First, humans cannot be reduced to a DNA code or something like this. The fact that monozygotic twins are genetically identical doesn't have to do with they exact physical constitution. For two physical thing to be identical, they have to have exactly the same characteristics (except by the spatio-temporal localization, since two bodies cannot occup the same space at the same time), that is, the exactly same physical composition. If a twin have one strand of hair more the other (which isn't necessarily a thing genetically determined), then they cannot be called "identical". Even the DNA of the cells can change in one twin but not in the other, due mutations or something (note that not every mutation is malefic; some are benefic and some doesn't fenotipic expression).
Second, even if we assume that monozygotic twins are exactly identical, which we know that is false, there is one more thing you didn't considered in your point. Human beings - actually, every animal, in general - are in certain way biologically shaped by the environment where they live in. There is a concept in neurology called "critical period", which is a period in life during which the nervous system is very responsive to environmental influence. For instance, if a kid isn't taught to learn some language until the critical period ends (about 12 years old) cannot - or, if so, very dificultly - learn language anymore. And, following Wittgenstein, as our thought depends on language, of course a twin for whom the language wasn't presented will think and probably behave very diferently from the other that learned a language.
Even if two twins are presented to the same stimuli, it doesn't have to do with theirs respondes to it.
In a manner analogous to the kantian transcendental idealism, what determines how the individual will behave isn't the stimuli itself, but the individual response to the stimuli, which isn't the same in several cases (for Kant, we are not supposed to say something about the object itself, the "noumena", but yet about the way that such an object is presented to us, the "phenomena"). But, you can ask, how can the response to the same stimuli be different? Well, it has to do with the disposition of the synaptic network on the brain of the person. If, for some unknown reason, a stimuli makes the neurons to react in a manner that makes the person feels good, then the corresponding synapses are strenghtened. For else, they are weakened. The human brain has the incredible capacity of regulate itself to suit the environment, due the neuroplasticity, and reguling itself makes it's further response to environment to be different from other person's one, even if they are genetically identical. I have to go bed now, but what I wanted to say is that we do have neurobiological fundaments to explain that, even though I couldn't bring they with required scientific rigor here, and that saying that because of this difference between twins there is something like a "mind substance" (which you didn't defined, but I suppose it's an immaterial thing) is a logical jump. Thanks for posting!

Yes but the differences in physical structure of the brain (so you claim) can't explain differences in personality of monozygotic twins. Why? All humans share the same body plan and that explains why our world is so well-structured. We all feel, think in similar ways and that's why we can depend on each other's interpretations of our intent and actions. These are similarities that can be adequately explained by physicalism. However, physicalism can't account for the differences between individuals. Why isn't everyone like each other? Could there be a mind-substance that makes each unique?

Monozygotic twins are those that develop from the same zygote (sperm+egg) and are described as identical twins. They have identical genetic codes. In other words the physical aspects of such twins are indistinguishable i.e. insofar as the physical is concerned monozygotic twins are perfectly identical.

Yet, even such twins are vastly different in mind. One may like action movies and the other comedy, etc. Each runs on different philosophy. There are also people with two heads and the same body with each head having a different personality i.e. their minds are different.

Now if physicalism is true then shouldn't monozygotic twins be mind-identical?

They are NOT. — TheMadFool

"Identical" simply means that a single zygote splits during development. It isn't using "identical" in a logical sense, so that we're talking about two things that are indiscernible. After all, if identical twins were indiscernible, if we were using the term in a logical sense, it would be literally impossible to tell them apart via appearance--that's the whole idea of indiscernibility (we also have to ignore that they're numerically discernible, which simply amounts to the fact that you can tell that there are two of them).

Under nominalism, by the way--and some of us are nominalists, no two numerically discernible things are logically identical in any respect.

Genetics aren't the only determinant of an organism. Not only environment plays a factor, too, but genetics are not expressed in some exact, clockwork manner. There are countless ways in which genetic expression varies--and after all, if that weren't possible, genetic mutation wouldn't be possible, and evolution couldn't work.

So this argument hinges on both ignorance of the different senses of "identical" and ignorance of what genetics amounts to.

Of course it could exists, but as I said, infering it from the fact that science aparently can't explain this or that is a logical jump. And difference of the physical structure can explain the differenct in personality! For instance, if a person has more quantity of a specific neurotransmiter in a specific region in the brain, the behaviour and personality of this person would be different of that if he had less neurotransmitter, or had in another area. In the 50's, for example, it was very common the lobotomy of some psychiatric patients, which is a surgery in which some connections of the frontal lobe to the subcortical area are broken, changing the personality of the patient.

