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Great question!

It is possible to use logic to arrive at a conviction of the truth of the dhamma, as Nagarjuna demonstrates and others such as Francis Bradley, Spencer Brown and (ahem) me. But this is map-reading. You can read a thousand books about fire and not know what it feels like to be burnt.

So while logic and reason are useful and trustworthy they are not a carriage that will carry us to Heaven. The Old Testament tale of the Tower of Babel is a teaching story.

Reason and logic applied to metaphysical questions must work by abduction, by the elimination of unworkable views. This means that metaphysical analysis can be a valuable guardian against error, as Aurobindo characterises it, but while it can proscribe truth by ruling out false views it cannot reveal truth or give it meaning for us. Revelation requires burning the maps and undertaking the journey.

It is much the same in physics. Most interpretative theories can be ruled out on the basis of analysis but no theory is provably 'true'. Reason and logic produce theories and having a theory of the existence of a holiday resort is not the same as going on holiday.

Meditation is necessary because truth outruns the intellect and cannot be discovered intellectually. For Mahayana the true nature of reality would be beyond conceptual fabrication and the categories of thought, so no amount of thought is able to take us there. As all the teachers say...

“Man can partake of the Perpetual. He does not do this by thinking he can think about it.”

Jan-I-Janan
Sentences of the Khajagan

I have read at various places that Nirvana can't be described or reached by logic or reason.

I think that's two questions: 1) described, 2) reached.

I think Nirvana is defined as being the end of craving -- not just a temporary pause or lull, but uprooting the "tendencies" and "effluents" which result in the arising of craving -- so changing or undoing habits (if craving is a kind of habit, and results from habits, etc.).

And you can't do something, or accomplish something ("reach" something), just by thinking about it -- you have to do it!

I suppose that's true of everything -- mundane things too not only Nirvana -- e.g. you can't learn to play piano or guitar just by thinking about: you'd have to do it, practice it.

Maybe that's true even of describing something -- I can't describe playing guitar or piano, nor even describe hearing piano or guitar -- i.e. you'd have to actually do it yourself, play it or hear it, to know it for yourself.

Nirvana can't be described or reached by logic or reason

Logic and reason are functions of the intellect-mind. Nirvana is beyond the intellect-mind.

What is the intellect-mind? The mind that works on and understands mathematics. The mind constructs the equations, then goes on verifying the left and right sides between the "=" are equal; then designs experiments to prove the equations. In brief, intellect-mind is a self-sustaining system, it goes in a loop of generating hypothesis then re-assumed the hypothesis to evidences, that become facts - which condensed and constructed the world. Say, the stone is solid and heavy. But to generate the stone is solid and heavy - the phenomena, it requires the intellect-mind to recognize the concept of stone, then recalls the attributes of the stone; then the physical body, sensory system and brain, etc., of the human will response to the totality of it, by not able to lift it, or not able to walk pass if it is blocking the road...

ONLY meditation is the way

No. Meditation cannot bring one to Nirvana. Those meditation teachers if telling you Nirvana is by reaching certain grade of Jhana, or certain Vipassana, they are just selling you a consumer product with catchy marketing slogan.

Even Vipaśyanā requires getting beyond the intellect-mind. Don't confuse it with the marketed "Vipassana" of Mr. Goenka's or many meditation "teachers", just like a motel with the neon sign "Paradise" doesn't mean it the Paradise. The Buddha's Vipaśyanā is about reaching high level Dhyana, where the sensory inputs are all cut off, the intellect-mind is surpassed, by then insight, the vipaśyanā, can operate.

Therefore intellect-mind is the mind of reason and logic, it is the mind we most familiar with, we use it all the time. No matter how intelligent one owns her/his intellect-mind, how high the IQ score, it doesn't give a slightest edge to this type of person for reaching Nirvana. Though being intelligent is a remarkable gift. Nirvana is removed from reason and logic.

While the less fluid mindset may easily misinterpret the above demoting the unique gift of human intelligence - logic and reason, how it contributes to modern scientific and technological achievements, it is misreading the meaning of this post. Hellenistic civilization after shaped by Aristotle is dominated by seeking analytical/empirical knowledge procured by the intellect. But it is not the totality of the mind. The mind is more mysterious contained much richer facets: such as how a maths genius conceived numbers.

Why Meditation cannot bring one to Nirvana?

Errr... often too advance an answer is not easy to comprehend :)))

I assumed most Buddhists understand that Nirvana cannot be realized by meditation. Apparently it's not the case.

a) The Buddha himself said so and demonstrated it, in the very beginning of his search. Let's go back to Chapter One -

The young Gautama became an ascetic first learnt from Ārāḍa Kālāma, whose specialty was dwelling in the "Sphere of Nothingness" which he regarded was Nirvana - the 7th Dhyana. After acquired the skill and dwelt in it Gautama immediately knew it was not.

