Reply To: Logic on Abortion Issues

#19058
gerard.casey
Participant

Mises007: I reproduce your new argument here for the sake of anyone else who might be following the discussion:

You wrote:
“Premise 1: If I own x, I can defend my ownership of x against all aggressors
Premise 2: Trespassers are aggressors
Premise 3: Those using my property without my explicit permission are aggressors
Premise 4: My body is my property
Premise 5: A fetus is trespassing my body and using it to sustain itself without my explicit permission
Premise 6: A newborn child still attached to the umbilical chord is using my body to sustain itself without my explicit permission
Premise 7: A parasitic twin is using my body to sustain itself without my explicit permission
Conclusion: It is morally acceptable to abort parasitic twins, fetuses and newborns still attached to the umbilical chord on the grounds that they are trespassing on and/or living off my body.” [end of citation of your argument]

In our logic, every argument capable of evaluation is either a categorical syllogism or a hypothetical syllogism. In each case, an argument will have two premises and a conclusion. Our rules for validity operate only on arguments in such forms. Your new argument, as it stands, isn’t either a categorical or a hypothetical syllogism [it’s got 7 premises and a conclusion!] so it’s not capable of being evaluated (as it stands) by our rules. Of course, it may well be possible to turn your argument into a form that is capable of being evaluated by our system. This will most likely transform it into a set of interconnected arguments, each of which can be evaluated separately. Before going on to see what I’ve made of your material, you might like to try your hand at reconstructing it in categorical or hypothetical form yourself.

Let’s start with your premise 3. This looks as if it might be a categorical proposition. Let’s take as our terms:
P: people who use my property without my explicit permission
G: aggressors
This should give us our premise 3 as: PAG [All people who use my property without my explicit permission are aggressors]
[n.b. If I was to be absolutely precise, I’d reflect the negative element in the subject (‘without’’) by means of a complement, but I’ll ignore that for the sake of simplicity]

Now let’s turn to premise 5. Here our terms might be:
F: foetuses
P: those who use my property without my explicit permission
Giving us: FAP [all foetuses are people who use my property without my explicit permission]

Now we can put the newly reformulated premises 3 and 5 together to give us the following

categorical syllogism I:
PAG [all people who use my property without my explicit permission are aggressors]
FAP [all foetuses are people who use my property without my explicit permission]
therefore
FAG [all foetuses are aggressors]

We can construct similar arguments taking the material in your premises 6 and 7 and, substituting for F in the foregoing argument N: umbilically connected newborn children and T: parasitic twins, respectively, we get categorical syllogisms II and III:

categorical syllogism II:
PAG [all people who use my property without my explicit permission are aggressors]
NAP [all umbilically connected newborn children are people who use my property without my explicit permission]
therefore
NAG [all umbilically connected newborn children are aggressors]

categorical syllogism III:
PAG [all people who use my property without my explicit permission are aggressors]
TAP [all parasitic twins are people who use my property without my explicit permission]
therefore
TAG [all twins are aggressors]

All three categorical syllogisms are valid (check for yourself, using the six rules for validity).

[Your premise 2 appears to be redundant. We can already get from lack of explicit permission to aggression without invoking trespass.]

Now we’ve dealt with premises 3, 5, 6 and 7 and eliminated 2 as seemingly redundant. That leaves 1 and 4. How can we use this material to get us towards your overall conclusion?

I suggest a slight reformulation of your premises 1 and 4 to get the constituent sub-propositions of what will be our hypothetical syllogism to connect up, as follows (using the simplified single-letter form of the constituent sub-propositions for the sake of simplicity)

Hypothetical Conditional Syllogism IV:
1a: If S is a person who owns x, then S is a person who is morally and legally entitled to defend x against aggressors [If P then Q]
4a: S is a person who owns x (her body) [P]
therefore,
8. S is a person who is morally and legally entitled to defend x (her body) against aggressors [Q]

This hypothetical conditional syllogism is valid.

Let’s now combine the conclusions of the valid categorical syllogisms I, II and III into the following composite categorical proposition, 9:

9. All foetuses, umbilically connected newborn children and parasitic twins are aggressors
Letting W stand for the composite term: foetuses, umbilically connected newborn children and parasitic twins
this gives us the categorical proposition: WAG

Putting premises 8 and 9 together, we get (in English)

S is a person who is morally and legally entitled to defend x (her body) against aggressors
All foetuses, umbilically connected newborn children and parasitic twins are aggressors
Therefore, S is a person who is morally and legally entitled to defend her body against all foetuses, umbilically connected newborn children and parasitic twins

Intuitively, this seems to be valid. Let’s try to put it into symbols:

We have the following terms:
S: S (anyone at all)
D: persons who are morally and legally entitled to defend x (their bodies) against aggressors
W: foetuses, umbilically connected newborn children and parasitic twins
G: aggressors
giving us the following two propositions:
8a. SAD
9. WAG

If 8a and 9 constitute the premises of a prospective syllogism, we have a problem inasmuch as we appear to have 4 irreducible terms.

Let’s see if we can reduce the four terms to three. A bit of material eduction seems to be in order to link up the terms D and G.

Example: from the proposition ‘A horse is an animal’ we can validly conclude that ‘The head of a horse is the head of an animal’ (by complex conception—lecture 6). Similarly, from WAG [All foetuses, umbilically connected newborn children and parasitic twins are aggressors] we can materially educe “All persons who are morally and legally entitled to defend x (their bodies) against foetuses, umbilically connected newborn children and parasitic twins are persons who are morally and legally entitled to defend x (their bodies) against aggressors”

Let W(2) stand for “persons who are morally and legally entitled to defend x (their bodies) against foetuses, umbilically connected newborn children and parasitic twins” and we already have what would be G(2), namely D: “persons who are morally and legally entitled to defend x (their bodies) against aggressors”.

So, 9—WAG transforms by material eduction into
9a.W(2)AD

And now the premises of our would-be syllogism are
8a. SAD
9a W(2)AD
and we’d like to get as our conclusion
10. SAW(2)—“ All Ss are persons who are morally and legally entitled to defend x (their bodies) against foetuses, umbilically connected newborn children and parasitic twins”

As the result of our application of material eduction, these two premises together now have 3 and only 3 terms but, unfortunately, since the middle term is D and it isn’t distributed in either premise, any syllogism formed by adding any conclusion whatsoever will be invalid by reason of failing rule 5 (the middle term must be distributed at least once). If only we could validly convert 9a!

Even if, on another reformulation, you could validly connect up the results of the two different trains of deduction, you would have established only that your argument is valid, i.e. if its premises were true, its conclusion would have to be true. The task of establishing the truth of your premises would still confront you and it is to establishing the truth of the premises that the argument would then shift.