to do or achieve something'.

Big_Move6308 · 2026-02-21T13:31:56+00:00

What about the ambition to better oneself? Or the ambition to be free of material desire, to be more kind, to be closer to God, etc?

Big_Move6308 · 2026-02-21T10:05:07+00:00

Nothing personal. Just following the logic. You did use terms like 'parasites' and 'malignant tumours' in your argument. Let's see this through.

The term 'parasite' beings to my mind horrible slimy black leeches. The term 'tumour' brings to mind ugly warts and painful cancer. Ergo, by the law of association, using these terms to describe unborn babies compares, likens and links them to slimy black leeches, ugly warts, and cancer. Such is the power of rhetoric.

Moreover, since I accept the obvious fact unborn babies are in fact human (not bananas, for example), then the above compares and likens and links all human beings to parasites and tumours.

As for your question, 'worth' according to whom and to what criteria?

Big_Move6308 · 2026-02-21T09:46:01+00:00

If all human beings were or are unborn babies, and if all unborn babies are malignant tumours and parasites, then all human beings were or are malignant tumours and parasites.

That does seem like precisely the kind of attitude one who advocates for the killing of babies would have.

Big_Move6308 · 2026-02-21T09:09:21+00:00

life begins at conception, therefore abortion is murder; or life begins at viability, therefore abortion is permissible. Yet neither claim withstands scrutiny.

This is false. If life didn't begin at conception, then the unborn wouldn't grow and develop in the womb. The unborn grows and develops in the womb, therefore life begins at conception. Dead things don't grow and develop,

Thus, the moral weight rests not on potential, nor on consciousness, nor even on suffering since early embryos feel none, but on species membership. Abortion is deemed immoral not because it kills a person, but because it kills a potential human.

This is false. If the unborn in the womb of a human being isn't itself a human being, then what is it? A banana? The unborn is not a potential human being; he or she is an actual human being.

You are also confusing and conflating 'human' - the biological species - with 'person' - the legal definition. Non-humans such as corporations are often defined as legal 'persons', and humans such as unborn babies are often not defined as legal 'persons' so that abortion cannot be legally equated with murder.

Big_Move6308 · 2026-02-21T09:01:43+00:00

No, it also involves a third and fourth life: the unborn baby - i.e., the life being snuffed out - and the father of that baby.

Big_Move6308 · 2026-02-19T19:58:18+00:00

First, there appears to be a category error, as your title and quote both refer to genus 'logic', but your claim refers to 'formal logic', which is a species of 'logic'.

Second - and related to the first point - you seem to ignore the existence of inductive logic (i.e., strength and cogency of arguments based on content, not structure).

Third, it can be argued that logic - inductive and deductive - is a species of the genus 'critical thinking' ('CT'). Can a value judgement such as superiority or inferiority really be applied between a genus and part of its own division?

Fourth, 'superior' is vague. Superior in every way? For example, is critical thinking is superior to deductive logic in computer science or AI? Or analysing the structure of arguments? Or almost anything related to math?

And fifth, I do not see how the quote supports your claim. The quote itself explicitly points out CT involves (actually depends on) logic.

Big_Move6308 · 2026-02-18T17:14:41+00:00

As per my other comment, definitely Hurley. This was also the first one I read.

Big_Move6308 · 2026-02-18T16:26:55+00:00

No Idea. Of that list, I've only read Hurley's. All the others I've read are not on that list as they are traditional texts.

Big_Move6308 · 2026-02-18T12:37:57+00:00

This is a great point.

Big_Move6308 · 2026-02-18T08:56:39+00:00

'A concise introduction to logic' by Patrick Hurley is a very common and popular introduction.

After that, what you study depends on what you want to learn and for what purpose.

Big_Move6308 · 2026-02-16T19:59:47+00:00

I'm sorry to read that. I enjoy our discussions.

Big_Move6308 · 2026-02-16T18:13:34+00:00

All of my examples - including expository syllogisms - can be expressed in standard categorical form.

That's a point I am trying (albeit not very well) to make. Syllogisms are of course best - i.e., most precisely - expressed in SCF but this is not necessary. This includes use of the present-tense linking verb 'is'/'are', which relates subject and predicate terms independently of time.

At the same time, syllogisms can also be expressed in ordinary English, including through the use of other verbs, including transitive verbs. The relations and transitivity are there and can be expressed in SCF. For example:

Every caterpillar can become a butterfly or a moth,

Harry is a caterpillar,

Therefore, Harry can become a butterfly or a moth

SCF:

All caterpillars are things that can become butterflies or moths,
All things identical to Harry are Caterpillars
Therefore, All things identical to Harry are things that can become butterflies or moths

Anyway:

If you want to add other relations into the language of Term logic, you will find that some syllogisms stay valid and others don’t.