He then learnt under Udraka Ramaputra, specialized in dwelling in the "Sphere of neither Perception nor Non-perception" - the 8th Dhyana. He thought that was Nirvana. After training 3 years Gautama skilled in it, but, to his disappointment, it was still not. He found there still subtle and fine "perception/consciousness" remained. And, when the power of Samadhi subsided, the practitioner would still fall back to the cycle of birth-death.¹

b) If still not enough to convince, let's look at Buddha's unique discovery - the 9th Dhyana.

The 9th Dhyana is called Nirodha Samapatti (想受滅定), meaning, cessation of thinking and perception. Practitioner entering this Dhyana is virtually dead, read the description of it in the Vinaya (probably not available in Pali text) about Utpalavarṇa and the 500 cow-robbers. Entering this Dhyana one loses her/his autonomy, say, if someone has destroyed her/his body, s/he wouldn't be awaken to stop it. S/he couldn't emerge from this Samadhi without a skillful one "called" her/him. Usually practitioner needs to give her/himself a hint before entering, so that s/he can emerge from it in time. From these characteristics, it hardly can be associated with Nirvana.

c) Nirvana is like someone who removed the headgear and exited from the AR game. Meditation is just the pause in the game, which allows the player to take a break, returns to her/his senses that s/he is just in the game. But to be released from the game, one needs to disengage in it. This analogy also gives better understanding to my two beginning paragraphs.

Or, meditation is like washing a broken dish, it can clean it to see the fracture more clearly, but it can't mend the crack. The Buddha said, the unenlightened's life is with effluence, only an Arhat has ceased the effluence.

_footnotes

_{1. 《佛本行集經》: 「仁者此法不能究竟解脫 (cannot reach ultimate liberation)... 大涅槃 (great Nirvana)。此法還入於生死 (this method still enters back into birth-death；所以者何？既生非想非非想處 (after born in the Sphere of neither Perception nor Non-perception)，報盡還入於生死 (when the effect subsides, [one] still enters into birth-death)。」}

In the book chapter entitled "Boiling and the Leidenfrost Effect" (an excerpt is quoted below), physicist Jearl Walker discussed the Leidenfrost Effect and explained how it may protect a firewalker from burns to the feet.

Eventhough logic and the scientific method had led him to have complete conviction in physics, he still had sweaty feet and had to clutch a physics textbook to bolster his faith in physics, while demonstrating the effect himself.

Similarly, logic may give you conviction in Buddhism, but logic may not free you from suffering.

The Leidenfrost effect may also play a role in another foolhardy
demonstration: walking over hot coals. At times the news media have
carried reports of a performer striding over red-hot coals with much
hoopla and mystic nonsense, perhaps claiming that protection from a
bad burn is afforded by ‘‘mind over matter.’’ Actually, physics
protects the feet when the walk is successful. Particularly important
is the fact that although the surface of the coals is quite hot, it
contains surprisingly little energy. If the performer walks at a
moderate pace, a footfall is so brief that the foot conducts little
energy from the coals. Of course, a slower walk invites a burn because
the longer contact allows energy to be conducted to the foot from the
interior of the coals.

If the feet are wet prior to the walk, the liquid might also help
protect them. To wet the feet a performer might walk over wet grass
just before reaching the hot coals. Instead, the feet might just be
sweaty because of the heat from the coals or the excitement of the
performance. Once the performer is on the coals, some of the heat
vaporizes the liquid on the feet, leaving less energy to be conducted
to the flesh. In addition, there may be points of contact where the
liquid undergoes film boiling, thereby providing brief protection from
the coals.

I have walked over hot coals on five occasions. For four of the walks
I was fearful enough that my feet were sweaty. However, on the fifth
walk I took my safety so much for granted that my feet were dry. The
burns I suffered then were extensive and terribly painful. My feet did
not heal for weeks.

My failure may have been due to a lack of film boiling on the feet,
but I had also neglected an additional safety factor. On the other
days I had taken the precaution of clutching an early edition of
Fundamentals of Physics to my chest during the walks so as to bolster
my belief in physics. Alas, I forgot the book on the day when I was so
badly burned.

I have long argued that degree-granting programs should employ
‘‘fire-walking’’ as a last exam. The chair- person of the program
should wait on the far side of a bed of red-hot coals while a degree
candidate is forced to walk over the coals. If the candidate’s belief
in physics is strong enough that the feet are left undamaged, the
chairperson hands the candidate a graduation certificate. The test
would be more revealing than traditional final exams.

