1. All knowledge comes either from sensory perception (e.g., visually perceiving a mountain) or reasoning (e.g., solving an algebraic equation).

2. Both perception and reasoning occur in our minds.

3. The external world is, by definition, “external,” which is outside our minds.

Therefore:

4. Because everything we know exists in our minds, we can not have any knowledge about the external world. — Thales

There's an (in)famous counter to this, from David Stove, a parody:
1. One only ever tastes oysters with one's mouth
2. Therefore one never tastes oysters as they in themselves
3. Therefore we do not know how oysters taste

Do you still think that argument you presented in the OP is convincing? Since you did present it, should we take it that you have some doubt?


Your account is muddled. Blaming me won't fix it.
And yet here you are...

Some folk might find the thread on Austin: Sense and Sensibilia of use.

With great care, Austin dismantles the accounts of perception that are so problematic here.

In any case, it is now apparent that is dreadfully confused. He will happily talk about not seeing objects, but seeing light - as if the light by which we see were more corrigible than the very things we see.

By change here I mean temporal change rather than spatial change. — MoK

Yep. Cheers.

Now (1) in the OP is

P1) Time is needed for any change — MoK

can be adjusted by simply specifying that the topic of discourse is change over time. but then what of (2)?

P2) Nothing to something is a change — MoK

Needn't someone simply say that the change from nothing to something is then not in the topic of discourse - that it does not occur over time?

Seems this needs addressing. Arguably, the beginning of time is not a change over time.

Well, why not play the game?

For my part the notion of "objective" truth causes more problems for those of a philosophical bent than it heals. In particular, there are folk who supose that because they cannot access "objective" truth (whatever that is), that there are no truths at all.

But it ain't so.

...when you agree to play the game in the right way. — Apustimelogist

Are you saying it is better to play the gamein the wrong way?

Why not play it in the right way, or at least, work out what the rules are...?

Is says “there does not exist any proposition x, such that is it true”; — Bob Ross

No, it doesn't. See here. It's doesn't say anything, because it is not well-formed. Literally, it says there does not exist an x such that x - which says nothing.

It cannot be constructed using the rules of syntax for a first order logic.

(I have a hunch that the "set of all sets that don't contain themselves" may trip me up here). — Dawnstorm

I suspect so. The usual conclusion is that one cannot have a set of all sets. If that is what your "set of all existing things" is, then it's ill-formed. But a big part of the problem here is that it is very unclear what "nothing" and "existing" and "something" are doing; they are not being used in the way they are usually used, and so it is unclear what conventions are in place.

And I'd point out again that it seems highly contentious that a logical argument could reach a conclusion that was not somehow implicit in the assumptions of the argument - that something could "pop into existence in a puff of logic", to misquote Douglas Adams.

Again, I think the style of this argument is corrupt, that there is something amiss in the way the issue is framed.

I think the correct statement is that time is necessary for change. By this, I mean that there cannot be any change if there is no time. — MoK

Well, this has proved to be a contentious issue, which is to me somewhat puzzling. There are plenty of folk hereabouts who will agree with you, but I am not one. I see no reason not to say that changes can occur across distances, as well as times. And I think the mathematics and physics back up this approach, since we can calculate change over distance (Δx/Δy) for various things, and we have the physics of statics, Hook's law and so on.

I'd be interested in why you think this to be the case.

I get your point. — MoK

Cheers.

...god’s eye truth... — Joshs

This sentence is six words long.

I don't much care what god thinks. There are true sentences, contra , and, it seems, your good self.

Of course - at the expense of not telling the truth.

T ← C. — Lionino

We don't usually write the implication backwards. C ⊃ T.

But, in the absence of further clarification, I Understand to be making the claim that time is necessary and sufficient for change, hence T ≡ C.

I think this an incorrect assumption, and that time can pass without change.

But again, I think the whole framing of this issue here is misguided. Logic does not allow us to derive anything that is not in the assumptions, and hence logic alone cannot deduce the existence of god or of a first cause or of something never coming from nothing. A logic does not have ontological implications outside of whatever presumptions that logic makes.

Logic is just a way of talking clearly.

The way I see it, these paradoxes show in a nice way how all truth is an idealization. — Apustimelogist

Trouble is, that's just an idealisation.



Happy sawing.

What did you make of the article after a read?

