Aristotle's syllogistic logic is too weak for serious work.
It does not readily express multi-place predicates. You cannot express two-place relations like, "John loves Mary", or three-place relations like, "John is standing between Mary and Joanne", without using some odd-looking additional apparatus for converting n-place predicates ...
From a modern point of view, Aristotle's Logic is a subset of predicate logic, called Monadic predicate logic:
monadic predicate calculus (also called monadic first-order logic) is the fragment of first-order logic in which all relation symbols are monadic (that is, they take only one argument). All atomic formulas are thus of the form P(x).
In logic an argument is 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.
Valid arguments must be clearly expressed by means of symbolic sentences called formulas.
The validity of an argument can be tested using the corresponding formulas: if some "interpretation" ...
So the question is:
WILL LOGIC STILL WORK WITHOUT DISJUNCTION INTRODUCTION?
The answer is "work for what purpose?"
What I mean by this is that what you're trying to do here (more broadly), namely "get rid" of the principle of explosion is a traveled path (well in the latter half of the 20th century) broadly known as paraconsistent ...
"No rock is sentient. Some mammals are sentient. Hence, no mammal is a rock."
X = rocks
Y = sentient things
Z = mammals
No X are Z. Some Y are Z. Therefore, no Z are X.
Euler diagram looks like this:
╭─rocks─────╮ ╭─sentient things───╮
│ │ │ │
│ ╭─────┼─────┼────╮ │
Suppose that there is a Mammal (call it a) that is also a Rock.
By first premises, a is not Sentient.
Thus, a is a Mammal that is not Sentient.
But this does not contradict the second premise, that states that some (not necessarily all) Mammals are Sentient .
The logical form is:
No Rock is Sentient --- ¬∃x(Roc(x) and Sen(x))
Some mammals are sentient --- ∃...
To add some bits here to Mauro's answer, from the SEP entry on Aristotle's logic (i.e. using its translation/terminology), Aristotle doesn't merely see logic as reduced to those "perfect deductions" (perfect syllogisms), which he cataloged, but the catch is that he doesn't have a formal system (i.e. a proof theory) for deriving what he called (in ...
Immaterial causes are unfalsifiable, so your argument doesn't/can't falsify them. It just tries to convince, but cannot prove anything.
The first part is also questionable. There are plenty of things where we don't know the cause, can't observe it, or there is none (radioactivity is spontaneous - while you can argue it has a material cause, there is nothing ...
These terms don't have universally agreed-upon definitions.
Syllogism is often associated with Aristotle, in particular with the (restricted) kinds of deductive inferences he described as "perfect" (teleios), but which others subsequently called "syllogisms", although Aristotle himself used the latter term in a boarder sense, according ...
it is really hard to see why "Some As are B" and "Some B As exist" are not paraphrases of each other.
You are right... because they are paraphrases of each other.
"Some As are Bs" is read as: "there is something that is an A and a B".
The truth condition for the "and" connective is that P ∧ Q is TRUE exactly ...
Either the word " this" ( used as subject in the conclusion) refers to something or not.
If it does not, the alledged conclusion has no meaning and therefore is not a proposition. In that case , there is no question as to the validity of the " argument" for there is no argument. For an argument is a sequence of genuine propositions. ( ...
Per David A. Wheeler's article "The Origin of All Men are Mortal" (which elsewhere cites this page!)
The earliest document I can find with this specific example is from 1843, specifically A System of logic: Ratiocinative and Inductive, Presenting a Connected View of the Principles of Evidence and the Methods of Scientific Investigation by John ...