Genetics aren't the only determinant of an organism. Not only environment plays a factor, too, but genetics are not expressed in some exact, clockwork manner. There are countless ways in which genetic expression varies--and after all, if that weren't possible, genetic mutation wouldn't be possible, and evolution couldn't work. — Terrapin Station

Indeed. Even when examining individual cells which are genetically identical, there can be marked differences in their behaviors and fates, never mind entire multicellular organisms.

https://en.wikipedia.org/wiki/Transcriptional_noise

Monozygotic twins are those that develop from the same zygote (sperm+egg) and are described as identical twins. They have identical genetic codes. In other words the physical aspects of such twins are indistinguishable i.e. insofar as the physical is concerned monozygotic twins are perfectly identical. — TheMadFool

This is false. I myself am a monozygotic twin. I am almost genetically identical to my brother. That we are not perfectly identical is evidenced by our differences in facial structure, height, weight, congenital conditions, fingerprints...

The fact that monozygotic twins are genetically identical — Nicholas Ferreira

It's not a fact. It's a common misunderstanding.

Why not?. Monozygotic twins are genetically identical, at least during the early development (which doesn't necessarily have to do with the two twins be physically identical). As I said, phenotypic differences between twins can occur due epigenetical events, or even due environmental stimuli.

"Monozygotic twins are those that develop from the same zygote (sperm+egg) and are described as identical twins. They have identical genetic codes. In other words the physical aspects of such twins are indistinguishable i.e. insofar as the physical is concerned monozygotic twins are perfectly identical."

I'm not convinced that the third sentence follows from the first two. Even if two individuals have an identical genotype, they aren't necessarily going to have an identical phenotype. That's because there's an element of randomness to fetal development.

"Yet, even such twins are vastly different in mind."

Probably not vastly different. But I'll acknowledge your point that they develop into distinct individuals,

But think about the human brain for a moment. It's hugely complex. There are so many neurons, and so many interconnections between the neurons, that the precise details can't all be coded by the information contained in one's DNA. The DNA apparently gives more general instructions: 'grow an axon in a particular direction, attracted by a particular sort of thing'. But the precise details are going to be pretty stochastic.

All of you claim that the same genotype (monozygotic twins) result in different phenotypes (slight differences in physical features and different personalities).

Ok. Here's a fact: All of us are different. No two people (even identical twins) are the same. However we share more similiarities than differences. Everyone finds lemons sour and cyanide kills without exception. We all feel the pain of losing someone and so and so forth. How do we explain these shared traits? It can't be nurture as we're brought up in different circumstances. So it must be nature i.e. these similarities are encoded in our genes. I've now explained our gene-based common traits.

Now how do we explain the differences? I'd like to focus on personalities. What makes me a mentally different person that anyone else? Say x happens between our DNA and our personalities. Does x have to be physical? Couldn't it be a mind substance?

I think I already answered it, but feelings and this kind of thing are something that were developed through the evolution of the species. I don't know exactly why, but for some reason thoses species which members had this feeling were more capable of surviving than the others, and this characteristic came to us, and it's probably passed through DNA, even if the enviromental interaction produces changes in the person's personality.
I think now I understood your point. You are saying that we can explain why are we so simillar, but aparently we do not have sufficient explanation to our differences. Is this? This is interesting, but I think you are treating primitive instincts/feelings as if it were like personality, which is a more complex thing. And for some reason you leading to believe that because we all feel the pain of losing someone, and this is not something learnt by nurture, then our personalities must follow this line too. I don't think it's a valid reasoning...

Why not?. Monozygotic twins are genetically identical, at least during the early development (which doesn't necessarily have to do with the two twins be physically identical). As I said, phenotypic differences between twins can occur due epigenetical events, or even due environmental stimuli. — Nicholas Ferreira

Okay, allow me to qualify. Taken at face value, your claim that monozygotic twins are genetically identical is a falsehood. But, given your above reply, it turns out that it's just very misleading, like the claims in the opening post. You should make clear that you're only talking about monozygotic twins at a very early stage, not monozygotic twins generally.

Hmm, you are right, I expressed myself in the wrong way. Thanks!