A Mistake of Memory

Comments

8 responses to “A Mistake of Memory”

1. 

   David Brightly

   June 9, 2023

   Bill,

   For if the present alone exists, then the wholly past does not exist. But what does not exist cannot be known.

   As usual, I’m not sure how to interpret the tense of these statements. Here is an attempt to clarify.
   Let U be the set of all things that have existed, exist now, or will exist. A common sense picture of existential change might be to say that at every time t we can partition U into three exclusive subsets: P(t), the things wholly past at t; N(t), the things present (‘Now’) at t; and F(t), the things wholly future at t. Our intuitions regarding existential change can be captured in a set of axioms such as

   t<t* → P(t) ⊂ P(t*),
   x ∈ P(t) → ∃t*. t*<t ∧ x ∈ N(t*),
   etc.

   We can extend this with an axiom about things known at time t,

   K(t) ⊂ P(t) ∪ N(t).

   This interprets your ‘what does not exist cannot be known’. But I get no feeling that there lurks a contradiction within this system.

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2. 

   BV

   June 9, 2023

   Thanks, David. Will sleep on it, and respond tomorrow.

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3. 

   BV

   June 10, 2023

   David,
   That is one well-crafted comment. >>Let U be the set of all things that have existed, exist now, or will exist.<< I hate to object right at the outset, but I must. First, if presentism is true, then there is no set of all things that have existed, exist now, or will exist. The existence of a set depends on the existence of its members, and the identity of a set is determined by the identity of its members. But if only what exists (present tense) exists simpliciter, then there is no set U. Or you could say that the set U is identical to the set of all things that exist now. But then a second objection kicks in: since sets have their members essentially, a set cannot change its members; but what exists is ever changing; hence there is no one set that is the set of all things that exist now. The point can be put like this. You can speak sensibly of the set U only if you allow a use of 'exists' that is tense-neutral. But if I understand your position, there is no such sense. If you claim not to understand the concept of existence simpliciter, the concept (in plain English) of that which simply exists, then your presentism amounts to an uninteresting tautology: Whatever exists (present tense) exists (present tense) -- "which nobody can deny."

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4. 

   David Brightly

   June 11, 2023

   Morning Bill,
   I won’t take the option of saying that U is the set of all things that exist now. Instead I will confront your objection that, if presentism is true, then there is no set of all things that have existed, exist now, or will exist. I think we can frame puzzles involving tensed language in set-talk independently of the truth of presentism. You say that the existence of a set depends on the existence of its members. On this we disagree. If you were right we would face the following problems:

   1. The invented examples by which set-talk is taught and examined would be vacuous.
   2. We could not reason about detective fiction, say, using set-talk.
   3. We could not reason in set-talk about the contents of a non-actual possible world.

   At worst, a set of non-existents, the even primes greater than two, say, is empty but not itself non-existent.

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5. 

   BV

   June 12, 2023

   Interesting objections, David, but I think that what I am saying is correct if carefully formulated. Apart from the null set, necessarily, a set S exists iff S has existing members. For example, {Socrates} exists iff Socrates exists.
   As for the set {Sherlock, Moriarty} where each of these is a purely fictional individual, why can’t I simply deny that that set exists, and say instead that it is a purely fictional set? If there are purely fictional nonsets, why can’t there be purely fictional sets?
   And why can’t I say that a set of merely possible nonsets is a merely possible set?
   The crucial question is: what do we mean by ‘exist(s)’? I say that to exist = to be real and actual outside the mind, outside language, and apart from its causes.

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6. 

   David Brightly

   June 12, 2023

   Hello Bill,
   Here is where our views of sets diverge. Your view I think is ‘externalist’, mine ‘internalist’.
   Suppose someone gives us an account of certain things, people, places, and events, all new to us. It seems to me that we can formulate this account in ‘untyped’ set-talk. We do not need to know in advance if the account is true and hence the sets exist; or whether they are fictional sets, or merely possible sets, or indeed past sets. We are merely translating the account into a more regimented language that brings out the logical relationships between its objects and facilitates reasoning about them. Cantor thought of sets as collections of objects of perception or thought and I like to think I am following in this tradition.
   What does it mean to say that a certain set exists? I cannot accept your ‘real and actual outside the mind and language’ formula in relation to sets. Several ZF axioms say that given some sets another set constructed from these in a certain way ‘exists’. I think this should not be seen as an existential claim in anything like the usual sense. Rather it is an ‘endorsement’ of the construction, ‘permission’, if you like, to construct (and by implication think and argue with) a new set by that method.

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7. 

   EG

   June 17, 2023

   David,
   I am inclined to agree with Bill, with your insistence about set-theoretic language, I do not think you have properly engaged Bill’s point about existence simpliciter.
   Bill,
   Does our ability to talk coherently about the past, and a plausible future–indeed let’s even say the ability to do Science, put paid to the Presentist position?
   Also, if we can articulate fictional objects etc, doesn’t this ground them in some lesser form of existence, but not non-existence?
   Thinking about this now, I don’t think we can think about Nothing or Non-Existence.

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8. 

   David Brightly

   June 22, 2023

   Hello EG. My proposal is to work within an untensed language in which the temporal relations between things are expressed through explicit functions from time to sets (ie, extensions). One version of presentism is simply to say that the extensions of concepts are time-varying. We might then have a neutral means of elucidating ‘existence simpliciter’. But we seem to have run foul of a disagreement in the ontology of sets. The sets P(t), N(t), F(t) seem quite innocent to me, merely referring to what things would be pre-theoretically agreed by all at t to be wholly past, present, and future. One might then make it axiomatic that P(t)∪N(t)∪F(t) = U for all t.

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