## On The Format of Logical Arguments

• 3
Do all logical arguments, or syllogisms, of propositional logic need to take a specific form such as modus tollens or modus ponens?

I was reading an old Christian religious work recently and it had this syllogism regarding the meaning of one of the verses. It goes as follows:

1. The kind of death which God threatens here is opposed to the kind of life which He promises to those who repent and persevere in well doing.
2. But this life is confessed by everyone to be eternal life.
3. Therefore, the death opposite to it must be eternal death.

I suppose that the conclusion of every sound logical argument flows is a reasonable deduction from the truth of its premises. However, does every argument need to follow a or some logical form for the conclusion to be reasonably deduced? If so, in the example above, what is the logical form that this argument takes.

I hope this makes sense.
• 97
It strikes me as a more than three-part "syllogism" because the remainder of the premises, background, ramifications etc will be contained elsewhere in the book you are reading and elsewhere in Scriptures and above all you have to choose what to your mind will be a discernibly authentic interpretation thereof (there are so many misleading interpretations doing the rounds).

In the real real world, indeed, logic has to help us grapple with multipartite questions, it is rare that a situation in its entirety is simple.

Nonetheless I think logical tools are meant to help us "chunk it down" and then we can arrive a jigsaw pieces (even tentative jigsaw pieces) for each "corner" of the issue so that we can then move on to seeing how the tentative jigsaw pieces might dovetail at the next level.

I'll leave it to other respondents to add their insight regarding tollens and ponens, for now (a challenge to me to do some homework on it myself).
• 13.8k
Argumentation in general does not need to, and most of the time does not, take a more traditional, structured approach a la formal, syllogistic, etc. logic "proper."

And if one has anything like a constructivist or other anti-realist view of what logic is, then there's no particular reason to favor a more formal logical approach anyway, except for what would amount to a personal aesthetic preference.

In my opinion, a lot of the more formal arguments that have been forwarded, typically in analytic philosophy, have seemed rather more stupid than the far less structured form of rhetorical argumentation.

Although none of this implies that fallacies aren't still a problem when they creep up.
• 4.2k
I suppose that the conclusion of every sound logical argument flows is a reasonable deduction from the truth of its premises. However, does every argument need to follow a or some logical form for the conclusion to be reasonably deduced? If so, in the example above, what is the logical form that this argument takes.

Following the standard set of procedures for presenting logic makes it more abstract and formal. More like math, which was probably the point. It can also make the structure of the argument clear. The only time I use it is when an idea is confused and mixed up with other stuff.

And that's the good part. It's also used to add a veneer of false legitimacy. You see that here on the forum a lot. My general thought is, if you can't say it in plain speech you don't understand it.
• 3
Alright, so what I gather for the most part from what everyone is saying is that formal logical argumentation or structure is unnecessary. A conclusion can reasonably be deduced from an argument, even if the argument is not formally formatted, provided that we can somehow "see" or clearly "detect" that the conclusion does indeed follow, though we may not formally know how it follows.
• 3.6k
provided that we can somehow "see" or clearly "detect" that the conclusion does indeed follow, though we may not formally know how it follows.

Mostly, no. Knowing and exhibiting the formal steps are different things, as are knowing and applying them. That is, you can can know and not exhibit, and as well know and not apply (arguably to not apply them you have to know them!), but if you don't know, then, well, you don't know.

The opposition here, then, is between ignorance and knowledge. (And even with knowledge, there's practice: you may know, but practice instructs as to how to use what you know.)

Perhaps think in terms of dance and dancing (or professional basketball or martial arts). Not knowing about or understanding - or knowing how to do - these activities means that while you may like and have a partial appreciation for what's happening, in fact you don't really have a clue. At best you have an imperfect, and incomplete, subjective model.

Is this a bad thing? Perhaps. But to some degree or other it's the condition of us all. Sometimes the best we can do is be like Socrates - or any other sensible person - and just acknowledge that we don't know. Fortunately, a lot of the world's work gets done - is doable - under penumbral shades of ignorance.

Back to formal argumentation. For a valid and true conclusion, it's built in, whether you "see" it or not. If it's not there, then your conclusion is suspect. To complicate matters, a division of logic is between analytical or formal (or informally just) logic, and rhetoric. Different animals, though with similarities.

As to your syllogism, I break it down this way:

God offers life or death.
The life offered is supposed to be eternal life.
Therefore the death is (must be) eternal death.

Which is an invalid "therefore." That the life has the quality of being eternal says nothing about the death.

Now, if the offering of God was in itself either eternal life or eternal death, then it's one or the other. But that's a different premise, and thereby a different argument. .
• 97
Your example sounds like one of the epistles of Paul, for example. Now, sending a letter was sticking one's neck out. Therefore they had to be on the brief side. Now he will have taught them at length when he saw them and they will also have had their regular teachers ever since.

Therefore, the bulk of the "premises" are outside this text. I think the word "if" is more like "you know when we said that . . . , well . . ." The logical basis of saying "because" or "seeing that" is contained in the background knowledge of the addressees of the text.