For those who don't see the point of the topic, consider

In contemporary metaontological discussions, quantifier variance is the view according to which there is no unique best language to de- scribe the world. Two equivalent descriptions of the world may differ for a variety of pragmatic purposes, but none is privileged as providing the correct account of reality. — Finn and Bueno

Hmm. The difference between injective and bijective functions is more complex than I had thought. This Maths Is Fun site sets it out pretty clearly, and talks about ONTO. Cheers. I think my two feet for each head is bijective... feet = 2(heads), for positive integers...?

Then why do you think bijection requires counting?



A quick look will tell you that there are twice as many feet as there are people. You do not need to count the number of people to know this to be true; just check for amputees...


Bijecting two feet for each person.

Hmm. Maybe I misunderstood 's issue. I had taken him to be suggesting bijection would not do the task set it...

well, this stuff.

You are perhaps right, but I don't see as it helps.

Again, the point is pedagogic, not logical. Here's the question:

If you start with a set of integers 1 to a million and another set of integers one to infinity and pair one to one up to a million then the set of infinity unpaired is infinity minus one million which is meaningless and undefined. — Mark Nyquist

One might understand this as: What is the cardinality of the integers that come after one million? It's still ℵ₀.

...infinity minus one million which is meaningless and undefined. — Mark Nyquist

Infinity minus any finite number is still infinity. Doubtless others might make this informal answer rigourous.

I don't see what is "undefined" here, let alone "meaningless".

The issue here is not one of logic, but of pedagogy. The logic is clear, there are multiple infinities. The issue is why some folk cannot see that to be the case, even when presented with the proof.

Consider:

A one to one to correspondence implies a count of one side compared to the other. But infinity is not reached or exhausted and cannot be counted to — Philosopher19

Is it that Philosopher19 has a picture of infinity such that, since one cannot count to infinity, one cannot have a grasp of infinity?

One way infinity is introduced to children by showing them that for any number, we can construct a bigger number - by adding one, or some other finite number. Then comes "Infinity plus one!". The child will have understood infinity not as something one counts to, but as the ability to carry on in the same way...

In a way, Cantor showed the child's "infinity plus one" to be a reality... :wink:

So Philosopher19 it seems has a notion of infinity that is dependent on actually counting to infinity, rather than "carry on in the same way...", and hence takes it as granted that a one-to-one correspondence must involve counting. Two approaches occur to me, when I put on my long-discarded teacher's hat: to show a variety of infinite one-to-one correspondences, making the point that we do not need to count them all, or even at all, to see that they go forever; and to look at infinity in other contexts - art, perhaps - in order to show that one can understand infinity apart from counting.

Anyway, we are not being paid to teach Philosopher19, so that goes by the by.

A valiant effort.

I suspect it is in vein, and that the issue here is not logical so much as pedagogic.

How would a difference in size be established between two sets when there is no counting of the number of items in the sets involved? — Philosopher19

By bijection. See Open Logic Ch.4.

If there is counting involved, how has one reached an infinite number of items? — Philosopher19

"Counting", and ill-defined notion, is not involved in bijection, although "enumeration", a well-defined notion, is.

If infinity is a quantity, how is it more than one different quantity? — Philosopher19

See Cantor's diagonal argument.

We can't help that you can not see what is going on here.

Then I'm sorry for you. All I can suggest is that you read the section of the Open Logic project on Russell's paradox again, very carefully.

Because the choice is between the whole of the remainder of that project being founded on an error unnoticed by more than a century of study by logicians world wide; and your being mistaken.

Which is most likely?

I think it's clear that one cannot count to infinity So one cannot say that x is an infinite sequence of numbers just because it goes on forever. — Philosopher19

How does one not laugh at this?

I enjoyed your recent chat with .

What has not been shown to me is how this logically obliges us to view the set of all sets as contradictory. — Philosopher19

And this shows that you have not understood R = {x : x ∉ x}:

How do we set up a set theory which avoids falling into Russell’s Paradox, i.e., which avoids making the inconsistent claim that R = {x : x ∈/ x} exists? Well, we would need to lay down axioms which give us very precise conditions for stating when sets exist (and when they don’t). — On the next page...

:wink:

And if you want a better understanding of the issues here, see Chapter Four of Open Logic.

Unlike Philosophy Forum, it's guaranteed free of psychoceramics.

Nice try, .

I see no point in continuing this discussion. — Philosopher19

Then have a look here:

Theorem 1.29 (Russell’s Paradox). There is no set R = {x : x ∉ x}.
Proof. If R = {x : x ∉ x} exists, then R ∈ R iff R ∉ R, which is a contradiction. — Open Logic: Complete build

Banno's Law says that it is easier to critique something if you begin by misunderstanding it. That is what your OP does.

