Logic 101

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Logic 101

Postby Ed3 » Thu Jun 06, 2019 9:31 pm

Logic 101

Recently, I have been thinking about formal deductive logic and how it is presented. The two presenters that have most recently impacted, or more truthfully frustrated, me are Dr. David Kyle Johnson via his lecture series entitled “Big Questions Of Philosophy” in the streaming series called “The Great Courses”, and our own Faust on his post “Logic 101”.

To give credit where credit is due, Faust, and I assume his editors, have put a lot of time and effort into what I would call a classic or textbook presentation. Additionally, my concerns might properly be addressed in a more advanced course.

As a simple matter of fact, Logic is not constrained to a bivalent or 2 value system. One can read about Kleene or Priest Logic in WIKI under “3-valued logic”.

As a corollary, the domain of all logical propositions is much larger than envisaged in the work of the two afore mentioned presenters.

Dr. David Kyle Johnson asks his audience to think of any examples where propositions are not either true or false and states that no one has come up with an example. It should be noted that the audience is largely made up of amateur or freshmen students. It is my experience that coming up with examples that are contrary in nature to the examples at hand can be difficult. (In general I regard this technique as an effort to obfuscate the subject at hand, though I cannot be certain as to Johnson’s intent in this particular case).

In Logic 101 under the section entitled Truth, Faust writes:

"Propositions are either true or false. If we cannot determine whether a declarative sentence is either true or false, then it does not contain a statement, for the purposes of logic. Another way to say this is that, logic presupposes that truth or falsity can be assigned to any proposition – an assignable truth or falsity being part of the definition of a proposition. While indeterminacy may be fascinating to the philosopher, it’s useless to the logician. And while the issue of indeterminacy has been insinuated into the subject of logic, we will not consider it here."

One can assume that the domain of propositions in formal deductive logic should be constrained to bivalent logic as Faust does in the above paragraph. However he expands on that point to state
“While indeterminacy may be fascinating to the philosopher, it’s useless to the logician.”, which is simply false. Note: indeterminacy is frequently a 3-valued logic with the values generally denoted True, False and Other.

It seems that multi-valued or at least three-valued logic creeps into the discussions on the topic of logic.

Examples:

Dr. Johnson proceeds to prove that if God is benevolent, all-powerful and all-knowing then God cannot exist. His argument is based on the assumption that each of these propositions have binary values. It seems clear to me that if God, assuming He exists, is not benevolent he could be either malevolent or other. This would ultimately would make Dr. Johnson’s argument invalid.

Under Argument Forms Faust writes:

“1. Either I am dead or I am alive.

2. I am not dead.

Therefore, I am alive.”

This is an example of simply assuming ones’ state of existence, regarding life and death, is bivalent. A person could be other. If you are not dead you could be either alive or other. In real life cases some people can be resuscitated while unfortunately others cannot.

I mention these cases simply to show how easy it is to assume that propositions are bivalent when in fact they may not be.

Other Examples:

The Literary Arts are full of examples of ethical multi-valued truth propositions.

Computer Data Values. Data sets can have a null value in addition to a specific data type.
Example: It is June 4, 2019. This can be true or it can be some other date (false) or there could be no date at all. (At least this was true back in the 1980s. It may have changed).

False dichotomy:

A common objection to a given argument is that we are being forced to choose between two divergent choices when other options exist. It seems, from the examples of Dr. Johnson’s argument that God does not exist and Faust’s argument about life and death, that there can be multiple options in the truth values as well.

Summation:

I do not object to teaching bivalent logic. It seems to me that there is a class of propositions which do evaluate to two and only two values. (One must be very careful when giving examples). It also provides intellectual discipline, something that may be sorely lacking these days.

However, trying to deny or minimize multi-valued logic simply distorts the world in which we live.

We should consider a more skeptical view of what is classically presented as a bivalent proposition and we should broaden our logical tools to include a multi-valued logic.
"Albert! Stop telling God what to do." - Niels Bohr
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Re: Logic 101

Postby Del Ivers » Thu Jun 06, 2019 10:22 pm

Ed3 wrote:..we should broaden our logical tools to include a multi-valued logic.

I think that's been done for some time now. For example, the logic of constructing a building and the building's values on different levels, e.g., hospital, restaurant, home, etc. You can measure twice and cut once but where that applies has its own values.

If I may ask, where do you stand on the relative/absolute argument about logic?
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Re: Logic 101

Postby Ecmandu » Thu Jun 06, 2019 11:45 pm

This reminds me of the social engineering experiment of Twix and snickers.

You have no choice but to choose left Twix or right Twix anymore.

My choice was to stop buying Twix.
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Re: Logic 101

Postby surreptitious75 » Fri Jun 07, 2019 12:52 am

Binary logic is merely a subset of all logic which is not always specific
As there is fuzzy logic which is not black and white but shades of grey

So one has to be careful about presenting binary choices where there may actually be more than two
What may appear to be binary may not actually be binary at all but the difference may be very subtle

The example given above however between being dead or alive is only binary because there are literally no other choices
Even if someone is medically dead but then are brought back to life they can only either be dead or alive and nothing else
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Re: Logic 101

Postby WendyDarling » Fri Jun 07, 2019 4:07 am

There are shades of grey to even being considered alive.
I AM OFFICIALLY IN HELL!

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Re: Logic 101

Postby barbarianhorde » Fri Jun 07, 2019 12:36 pm

Hello Ed.