The text being apparently about life, the question of whether it says anything about death as well is not contained in the extract you gave.

There may be clues elsewhere in the text of the letter - and St Paul (if it is him - I haven't matched it up exactly) no doubt says something about that. Depending on the shared theology of the writer and addressees, we may be able to deduce something of that.

This even depends on the larger context of the correspondence, for example any letter that the addressees had sent to the writer enquiring on a point and asking him to explain it more.

If we are outsiders, spectators, not in the loop, then what we can do is like Tim Wood says, use epoche, remain agnostic, identify an antinomy (which is a perfectly respectable thing).
• 983
Do all logical arguments, or syllogisms, of propositional logic need to take a specific form such as modus tollens or modus ponens?

Knowledge as a justified (true) belief (JtB), is a modus-ponens arrow:

justification $\Rightarrow$ knowledge claim

The justification must contain all elements, including definitions, that support the arrow. The knowledge claim must necessarily follow from the justification. The justification itself, however, does not need to be justified.

So, yes, knowledge must always be phrased as a modus ponens.
• 3.1k
So, yes, knowledge must always be phrased as a modus ponens.

The sun will rise tomorrow.
• 983
The sun will rise tomorrow.

if ( time = tomorrow, 5h30 ) then { the sun will rise }

So:

time = tomorrow, 5h30 $\Rightarrow$ the sun will rise

It is still the modus ponens. If you want a counterexample, you will need to find something that looks like:

The sun will rise.

In that case, you do not justify, and then the question becomes ... Why? Why will the sun rise?
• 4.7k
1. The kind of death which God threatens here is opposed to the kind of life which He promises to those who repent and persevere in well doing.
2. But this life is confessed by everyone to be eternal life.
3. Therefore, the death opposite to it must be eternal death.

1. God's promised life is opposed to God's threatened death
2. This life is eternal
[2a]. This life is God's promised life
Therefore
3. Death is eternal

This life is eternal
If this life is eternal then this life is God's promised life
If this life is God's promised life then death is God's threatened death
God's threatened death is eternal death
This life is God's promised life
Death is God's threatened death
Death is eternal death

1. El........................premise
2. El > Pl.................premise
3. Pl > d = Gd.........premise
4. Gd = Ed..............premise
5. Pl........................1, 2 MP
6. d = Gd.................3, 4 MP
7. d = Ed.................4, 6 Id

l = this life
Ex = x is eternal
Px = x is God's promised life
d = death
Gd = death is God's threatened death

I tried very very hard but it seems it's not that argument forms are necessary to make an argument. It's just easier to work with forms that've been pre-validated. This makes me want to ask a question which I will in the logic section. If you're interested look there.
• 97
TMF (a day ago), I was trying to point out that in the example cited by the OP, and in your version of it, there are far more premises than the ones stated and that both of you are probably misinterpreting those that you give. A text like that which is probably behind this thread was not designed or intended to be used that way, not by the actual recipients either.

Arguments can be of a huge variety of different kinds. The things that have been pre-validated don't need to be stated afresh.
• 97

Therefore what Alcontali is saying is that IF the content had been stated explicitly, this would be what is happening, yes.
• 4.7k
Yes, I had to fit the argument within the limits of my comprehension ability which is average/less. It was extremely difficult so I had to ignore some parts of the argument. Did I not do justice to the argument? Did I leave key elements (premises/subconclusions) out? If yes, what are they?
• 97
You are reproducing the reasoning of Michael Yoo, very well.

What makes it in this case not a ponens is that the detail that is understood by the writer and his readers is matters like, whether there is symmetry in their god's treatment of life and death issues, how to unpack the concept of "well doing", what facets of everyday life are being referred to in the phrase "this life", what indeed powers or fuels the things implied (not just "people pleasing" or ingratiating, I fancy).

The extract is not a complete treatment of the subject in itself and may not have been part of a complete treatise. The bulk of the subject matter may have been given to the recipients orally, by this writer and / or other persons.

It is fascinating to wonder what is considered an "explanation". Much good is done by keeping talking round a subject, in fresh words, hinting at fresh angles.
• 4.7k
You are reproducing the reasoning of Michael Yoo, very well.

What makes it in this case not a ponens is that the detail that is understood by the writer and his readers is matters like, whether there is symmetry in their god's treatment of life and death issues, how to unpack the concept of "well doing", what facets of everyday life are being referred to in the phrase "this life", what indeed powers or fuels the things implied (not just "people pleasing" or ingratiating, I fancy).

The extract is not a complete treatment of the subject in itself and may not have been part of a complete treatise. The bulk of the subject matter may have been given to the recipients orally, by this writer and / or other persons.

It is fascinating to wonder what is considered an "explanation". Much good is done by keeping talking round a subject, in fresh words, hinting at fresh angles

:ok:
• 97
I think I have identified this as Romans 2:7. The majority of the missing premises aren't even in Romans at all!
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