# “One property may be said to include another if the first is necessarily such that anything that has it also has the second.”

Here is a sentence from philosophical work written by Roderick Chisholm Theory of knowledge. Which i failed to translate and understand. Explain it please in simple words.

One property may be said to include another if the first is necessarily such that anything that has it also has the second.

• You mean like "All men are mortal?" So the quality of being a man includes the property of being mortal. Because if something is a man then that thing is mortal. This reverses the usual convention that the set includes the subset. If every element of A is an element of B, we say that A is a subset of B or B includes A. Your quote has the "include" relationship the other way 'round. – user4894 Oct 5 '14 at 7:13
• Can you give us the reference (page #)? Also when you say "translate" do you mean state in formal logic or render in a different human language or make comprehensible in English? – virmaior Oct 5 '14 at 8:19
• @virmaior page #19. By translate i meant as you said "human language", on russian. – user71305 Oct 5 '14 at 17:11

Maybe an example will help you: redness is such that necessarily, anything that is red is also colourful. So redness contains colourfulness. Necessarily means that you cannot conceive of something having the first without also having the second.

• Ok, thanks. I will use this as a note for a translation. As an explanation example. I used to think in that way too, when one property contains many. I asked this because words order here is seems alogical for me. Also i confused by unusual using of words as for non-philosopher. – user71305 Oct 6 '14 at 7:05

Let ϕ and ψ be properties, let x stand for a thing.

ϕ includes ψ means, for any x, ϕ(x) implies ψ(x).

Edit: This appears to be defined backward!!!

Let A = {x:ϕx}, B = {x:ψx}

(∀x) ϕ(x) ⇒ ψ(x) implies (∀x) x ∈ A ⇒ x ∈ B implies A ⊂ B, Which means A is contained by B!

• @user71305: This is odd. A property is equivalent to a set; a term having a property is equivalent to belonging to a set. Let A = {x:ϕ(x)}, B ={x:ψ(x)}, then ϕ(x) implies ψ(x) means ∀x, x ∈ A implies x ∈ B, which in turn implies A is included by B. This is exactly the opposite of the above definition! – George Chen Oct 5 '14 at 19:33
• @user71305 When speaking of intension, we use imply; when speaking of extension, we use include. This book has shown signs of muddle-headedness. – George Chen Oct 5 '14 at 20:35
• This answer is incorrect, strictly speaking because the necessity was droped and only extensions are considered. – Quentin Ruyant Oct 5 '14 at 21:03
• I don't think it's muddle-headed, it's just a specific vocabulary suited for metaphysics rather than logic: a property is said to include the other if it implies it necessarily (=in every possible world). – Quentin Ruyant Oct 5 '14 at 21:15
• @GeorgeChen - there is no error. If we consider "for all x (if P(x), then Q(x))" and read it extensionally, we consider P and Q as "extension" of two sets P and Q; thus, it is correct to say that P is included into Q. But "traditional logic" consider also intensions (i.e. concepts). Consider now the property of "beeing a square"; a square is a quadrilateral with some more "specifications"; thus, from an intensional point of view, the property or characteristic of "being a quadrilateral" is contained into that of "being a square". – Mauro ALLEGRANZA Oct 6 '14 at 12:05