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on December 13, 2019

Is this a safe statement?

The sum of a "Sufficient Condition" is its "Necessary" parts. For instance, being human (in the biological sense) is sufficient to ensure you have a physical body made of fundamental elements combined together to form molecules, cells, organs, organ systems, brain structures, DNA, etc. -- the term HUMAN in this example is the parameter, and the structures of the body that make it HUMAN are its necessary parts. In other words, can it be argued that a sufficient condition is a factual observation of all the necessary conditions that combine together to make it a singular whole? Or, that the idea of sufficiency outlines the parameter whereby all things necessary conform to synthesize its unique existence? That feels overly complicated... however, trying to describe the visual in my mind is somewhat a challenge. My hope is that my question suffices (lol) in painting that visual to you. Any further clarification or correction will be greatly appreciated. Thanks!

4 Replies

Ben on December 13, 2019

Hi Auty, thanks for bringing this up.

It is an interesting way of thinking about it for sure. However, I don't think that it is the most rigorous, nor the most correct method of approaching, even if only for visualization purposes.

While I have never considered this line of reasoning before, I see how it appears quite often. That something which is necessary is part of the whole.

E.g. If water, then we know hydrogen and oxygen
If book, then we know pages

However, keep in mind that so, so many other conditional statements do not have a whole to part, nor part to whole relationship.

Think about conceptual conditions:

E.g. If I listen to music, my mind is at peace (where is the part and where is the whole?)
If you do this for me now, I'll do you a favour later. (Again, failing to the parts and sum idea)

The more accurate way to think of sufficient and necessary (and IMO, simpler), is to think of this:

The sufficient condition is enough to know for sure that the necessary occurs as well. Whether in the past, present, or future, we know the necessary is happening. Because we have the sufficient condition, which is enough.

E.g. If I don't eat soon, I will faint (NOT eat soon - > Faint)
If you had told me about this issue sooner, we would have resolved it yesterday. (TMS - > RY)
If I fall asleep on the train, I drool. (FAonT - > Drool)

It really doesn't matter what the condition is as you see, all we know is that once we have the sufficient, then we have the necessary.

And that is why the conditional statement points from the sufficient to the necessary because it is certain the necessary will occur.

On the other hand, we have the necessary condition. This is required in order for the sufficient to occur because, by name and definition, it is necessary. It can occur without the sufficient. But without it, the sufficient cannot occur.

That is how we get a contrapositive.

A - > B

In this case, A is sufficient and guarantees B, which is necessary. B can occur without A. It is just a prerequisite. But A cannot occur without its necessary B.

The contrapositive represents this:


I hope this helps. Please let me know if you have any other questions.

on December 13, 2019

I love your response, thank you!

Just to repeat back what I believe you're saying: The idea of the whole to part, or part to whole relationship may be true in some, albeit unique instances, it doesn't necessarily generalize to all sufficient and necessary relationships.

The better path, the simpler path, is to argue that something is sufficient if it guarantees the existence of the necessary, and that if the necessary does not exist, then that guarantees the non-existence of the sufficient.

Would you consider this a correct understanding of what you have stated? Thank you!

Ravi on December 14, 2019

@Auty, I think you've summarized what Ben has said very well. If Ben has any additional feedback, I'm sure we'll hear from him as well. Keep up the hard work!

Ben on December 14, 2019

Hi Auty, yes that's exactly the way to think about conditional reasoning!

I'm glad I could be of assistance :)