Well reason, inferences, logic and all that are not knowledge. Only a few puthujjanas claim that there is such a thing as ''intellectual knowledge'' or ''intellectual understanding''.
Those puthujjanas qualify themselves of rationalist. In fact any puthujjana is a rationalist or an intellectual or a philosopher. This is what is natural for a puthujjana.
They claim that truth is reached through debate or truth is reached through inferences of some axioms through some rules of inferences that they themselves invented.
For those people, truth is a quality of a statement: a statement is true, like a banana is ripe or yellow and a true statement means that the statement ''accurately describes'' some event or experience.
All those inferences are fantasies and Those puthujjanas know that they are at sea among all those fantasies that they create.
Those puthujjanas still try to create a way to discriminate among the fantasies that they create: today the most famous discrimination is the one of the scientist where some statement is inferred either form a previous ''proved'' statement or from ''statistical evidence''.
This is for the puhujjana who is a ''secular rationalist''. For the religious puthujjana who is a rationalist, ''reason'' is the way to understand their gods [like the christians] and morality.
Typically, the ''secular rationalists'' claim that the ''inferences'' of the ''religious rationalists'' are fantasies (because ''not grounded in reality'') and that only the ''inferences'' of the ''secular rationalists'' ''make sense''.

Of course those puthujjanas are completely wrong. Truths are not how good a statement describe reality. Truth is at best an event and in terms of event, that's what stops you from ''searching truth'', meaning what appeases you, which precisely means nibanna.
That's called dhammakaya.

So in terms of knowledge, there is only ''direct knowledge'' (in opposition to ''intellectual knowledge'' whose existence that puthujjanas crave so much, but which really does not exist, no matter what logician, philosophers, intellectuals and other ''pragmatic people'' claim) and the task is to know directly dukkha, the origin of dukkha, the cessation of dukkha.

It turns out that knowing directly anicca, anatta, origin of vedana, cessation of sanna and all that requires a calm citta, which is called ''a citta which has samadhi'' and also sati.
THis is why a non-puthujjana can reach the destination of the path while the citta is in samadhi, since non-puthujjanas know already what to look for.

Puthujjanas must memorize the word of the buddha and get their citta into samadhi. And to get the citta into samadhi, what is required is to judge your thoughts as either thoughts of illwill and lust and thoughts of good will and renuncitation and follow only those latter.

Here are plenty of dualities to contemplate and make you an arhant or once returner.

For the sake of knowing qualities of dualities as they actually are.’
Which duality are you speaking about? ‘This is stress. This is the
origination of stress’: This is one contemplation. ‘This is the
cessation of stress. This is the path of practice leading to the
cessation of stress’: This is a second contemplation. For a monk
rightly contemplating this duality in this way—heedful, ardent, &
resolute—one of two fruits can be expected: either gnosis right
here-&-now, or—if there be any remnant of
clinging-sustenance—non-return.”

That is what the Blessed One said. Having said that, the One
Well-Gone, the Teacher, said further:

“Those who don’t discern stress,

what brings stress into play,

& where it totally stops,

without trace;

who don’t know the path,

the way to the stilling of stress:

lowly

in their awareness-release

& discernment-release,

incapable

of making an end,

they’re headed

to birth & aging.

But those who discern stress,

what brings stress into play,

& where it totally stops,

without trace;

who discern the path,

the way to the stilling of stress:

consummate

in their awareness-release

& discernment-release,

capable

of making an end,

they aren’t headed

to birth & aging.1

here is another one

“Now, if there are any who ask, ‘Would there be the right
contemplation of dualities in yet another way?’ they should be told,
‘There would.’ How would that be? ‘Whatever is considered as “This is
bliss” by the world with its devas, Māras, & Brahmās, by this
generation with its contemplatives & brahmans, its royalty &
commonfolk, is rightly seen as it has come to be with right
discernment by the noble ones as “This is stressful”’: This is one
contemplation. ‘Whatever is considered as “This is stressful” by the
world with its devas, Māras, & Brahmās, by this generation with its
contemplatives & brahmans, its royalty & commonfolk, is rightly seen
as it has come to be with right discernment by the noble ones as “This
is bliss”’: This is a second contemplation. For a monk rightly
contemplating this duality in this way—heedful, ardent, & resolute—one
of two fruits can be expected: either gnosis right here-&-now, or—if
there be any remnant of clinging-sustenance—non-return.”

https://www.dhammatalks.org/suttas/KN/StNp/StNp3_12.html

It is with meditation that results in seeing clearly. Seeing clearly (vipassana) non-self & impermanence, one gets diapassioned. Getting dispassioned, one lets go. This is precisely the reason why one cannot reason out one's way to nibbana because nibbana is not something to acquire, but it is the letting go of all ignorance which doesn't happen by just intellectually understanding certain teachings, but by understanding plus practise. With intellectual knowledge the causes & conditions are still in place for ignorance to arise

