Negate this necessary assumption: PT8, LR1, Q6, TCR (C) Forum

[who_ate_my_cake]

TCR in my own words: A person cannot [...] unless such-and-such state of affairs.


What is the best way to negate this statement? I tried "it is not the case that if a person can, then such-and-such state of affairs," but maybe there are better/easier ways to go about his. Advice?

[Want_My_Life_Back]

With "unless" statements you can just negate the sufficient clause to make it easier to read. If a person can [...] then such-and-such state of affairs. So the proper negation of this would be If not such-and-such state of affairs then a person cannot.

[suspicious android]

Well, you can negate any sentence by putting "it's not the case" in front of it, but I think for most any complex statement that becomes more confusing than helpful. Another option is just converting it into an "if/then" statement, then negating it:

If a person can XYZ, then PQR.

The negation of this would be "even if a person can XYZ, not necessarily PQR". Note that the proper negation of a conditional statement is not another conditional statement. To negate any conditional statement you need to show that the sufficient condition can exist without the necessary condition.

[tehrocstar]

The quick and dirty would be to negate the phrase before and after "unless" at the same time and move on.

Given that phrases like "unless" are logically equivalent to "if not," you can begin by substituting that word and reversing the sufficient and negative conditions. But instead of reversing the order of the sufficient and necessary, it's preferable to just negate the sufficient.

To negate a conditional statement in general, you need to negate the necessary condition, thus.

Original statement modified to a conditional statement

Original:
A person cannot, unless such-and-such state of affairs

After modification and substituting unless:
(If a person can, then such and such state of affairs)

Finally negating the conditional:
If a person can, then not such and such state of affairs

I would imagine that you wouldn't run into this scenario too often though.

[Attorney at Play]

A person cannot [...] unless such-and-such state of affairs.

NEGATED: A person can [...] without such-and-such state of affairs.

Correct me if I'm mistaken, but that just seems like the easiest and most intuitive way of comprehending it.

[tehrocstar]

A person cannot [...] unless such-and-such state of affairs.

NEGATED: A person can [...] without such-and-such state of affairs.

Correct me if I'm mistaken, but that just seems like the easiest and most intuitive way of comprehending it.

Without and unless are logically equivalent, thus your answer is incomplete.

[uchi15hopeful]

It has been answered correctly in this thread:

A person cannot [...] unless such-and-such state of affairs = Not A unless B

Not B -> Not A; Contrapositive: A -> B

Done and done.

Edit: My bad, I thought we were diagramming.

[Attorney at Play]

A person cannot [...] unless such-and-such state of affairs.

NEGATED: A person can [...] without such-and-such state of affairs.

Correct me if I'm mistaken, but that just seems like the easiest and most intuitive way of comprehending it.

Without and unless are logically equivalent, thus your answer is incomplete.

Why is it incomplete? I used without to make it easier to understand. Right, its logical equivalence makes it the same as unless. However, cannot is changed to can.

So where the original statement is 'You cannot blank without blank.' The negation would be 'You can blank without blank.'

[jamesireland]

The quick and dirty would be to negate the phrase before and after "unless" at the same time and move on.

Given that phrases like "unless" are logically equivalent to "if not," you can begin by substituting that word and reversing the sufficient and negative conditions. But instead of reversing the order of the sufficient and necessary, it's preferable to just negate the sufficient.

To negate a conditional statement in general, you need to negate the necessary condition, thus.

Original statement modified to a conditional statement

Original:
A person cannot, unless such-and-such state of affairs

After modification and substituting unless:
(If a person can, then such and such state of affairs)

Finally negating the conditional:
If a person can, then not such and such state of affairs

I would imagine that you wouldn't run into this scenario too often though.

This is not quite right. As suspicious android correctly points out, the negation of a conditional is not another conditional. The negation of 'If A then B' is 'A and not-B'.

[suspicious android]

I really cannot get enough of these threads.

[tehrocstar]

Yep, you're right jamesireland, thanks

[who_ate_my_cake]

If a person can XYZ, then PQR.

The negation of this would be "even if a person can XYZ, not necessarily PQR". Note that the proper negation of a conditional statement is not another conditional statement. To negate any conditional statement you need to show that the sufficient condition can exist without the necessary condition.

Thanks, this is very useful. Definitely easier than "It is not the case that..." I appreciate that.

Also, thanks to everyone who replied