You, too,

, you may find the Open Logic text useful.

By my lights, one could parse nothingness as ~∃x (x) or ~∃x (Exists<x>). — Bob Ross

But ~∃x (x) is not well-formed - it doesn't say anything.

And ~∃x (Exists<x>)?

I guess you could go for a free logic and write something like ~∃x (∃!(x)) which (I think) just says that "It is not the case that there exists an x such that there exists exactly one x.", at the expense of throwing out classical logic. Why do that?

The thing about parsing is that one has to be specific about what one means, and that is absent in the OP.

Or we might follow Quines' "to be is to be the subject of a predicate" and only talk about non-empty domains...

So how does Quine defend his criterion of ontological commitment from the menace looming from the empty domain? By compromise. Normally one thinks of a logical theorem as a proposition that holds in all domains. Quine (1953b, 162) suggests that we weaken the requirement to that of holding in all non-empty domains. In the rare circumstances in which the empty universe must be considered, there is an easy way of testing which theorems will apply: count all the universal quantifications as true, and all the existential quantifications as false, and then compute for the remaining theorems.

Is Quine being ad hoc? Maybe. But exceptions are common for notions in the same family as the empty domain. For instance, instructors halt their students’ natural pattern of thinking about division to forestall the disaster that accrues from permitting division by zero. If numbers were words, zero would be an irregular verb. — SEP: Nothingness

...in which case there is never nothing.

Suits me.

(But I suspect this is going nowhere.)

I dunno.

Equivalence: Usually "≡", sometimes ↔︎, means "(p⊃q).(q⊃p)"

:meh:

Odd.

Whatever.

:meh:

Quine didn't seem to understand that facts are analytic — PL Olcott

:worry:
I'll leave you to it.

And yet Cantor.

So you have gone astray somewhere.

At the least, it might be worth setting out what you take Quine's objection to be and how this overcomes it.

As it stands, "expressions of language that are stipulated to be true"makes it appear that is saying that it is analytic if he says it is analytic.

Ok. I think is right. I'll leave you to it.

No, C is biconditionally implicated to T; not equivalent. — Bob Ross

That's what logical equivalence is. Ok, so you think it means something like that if time passes, then change happens, and if change happens then time passes. I guess so.

The quantification to which I gestured is "U" and "∃". So "Nothing is red" parses as ~∃(x) (x is red), or as U~(x)(x is red), but "U" and "∃" cannot be used to parse

it doesn't prove it is logically impossible; even if the premises are granted. — Bob Ross

Yep.

'tis an odd thing, culinary appellation. "Gherkin" tends hereabouts to be used for all sizes of pickled cucumbers; that seems not to be the case in foreign parts. "Pickle" tends to be used mostly for what others call "relish", especially in the favourite, mustard pickle, which consists mostly of green tomatoes and cauliflower, and is done towards the end of the season. "Pickle" is also used as a generic term for anything preserved in salt or vinegar.

The potato salad of family tradition consists in white potatoes, cut into small cubes and boiled in well-salted water until precisely al dente, then combined with chopped boiled egg and chives, the very best olive oil and a mild vinegar, usually white wine; seasoned with pepper and salt. That's it.

A thing of subtle beauty, it will not be adulterated with gherkins, pickles, capers or any other abominations.

And certainly no mayonnaise.

All of which is somewhat off the task at hand here, so I'll add that your "time cannot have begun" might just mean that there was no point in time at which there was no time... which is I think a point of grammar rather than a bit of ontology?

P1: T ↔ C — Bob Ross

Hmm. T is equivalent to C?

I suspect it's an implication - "if there is a change then there is a passage of time" or some such.

But the problem is that the "nothing" is embedded in a relation - "nothing to something" - except in (3). Somehow the parsing needs to quantify nothing...

There isn't a way to quantify over "nothing", without treating of an individual. So "nothing is red" can be quantified, it might be parsed as

~∃(x)(x is red)
(read: it's not the case that there is an x such that x is red)

But "there is nothing" can't be treated in this way.

Hence the general criticism, that these sorts of arguments reify "nothing" by treating it as an individual.

Most "paradoxes" are simply self-contradictory, self-refuting or circular statements or statements based on a false hypotheses. In short, invalid statements. — Alkis Piskas

Trouble is, the paradox is right there in the initial version of Principia Mathematica; that is, an "invalid" statement was implied by the formalisation of mathematics in a first order logic. It looked as if the whole edifice would collapse.

ZFC is, I believe, set up specifically so that "a list can't list itself". That's how it avoids the various paradoxes.