Dr. Dev Pradhan – Intellectually we have wandered too much, The simple question was, Why can't we reason or logic our way to NIrvana?, needs at first instance the same way of answer. When asking by group., as we, its simple answer is that Nirwana is void of any kind self of any group or individual. Hence there you can not use I, you or we. Its very appearance is possible only with the alignment of understanding of ANATTA. Where you have to drop I you and we with the realization of not only DUKKHA, nor ANICCHA, but ANATTA, means no self.There you have to drop thinking, mind, and logic also. You remain only in a state of experience of universe. Buddha already said do not reveal para human things to laymen. Scientist are spell bound about universe, and at a loss to know even black holes. Our state of mind is like that. We with out the guided path try to explore universe. This is what happening with us. When you want to know universe you have to leave earth planet. Without leaving earth if you want to know universe it won't be real experience. Hence if you want to know Nibban you need to learn how to drop the self to view the window of nirwana. After the dives of eight times and fully acquainted, then you will be able to reach the height of NIBBANA. That's why throughout the world people become Bhikkus. It needs practice of nine stages, along with the armor of SILA SAMADHI, PAYYAA. And this only can be explored by individual Buddha, Bodhisatwa, or Arhat. What Peter J says puthujjanas means laymen, the have to be acquainted and trained of primary knowledge of Sil and Samadhi. Once they acquired foundation they can be taught Pragya, Abhidharama and Parmarthdharmas.

Why Nibbana can't be described?

This is my simple answer:

How would you explain something that you've already experienced to someone who has never had that experience (not even in his/her dreams)? First you may try to explain its attributes. you describe its shape. But what if that thing has no shape?? Then you try to describe its colors, what it smells like, what it tastes like, what sounds it makes, what it feels like, etc... But what if that thing has none of these attributes?? You may try to explain its location. But what if that thing has no location?? What if that thing only experience through your consciousness? i.e. What if that thing only visible to your mind? How would you describe such a thing?

All the above mentioned statements are also applicable to Nibbana. Words are formed by people to describe worldly things. Shakyamuni Tathagata Lord Buddha preached this Dhamma (which describe ultimate truth) with the help of the words used in conventional truth. One should understand ultimate truth only through the help of conventional truth because we (five aggregates) are in a conventional world. In tipitaka Nibbana is described as much as possible with its features and attributes because Nibbana has no similar dhamma in this entire universe.

For further explanation see this answer which describes Nibbana.

Why Nibbana can't be reached by logic or reasoning?

Every consciousness arise with the help of an object. If there is no object there will be no consciousness. Two things cannot be the object for one consciousness at the same time and only one attribute of one object can be taken as the object of one consciousness. Nibbana is an ultimate dhamma. Nibbana is the object for the eight supermundane consciousness. It cannot be the object of any other consciousness. The supermundane wholesome path consciousness arise in mental processes (citta veeti) when someone enter four stages of enlightenment [Stream-enterer (Sotapanna), Once-returner (Sakadagami), Non-returner (Anāgāmi), Arahant]. Different consciousness arise according to a defined sequence in mental processes. (Note: This is not defined by an almighty god but merely happened due to the citta niyama.) No one has the ability to change this citta niyama. (This also prove the anatta mark of existence in every dhamma) So you cannot suppress some consciousness in a mental process or generate supermundane consciousness in another mental process which is used to reasoning or logic. Meditation is the only way to follow this sequence of mental processes and finally attain Nibbana.

Nirvana is the "formless". Opinions, words, beliefs are concepts, forms. All of the opinions, beliefs, judgements, desires are obstacles in the way of reaching Nirvana. Thich Nhat Hanh said that Nirvana is "Freedom from views". So trying to reach Nirvana with views, logic etc.. is the opposite direction. But the concepts can be helpful If you use them as pointers to become free from your attachments to concepts. Just like "I have to meditate for many hours" thought can change your life entirely. So there is also an irony here.

Meditation can be done in many ways. Meditation can be done in sitting in a meditation posture, or during a bus trip etc..The choices are many. So doing "meditation" is absolutely necessary unless the person has a spontaneous enlightenment. But that doesn't mean that a person can only experience Nirvana during a meditation session. The experience of Nirvana comes through seeing impermanence suffering and non-self clearly. Practising mindfulness doesn't lead you to think about the future but still is like making reservation in the higher realms of existance. Also If a person really does meditation with effort in proper ways, s/he enters to a temporary stream of awareness which makes that mindfulness continous temporarily even when the person isn't doing anything to be mindful. So seeing the meaninglessness of all forms that will cause the experience of Nirvana can come anytime in daily life for the meditator. But unless the person is very lucky to have a spontaneous enlightenment or unless the person already experienced Nirvana before and attained Stream Entry or other enlightenment stages, it is impossible to experience Nirvana without practising meditation/mindfulness.