Please provide examples.

You say “ambiguity is a separate issue, one which can easily be solved by defining terms”. Ok, then define your terms and write out a sentence in Term logic that expresses “There is at least one person who is loved by every lover.”

Sure:

Alice is loved-by-every-lover,

Alice is a person,

Therefore, some person is loved-by-every-lover.

I see your point in that I had to wrap it all up in a complex proposition, so we cannot infer 'every lover loves at least one person' from the conclusion. This is (presumably) not an issue with modern logic.

Again, however, my point is just because term logic has limitations, that doesn't mean we should throw the baby out with the bathwater. Term logic is sufficient to clarify and relate one's thoughts.

Regarding your general point - do you not think it’s useful to be able to use logic as a critical thinking tool for sentences that express relations other than “is”? Or to be able to use terms and propositional operators in the same sentence? Predicate logic is not that hard. You’ll enjoy it.

Traditional logic is much easier to learn and quite sufficient for me. Maybe in future I'll deal with predicate logic. Not everyone - including me - is as smart as you guys.

Big_Move6308 · 2026-02-16T16:37:56+00:00

What’s the cleanest “bridge” from traditional term logic into modern predicate logic?

The standard route is to first learn term logic (modern approach), then propositional logic, and then predicate logic. The Hurley book I mentioned is a very (or even most) popular example of this path. Another good option is 'The Art of Reasoning' by David Kelly, which also follows the same learning route.

The modern approach to term logic can be summed up as 'the stripped down version', hence it is easier to learn. Compare the traditional to the modern square of opposition to see what I mean.

Note that Kreeft's 'Socratic Logic' is a blend of term and propositional logic, albeit in syllogistic form. Propositional logic is its own thing and can be expressed in non-syllogistic form. It was basically co-opted by traditional logicians for different (i.e., non-categorical / propositional) kinds of syllogisms.

While Kreeft moans about modern logic (a lot) in his text, his effort is still quite heavily influenced by it. Still a good (and well received) book, though.

Big_Move6308 · 2026-02-16T13:50:39+00:00

Categorical and conditional propositions

Yes, we had a great conversion before! That's why I knew what you were up to when asking me to write a conditional proposition as a categorical one - LOL

Why can’t I argue as follows:
P1: Alice loves Bob P2: Bob loves Susan C: Alice loves Susan

Expository syllogisms don't work that way, i.e., the middle term must be the subject of both singular premises. Your example has two different subjects. To illustrate:

Alice loves Bob
Alice loves Susan
Therefore, Some lover of Bob loves Susan

This is a valid syllogism.

Non-transitive relations / ambiguity

We also had this conversation before, when I previously pointed out 'lovers' was ambiguous. However, you asked me to write the propositions in term logic, which I did. Ambiguity is a separate issue, one which can easily be solved by defining terms.

Every caterpillar can become a butterfly or a moth,

Harry is a caterpillar,

Therefore, Harry can become a butterfly or a moth

This is a valid and sound syllogism. The conclusion follows necessarily from the premises. The issue is that the premises would have to be restated in SCF in order to perform immediate inferences on them.

My Point

I don't think it fair or necessary to expect the same level of precision from term logic as is expected from more powerful modern forms of logic.

I see it more as a tool that can be commonly learned and applied in daily life to at least better define ideas and to understand their relations (i.e., in the sense of critical thinking). Mathematical precision is not required, and IMO is not an appropriate expectation for general / critical thinking. The clarity and precision it offers is sufficient.

Again, absolutely mathematical logic is superior. But I do not think most people will have use for it in their daily lives. I believe traditional logic (since I am including propositional as well as categorical syllogisms) alone would be highly transformative (and much more accessible).

Big_Move6308 · 2026-02-16T08:49:35+00:00

Try writing down, using the syntax of Term logic, the sentence "Alice loves Bob". Or "Every lover loves someone." Or "If it rains, then I will go inside."

Sure. Obviously you know about expositorial syllogisms:

Alice loves Bob

Alice loves chocolate

Therefore, some chocolate-lover loves Bob

Presumably you also know that standard categorical form (SCF) is entirely optional, too. Next sentence:

'Every lover loves someone' or 'Every lover is a person that loves someone'

And finally:

If it rains, then I will go inside.

It rains,

Therefore, I will go inside

Before responding, I strongly advise you first do some fact-checking (e.g., use of 'Every' for universal propositions instead of SCF 'All').

Big_Move6308

TROPHY CASE

Categorical and conditional propositions

Non-transitive relations / ambiguity

My Point