• James Bejon
    3
    Dear All.

    I was hoping someone could give me a hand with expressing a couple of statements in terms of logical notation. I’m looking at verse 3 of the Gospel of John, which (for the present purposes) can be understood as follows:

    3a: All (made) things came into being through the Word,

    3b: and apart from the Word nothing came into being which has come into being.
    — John 1.3

    I’d like to represent these statements logically. Something like:

    Let X = the set of all made things,

    and let P(x) = ‘x came into being by the Word’

    Then 3a can be expressed as ∀ x ∈ X: P(x)

    And 3b can be expressed as ¬ (∃ x ∈ X: ¬P(x))

    But I doubt I’ve written these right. It’s a long time since I did anything like this.

    Thanks in advance,

    James.

  • HappenstanceAccepted Answer
    71
    Maybe, if The Word then all things being, and if not The Word then not the case that all things being: ∃x∀y[(Wx→By) & (¬Wx→¬By)]
  • James Bejon
    3
    Thanks for the reply! Is there a difference/advantage in wrapping it all up in one statement? What was your rationale here?
  • Happenstance
    71
    I noticed that 3b. started with the connective word and. Also I put 3a and 3b into truth functional form, atomic sentences within if.. then conditionals whilst attempting to keep the semantics intact. Basically, writing them as propositions with no semantic loss, IOW keeping the meaning in the original statements. I also noticed that there was no change in what was being quantified in both statements hence wrapping around the conditionals within: ∃x∀y[...]
bold
italic
underline
strike
code
quote
ulist
image
url
mention
reveal
youtube
tweet
Add a Comment

Welcome to The Philosophy Forum!

Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.