On The Format of Logical Arguments
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.
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.
Comments (16)
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).
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.
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.
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).
Knowledge as a justified ([s]true[/s]) belief (J[s]t[/s]B), is a modus-ponens arrow:
justification [math]\Rightarrow[/math] 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.
The sun will rise tomorrow.
if ( time = tomorrow, 5h30 ) then { the sun will rise }
So:
time = tomorrow, 5h30 [math]\Rightarrow[/math] 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?
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.
Arguments can be of a huge variety of different kinds. The things that have been pre-validated don't need to be stated afresh.
Therefore what Alcontali is saying is that IF the content had been stated explicitly, this would be what is happening, yes.
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.
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