I think that if we want to demonstrate multi value logic we must start out entirely aside from true and false logic.

Because we can not show the existence of non binary logic through the vessel of binary logic. I would argue that "neither true nor false at the time" is not a proper logical value, it is a suspended state, like Schroedingers cat.

On the other hand, we could very well imagine any number of contrasting truth values without a falsity in sight, if we proceed from the beginning, which is the world.

For example we could use with a 7 folded colour logic.
We can take each of the seven primary colours as legitimate logical values, outcomes of arguments.

Still it can be argued that "red" is "yes red" rather than "not red". But this isn't complete, as "yes red" is also either "no blue" or "yes blue" in which case "yes red" can also mean "yes purple".

So you get very non binary logic. There is no reason why the negation of one thing is just one thing. The negation of one value can be several values.

So while we may try to render multivalued logic into binary logic by just translating the elements in the equation and appropriating them into yesses and nos, this may not at all be the real mechanism whereby things are being categorized.

I almost made the error of saying "by which things are included and excluded" where of course that is a reference to a binary true/false system.

We could say binary logic is the most radical logic.

Ive now treated multi-poled logic. There is also monadic logic, where "false" is simply a syntax error.
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Re: Logic 101

Postby Ed3 » Sat Jun 08, 2019 9:04 pm

Hi to all,

I appreciate all of the responses. Thank you.

I would like to respond to Del & Surreptitious specifically even if unfruitfully.

Hi Del,

I don’t know if I can intelligently answer your question regarding relative or absolute logic. I do know that logic has changed over time and some of the responders have addressed those issues. Personally I think that the main goal is truth preservation and I think that generally we are gaining better tools. Even the rejection of the law of the excluded middle may be useful in some domains. I wish I could have a better response.

Thanks Ed

Hi Surreptitious75,

I have puzzled most over your response. Your first two paragraphs seem to be spot on.

Your comments about life and death have made me question my statements in the OP. I think that many people, probably the most people, think that you are either alive or dead. The best that I picture the situation is as follows:

Ed3 surreptitious75
{{Alive}, {Medically Dead}, {permanently dead}} {{Alive}, {Medically Dead, Permanently Dead}},
where Medically Dead is an indetermanent state.

I am not sure if you agree with this representation.

Thanks Ed
"Albert! Stop telling God what to do." - Niels Bohr
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Re: Logic 101

Postby Karpel Tunnel » Sat Jun 08, 2019 9:39 pm

Ed3 wrote:Ed3 surreptitious75
{{Alive}, {Medically Dead}, {permanently dead}} {{Alive}, {Medically Dead, Permanently Dead}},
where Medically Dead is an indetermanent state.

I am not sure if you agree with this representation.

or...
{{Pursuing one's goals, dealing with one's passions and all emotions, exploring}, {Leading a decent heavily compromised life with some self-medicating with distractions}, {couch potato, unaware of most of one's feelings and desires}} {{Heavily psychotopically medicated, permanently institutionalized}, {long term comatose}} + medically dead + dead dead

Though these are obviously not discrete states. People can move in between them over time, further near infinite gradations exist.

I would guess that there would even be ways to measure the differences, perhaps mitochondial efficiency, or metabolic flexibility and base rates, differences in the curves related to stress hormones in the blood, skin resistence to electricity and so on related to dealing with stress.
Last edited by Karpel Tunnel on Sun Jun 09, 2019 4:28 am, edited 1 time in total.
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Re: Logic 101

Postby Meno_ » Sun Jun 09, 2019 12:43 am

And there is the famous propositional paradoxical test, of the verity of "an apple can't be red and green all over."., as an example worthy of discussion in this context?

How has that changed the rules by instituting logic into the realm of perception and meaning? Has that changed the gap between binary and multivalued logic?


PS: who remembers something among this line?
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Re: Logic 101

Postby Del Ivers » Mon Jun 10, 2019 10:22 pm

Ed3 wrote: Personally I think that the main goal is truth preservation and I think that generally we are gaining better tools.

Yes, I would agree with that as a healthy enough general statement. The complications arise when someone asks what 'truth' is it that is being preserved. The easy answer is what is evident as beneficial. But that won't go easy with some, especially absolute determinists and assorted brain-in-a-vat types. :)
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Re: Logic 101

Postby Meno_ » Mon Jun 10, 2019 11:14 pm

The only difference between brains in vats and those out of them is that their awareness may only shift from one to the other, as they always have to stay outside, for fear of being drowned by having to guess at it.

That they have to, is a measure of the reduced sense of their simple minded , folksy assessments of 'what it must be like " in there".



Oops. Del, no offense. only a general reply to a general statement, honest, just looked at source.

Ref: my forum here: "Philosophy not for the faint heart"

Not yet an ad hoc ad hominem, that in support of the kind of self assessment I managed to eek out .
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Re: Logic 101

Postby Del Ivers » Tue Jun 11, 2019 3:55 am

Meno_ wrote:Oops. Del, no offense.

No offense taken

Taken Offense No
An Offense Token
Takeoffs En None
Fake Soften Neon
Nonfat Keen Foes
A Keen Sonnet Off
Anon Keenest Off
Safe Often Ken On
Snake One Ten Off
Sneak One Net Off

:)
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Re: Logic 101

Postby Meno_ » Tue Jun 11, 2019 5:51 am

Oh , Del, You say the nicest things. You're You're Ok, in my book.
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